CN111383091A

CN111383091A - Asset securitization pricing method and device

Info

Publication number: CN111383091A
Application number: CN202010107833.3A
Authority: CN
Inventors: 朱祖恩; 谢钦; 黄德荣; 陈卫; 杜雯雯
Original assignee: China Construction Bank Corp; CCB Finetech Co Ltd
Current assignee: China Construction Bank Corp
Priority date: 2020-02-21
Filing date: 2020-02-21
Publication date: 2020-07-07

Abstract

The invention discloses an asset securitization pricing method and device, and relates to the field of finance. One embodiment of the method comprises: obtaining model factors from the multiple loan data, and performing model training to predict the occurrence probability and early-payment result of early-payment events and default events by using the early-payment and default models obtained by training; preprocessing the interest rate factors in the model factors, inputting the interest rate models, and performing parameter verification to predict future interest rates by using the verified interest rate models; carrying out iterative calculation stage by stage to obtain an initial predicted value of the multi-stage cash flow, and determining a final predicted value of the multi-stage cash flow by using a Monte Carlo method; and performing discount on a plurality of cash flow paths according to the basic price of the product issued by the securitization of the loan assets to obtain a discount rate curve of the product, and obtaining the price valuation of the product by combining the discount rate curve and the final predicted value. The method improves the accuracy of cash flow prediction and realizes the price estimation of products.

Description

Asset securitization pricing method and device

Technical Field

The invention relates to the field of finance, in particular to an asset securitization pricing method and device.

Background

Since the securitization business of credit assets in China enters an extended trial stage in 2013, the securitization market of personal loans is developed vigorously. Between 2014 and 2017, the issuance volume of a personal loan asset support security (hereinafter referred to as "RABS") rapidly increases at a rate of 1.9 times per year; the market releases 2861 billion yuan of RABS products 8 months before 2018, which is 1.7 times of the annual release quantity in 2017. Through these years of development, the release pace of RABS products is becoming more regular and increasing every year.

In contrast to the explosive growth of the RABS primary market (for issuing securities), the RABS secondary market (for trading securities) is rarely traded. The secondary market fan is not beneficial to the continuous growth of the primary market, the liquidity management of a product holder and the interest rate conduction function of the RABS market. The primary reason for the rarity of secondary market transactions is that market participants are unable to form consistent approvals of product pricing. Therefore, it is significant to develop an evaluation study of RABS products.

At present, the estimation theory and the technical method of the existing RABS product in China are based on markets of other countries, but due to the difference between the RABS market in China and other countries, for example, whether a loan institution can be changed during the loan preservation period, the activity difference of secondary market transaction, the loan interest rate, repayment arrangement and other detail differences, the actual operability of pricing models in other countries in China is poor, and the related estimation theory and the technical method can not provide accurate estimation results in the practical application process.

Disclosure of Invention

In view of this, embodiments of the present invention provide an asset securitization pricing method and apparatus, which determine a final predicted value of a multi-stage cash flow by obtaining a model factor from a set dimension and combining a machine learning algorithm, a interest rate model, and a monte carlo method, so as to improve accuracy of cash flow prediction and realize price estimation of a product.

To achieve the above object, according to an aspect of an embodiment of the present invention, there is provided an asset securitization pricing method.

The asset securitization pricing method of the embodiment of the invention comprises the following steps: obtaining model factors from the multi-loan data according to the set dimensionality, inputting the model factors into a machine learning algorithm for model training, and predicting the probability of occurrence of early-paid events and default events and early-paid results by using early-paid and default models obtained by training; preprocessing the interest rate factors in the model factors, inputting the preprocessed interest rate factors into an interest rate model, and performing parameter verification on the interest rate model to predict future interest rate by using the verified interest rate model; updating the loan data according to the predicted probability, the early-compensation result and the future interest rate, obtaining an initial predicted value of the multi-stage cash flow by iterative calculation stage by stage, simulating a plurality of cash flow paths by using a Monte Carlo method, and determining a final predicted value of the multi-stage cash flow; and according to the basic price of the product issued by the loan asset securitization, performing discount on the plurality of cash flow paths to obtain a discount rate curve of the product, and combining the discount rate curve and the final predicted value to obtain the price valuation of the product.

Optionally, iteratively calculating, on a per-period basis, an initial predicted value of the multi-period cash flow, including: generating a plurality of interest rate paths, wherein the interest rate paths comprise a plurality of interest rates in a plurality of periods, and calculating the interest rate in each period of each interest rate path as follows: respectively summing up the bottom loan unpaid principal, the bottom loan principal repayment and the bottom loan interest repayment to correspondingly obtain an asset pool unpaid principal, a current repayment and an interest repayment; calculating the cost of the recovery money according to the interest return payment, calculating the cost of each period according to the outstanding repayment fund of the asset pool, calculating the cost of the first period according to the priority scale and the asset pool scale under the condition that the first period payment is needed, and calculating the cost of the end of year under the condition that the current time is the end of year; differentiating the sum of the current-period reimbursement fee, the current-period fee, the first-period fee and the last-year fee to obtain a pre-redemption disposable amount, and calculating an actual redemption amount in combination with a redemption rate; and according to the priority order of product redemption, under the limit of the actual redemption amount, redeeming priority interest and priority principal, updating the priority residual principal, the security residual principal and the principal repayment amount of the current cash flow in the current period, and repeating the calculation process until the priority residual principal is 0.

Optionally, the model factor is obtained by mining the loan data from four dimensions of a loan factor, a borrower factor, the interest rate factor and a season factor by using a big data technology; the loan factors comprise contract amount, outstanding principal balance, loan interest rate, repayment type, contract release date, account age and remaining term, loan city, house type, mortgage value and monthly repayment payment data; the borrower factors comprise the age, the sex, the income and the occupation of the borrower; the interest rate factor comprises a first time period reference loan interest rate and a second time period national debt exploitation rate corresponding to the contract issuing date, and the first time period reference loan interest rate and the second time period national debt exploitation rate in the current period; the season factor comprises a month corresponding to loan issuance days and a month corresponding to repayment days per period.

Optionally, inputting the model factor into a machine learning algorithm for model training, including: dividing model factors obtained from the plurality of loan data into a training set, a verification set and a test set; training: determining a group of hyper-parameters of a machine learning algorithm, inputting the training set into the machine learning algorithm for training to obtain an initial early-compensation and default model which enables a set target function to be minimum; and (3) verification: verifying the performance of the initial early-compensation and default model by using the verification set, and repeating the training step and the verification step until a specified hyper-parameter combination is searched; selecting an initial early-compensation and default model with the minimum error on the verification set as an intermediate early-compensation and default model, combining the training set and the verification set as a whole, and training the intermediate early-compensation and default model to obtain a trained early-compensation and default model; and inputting the test set into the early-compensation and default model for prediction.

Optionally, the interest rate model is any one of a reference interest rate model and a national debt and demand earning rate model, wherein the reference interest rate model uses a GARCH model, accordingly, the preprocessing includes unity interest rate adjustment amplitude, and the parameter verification uses a garchfit method; the on-demand profitability model of the national debt uses a BK model, correspondingly, the preprocessing comprises data conversion, and the parameter verification is realized by calculating a confidence interval.

Optionally, the early-compensation result comprises an early-compensation type when the early-compensation event occurs, wherein the early-compensation type comprises a reduced-amount early compensation and a reduced-period early compensation; updating the loan data based on the predicted probability, the early-compensation result, and the future interest rate, comprising: judging whether the current loan is default or early-payment according to the predicted probability and judging the type of the early-payment when the early-payment occurs; in the case of default of the current loan, updating the current non-repayment principal and the current amortization principal of the loan data to be both 0; under the condition that the current loan is paid early and the early payment type is reduced early, calculating the next unreturned principal according to the current unreturned principal and the current principal repayment proportion, and respectively calculating the current due and the current due in two repayment modes of the equal-cost principal and the equal-cost; under the condition that the current loan is compensated early and the early compensation type is the reduced early compensation, calculating the number of uncompensated remuneration dates in two compensation modes of equal principal and equal principal, and then calculating the current due and the current due principal in the two compensation modes according to the reduced early compensation mode; and correspondingly updating the corresponding fields of the loan data according to the calculation results of different early compensation types.

Optionally, when the loan data is a pool of assets formed by securitization of loan assets, the method further comprises: respectively calculating a shrinkage proportion, a shrinkage proportion and a default proportion, wherein the shrinkage proportion, the shrinkage proportion and the default proportion are respectively the ratios of the shrinkage early-paid amount, the default amount and the current unreturned principal; calculating the cash flow of the current principal fund according to the reduced amount early-payment amount, the reduced period early-payment amount and the default amount; calculating future principal cash flow according to the reduction proportion and the default proportion; calculating the cash flow of interest in the current period according to the default proportion; and calculating the future interest cash flow according to the shrinkage proportion, the shrinkage proportion and the default proportion.

Optionally, the cashing the plurality of cash flow paths to obtain a discount rate curve of the product, including: respectively discounting the plurality of cash flow paths by adopting a static difference method to obtain static differences under the plurality of cash flow paths; and calculating the average value of the plurality of static differences to obtain the discount rate curve of the product.

Optionally, separately discounting the plurality of cash flow paths comprises: and constructing an implicit form of the early-stage compensation right by utilizing the relationship between the final predicted value of the multi-stage cash flow and the future interest rate so as to estimate the cash value of the early-stage compensation right.

To achieve the above object, according to another aspect of the embodiments of the present invention, there is provided an asset securitization pricing apparatus.

The invention provides an asset securitization pricing device, which comprises: the early-payment default prediction module is used for acquiring model factors from the multi-loan data according to the set dimensionality, inputting the model factors into a machine learning algorithm for model training, and predicting the probability of the occurrence of the early-payment events and default events and the early-payment result by using the early-payment and default models obtained by training; the interest rate prediction module is used for preprocessing the interest rate factors in the model factors, inputting the interest rate models, and performing parameter verification on the interest rate models to predict future interest rates by using the verified interest rate models; the cash flow prediction module is used for updating the loan data according to the predicted probability, the early-compensation result and the future interest rate, obtaining an initial prediction value of the multi-period cash flow by iterative calculation stage by stage, simulating a plurality of cash flow paths by using a Monte Carlo method, and determining a final prediction value of the multi-period cash flow; and the product pricing module is used for discounting the plurality of cash flow paths according to the basic price of the product issued by loan asset securitization to obtain a discount rate curve of the product so as to obtain the price valuation of the product by combining the discount rate curve and the final predicted value.

Optionally, the product pricing module is further configured to: generating a plurality of interest rate paths, wherein the interest rate paths comprise a plurality of interest rates in a plurality of periods, and calculating the interest rate in each period of each interest rate path as follows: respectively summing up the bottom loan unpaid principal, the bottom loan principal repayment and the bottom loan interest repayment to correspondingly obtain an asset pool unpaid principal, a current repayment and an interest repayment; calculating the cost of the recovery money according to the interest return payment, calculating the cost of each period according to the outstanding repayment fund of the asset pool, calculating the cost of the first period according to the priority scale and the asset pool scale under the condition that the first period payment is needed, and calculating the cost of the end of year under the condition that the current time is the end of year; differentiating the sum of the current-period reimbursement fee, the current-period fee, the first-period fee and the last-year fee to obtain a pre-redemption disposable amount, and calculating an actual redemption amount in combination with a redemption rate; and according to the priority order of product redemption, under the limit of the actual redemption amount, redeeming priority interest and priority principal, updating the priority residual principal, the security residual principal and the principal repayment amount of the current cash flow in the current period, and repeating the calculation process until the priority residual principal is 0.

Optionally, the early-compensation default prediction module is further configured to: dividing model factors obtained from the plurality of loan data into a training set, a verification set and a test set; training: determining a group of hyper-parameters of a machine learning algorithm, inputting the training set into the machine learning algorithm for training to obtain an initial early-compensation and default model which enables a set target function to be minimum; and (3) verification: verifying the performance of the initial early-compensation and default model by using the verification set, and repeating the training step and the verification step until a specified hyper-parameter combination is searched; selecting an initial early-compensation and default model with the minimum error on the verification set as an intermediate early-compensation and default model, combining the training set and the verification set as a whole, and training the intermediate early-compensation and default model to obtain a trained early-compensation and default model; and inputting the test set into the early-compensation and default model for prediction.

Optionally, the interest rate model is any one of a reference interest rate model and a national debt and immediate earning rate model, wherein the reference interest rate model uses a GARCH model, and accordingly the preprocessing of the interest rate prediction module includes unitizing an interest rate adjustment amplitude, and the parameter verification uses a garchfit method; the on-demand yield model of the national debt uses a BK model, correspondingly, the preprocessing of the interest rate prediction module comprises data conversion, and the parameter verification is realized by calculating a confidence interval.

Optionally, the early-compensation result comprises an early-compensation type when the early-compensation event occurs, wherein the early-compensation type comprises a reduced-amount early compensation and a reduced-period early compensation; the cash flow prediction module is further configured to: judging whether the current loan is default or early-payment according to the predicted probability and judging the type of the early-payment when the early-payment occurs; in the case of default of the current loan, updating the current non-repayment principal and the current amortization principal of the loan data to be both 0; under the condition that the current loan is paid early and the early payment type is reduced early, calculating the next unreturned principal according to the current unreturned principal and the current principal repayment proportion, and respectively calculating the current due and the current due in two repayment modes of the equal-cost principal and the equal-cost; under the condition that the current loan is compensated early and the early compensation type is the reduced early compensation, calculating the number of uncompensated remuneration dates in two compensation modes of equal principal and equal principal, and then calculating the current due and the current due principal in the two compensation modes according to the reduced early compensation mode; and correspondingly updating the corresponding fields of the loan data according to the calculation results of different early compensation types.

Optionally, when the loan data is a pool of assets formed by securitizing loan assets, the apparatus further comprises: the early-paid approximation module is used for respectively calculating a shrinkage proportion, a shrinkage proportion and a default proportion, wherein the shrinkage proportion, the shrinkage proportion and the default proportion are respectively the ratios of the shrinkage early-paid amount, the default amount and the current unreturned principal; calculating the cash flow of the current principal fund according to the reduced amount early-payment amount, the reduced period early-payment amount and the default amount; calculating future principal cash flow according to the reduction proportion and the default proportion; calculating the cash flow of interest in the current period according to the default proportion; and calculating the future interest cash flow according to the shrinkage proportion, the shrinkage proportion and the default proportion.

Optionally, the product pricing module is further configured to: respectively discounting the plurality of cash flow paths by adopting a static difference method to obtain static differences under the plurality of cash flow paths; and calculating the average value of the plurality of static differences to obtain the discount rate curve of the product.

Optionally, the product pricing module is further configured to: and constructing an implicit form of the early-stage compensation right by utilizing the relationship between the final predicted value of the multi-stage cash flow and the future interest rate so as to estimate the cash value of the early-stage compensation right.

To achieve the above object, according to still another aspect of embodiments of the present invention, there is provided an electronic apparatus.

An electronic device of an embodiment of the present invention includes: one or more processors; a storage device for storing one or more programs which, when executed by the one or more processors, cause the one or more processors to implement a method for securitization pricing of assets of an embodiment of the invention.

To achieve the above object, according to still another aspect of embodiments of the present invention, there is provided a computer-readable medium.

A computer-readable medium of an embodiment of the present invention has stored thereon a computer program that, when executed by a processor, implements a method of securitized pricing of assets of an embodiment of the present invention.

One embodiment of the above invention has the following advantages or benefits: the model factors are obtained from the set dimensions, the probability and early compensation results of early compensation events and default events are predicted by combining with a machine learning algorithm, the future interest rate is predicted by combining with an interest rate model, the initial predicted value of the multi-stage cash flow of the basic assets is further calculated by iteration stage by stage, the final predicted value of the multi-stage cash flow is determined by a Monte Carlo method, the accuracy of cash flow prediction is improved, and the price estimation of products is realized; calculating an initial predicted value of the multi-stage cash flow by combining loan level influence factors, further ensuring the accuracy of cash flow prediction and improving the accuracy of product price valuation; obtaining model factors from multiple dimensions by utilizing a big data technology, and ensuring the accuracy of subsequent cash flow prediction by using the screened model factors; the machine learning algorithm is used for asset securitization pricing, and the error between the cash flow prediction result and the actual value is reduced.

One embodiment of the above invention has the following advantages or benefits: the GARCH model is used for predicting future interest rate, model parameters are few, and the parameters can still be reasonably estimated under the condition of insufficient data volume; the BK model is used for predicting the future interest rate, so that the prediction of short-term volatility and long-term regression can be realized at the same time; due to early compensation and default, the loan data needs to be updated before the cash flow is predicted, so that the accuracy of cash flow prediction is ensured; when only cash flow of a capital pool exists, the cash flow is predicted in an early-compensation approximate mode; the conversion rate curve of the product is determined by adopting a Monte Carlo method, so that the flexibility is good and the realization is easy; and the consideration of the risk premium condition is increased during discount, and the accuracy of the product price estimation is further improved.

Further effects of the above-mentioned non-conventional alternatives will be described below in connection with the embodiments.

Drawings

The drawings are included to provide a better understanding of the invention and are not to be construed as unduly limiting the invention. Wherein:

FIG. 1 is a schematic diagram of the main steps of an asset securitization pricing method according to an embodiment of the invention;

FIG. 2 is a schematic flow diagram of a principal of a method for securitized pricing of assets according to an embodiment of the invention;

FIG. 3 is a block flow diagram of a prediction of the prediction _ prob using different algorithms in an embodiment of the present invention;

FIG. 4 is a block flow diagram of a prediction of a prefix type using a different algorithm in an embodiment of the present invention;

FIG. 5 is a block flow diagram of a framework for predicting a prediction _ ratio using different algorithms in an embodiment of the present invention;

FIG. 6 is a schematic diagram of a product pricing flow of an embodiment of the invention;

FIG. 7(a) is a schematic diagram of cash flow distribution under the condition of the standard situation discount rate in the embodiment of the present invention;

FIG. 7(b) is a schematic diagram of cash flow distribution under the condition of increasing discount rate in the embodiment of the present invention;

FIG. 7(c) is a schematic diagram of cash flow distribution under the condition of reduced discount rate in the embodiment of the present invention;

FIG. 8 is a schematic diagram of the main modules of an asset securitization pricing apparatus according to an embodiment of the invention;

FIG. 9 is an exemplary system architecture diagram in which embodiments of the present invention may be employed;

FIG. 10 is a schematic diagram of a computer apparatus suitable for use in an electronic device to implement an embodiment of the invention.

Detailed Description

Exemplary embodiments of the present invention are described below with reference to the accompanying drawings, in which various details of embodiments of the invention are included to assist understanding, and which are to be considered as merely exemplary. Accordingly, those of ordinary skill in the art will recognize that various changes and modifications of the embodiments described herein can be made without departing from the scope and spirit of the invention. Also, descriptions of well-known functions and constructions are omitted in the following description for clarity and conciseness.

Technical terms related to the present invention are explained below.

Personal loan: the bank or other financial institution sends the local and foreign currency loan for personal consumption, production and management and other purposes to the natural person meeting the loan condition.

A neural network: in the field of machine learning, neural networks are designed to mimic neurons and connections in the brain. It depends on the input characteristics, and obtains a fitting function through continuous approximation of interconnected 'neurons', and further calculates an effective approximate estimation.

Securitization of assets: and (3) taking cash flow generated in the future of the basic assets as repayment support, and carrying out credit enhancement through structured design, and issuing the process of supporting securities on the basis. It is a financing form that issues tradeable securities, supported by a particular portfolio or a particular cash flow.

Basic assets: refers to assets on which derivative financial instruments (e.g., options, exchanges) trade. In the process of securitization of assets, legal qualification of the underlying assets should be sought within the scope of existing rights, such as claims, intellectual property, property rights, equities, and the like.

And (4) cash flow: generally referred to as cash flow, refers to the total number of cash payments for cash-out and cash-in of an investment project over its lifetime.

Asset support certificates: is a trust benefit share issued by a trusted authority representing a trust of a particular purpose. The trusted authority assumes the obligation of paying the asset supporting the certificate revenue to the investment authority with the trusted property as a limit. Its payment is essentially derived from the cash flow generated by the pool of assets supporting the security. The property under term is typically a financial property such as a loan or credit receivable, the payment being regular according to their terms.

An asset pool: the pool of assets in the securitization of assets is a fairly large portfolio of assets with certain characteristics.

Securitization of credit assets: the method is a process of converting the income right of future cash flow generated by a group of assets into bond-type securities which can flow in the financial market and have higher credit rating on the basis of recombining a group of credit assets with poor liquidity, such as bank loans and accounts receivable of enterprises, to form an asset pool, so that the cash flow income generated by the group of assets is relatively stable and is expected to be stable in future, and matching with corresponding credit guarantee.

Because market participants can not form consistent approval for product pricing, secondary market trading in China is rare, and the method is not beneficial to the continuous growth of a primary market, the liquidity management of a product holder and the interest rate conduction function of a loan securitization market. Therefore, it is significant to develop an evaluation study of products, including:

promoting second-level market transaction, reducing liquidity premium and reflecting the real value of the product; the market acceptance is enhanced, the current situation that the product pricing is guided by the capital cost of investors is turned, and the purchase willingness and the purchase ability of the investors are improved; the system can help enterprises to carry out asset pool screening and structural design of new products, and improve the performance of the products in the life cycle; the method can provide reference for enterprises to develop personal housing mortgage loan management, and is favorable for improving the accuracy of early compensation rate and default rate prediction. The asset securitization pricing method of the embodiment of the invention is explained in detail below.

FIG. 1 is a schematic diagram of the main steps of an asset securitization pricing method according to an embodiment of the invention. As shown in fig. 1, the asset securitization pricing method of the embodiment of the invention mainly comprises the following steps:

step S101: and obtaining model factors from the multi-loan data according to the set dimensionality, inputting the model factors into a machine learning algorithm for model training, and predicting the probability of the early-payment event and the default event and the early-payment result by using the early-payment and default model obtained by training. And mining the loan data from the loan factor, the borrower factor, the interest rate factor and the season factor by utilizing a big data technology to obtain a model factor.

The process of model training is as follows: dividing the model factors into a training set, a verification set and a test set, inputting the training set into a machine learning algorithm for model training, and finding out the optimal hyper-parameter; then, the trained initial early compensation and default model performance is verified by a verification set, the model hyper-parameters are determined, and the optimal model is selected; and finally, performing performance evaluation on the trained model by using the test set. After the model is trained, the model factor is used as a characteristic value to be input into the trained early compensation and default model, and the probability of occurrence of the early compensation event and the default event and the early compensation result are output.

Step S102: and preprocessing the interest rate factors in the model factors, inputting the preprocessed interest rate factors into an interest rate model, and performing parameter verification on the interest rate model to predict future interest rate by using the verified interest rate model. The interest rate model is a benchmark interest rate model or a national debt on-demand earning rate model. In the examples, the reference interest rate model uses the GARCH model, and the national debt on-demand profitability model uses the BK model.

For the GARCH model, after the adjustment range of the interest rate needs to be unitized, the GARCH model is input, the parameter is verified by using a garchfit method, and then the future interest rate can be predicted according to the set time unit. For the BK model, after the interest rate factor is subjected to data conversion, the BK model is input, parameter verification is achieved through calculation of a confidence interval, and then the future interest rate can be predicted according to a set time unit.

Step S103: updating the loan data according to the predicted probability, the early-compensation result and the future interest rate, obtaining an initial predicted value of the multi-stage cash flow by iterative calculation stage by stage, simulating a plurality of cash flow paths by using a Monte Carlo method, and determining a final predicted value of the multi-stage cash flow. Under the influence of early compensation and default, before the cash flow is predicted, loan data needs to be dynamically updated, and a plurality of cash flow paths are simulated by combining a Monte Carlo method so as to ensure the accuracy of the predicted cash flow.

When predicting the cash flow of the products issued by securitization of loan assets, it is possible to first determine whether the current loan is for early payment, and if so, determine the type of early payment, and update the corresponding fields of the loan data, such as the remaining principal, the remaining term, and the repayment schedule. And then summing the information to obtain a predicted value of the current cash flow of the basic assets. And (4) carrying out iterative calculation stage by stage to obtain a predicted value of the cash flow of the basic assets at each stage. On the basis, a plurality of cash flow paths are simulated by a Monte Carlo method, and the average value of the cash flow paths is taken to obtain the predicted value of the cash flow of the product.

Step S104: and according to the basic price of the product issued by the loan asset securitization, performing discount on the plurality of cash flow paths to obtain a discount rate curve of the product, and combining the discount rate curve and the final predicted value to obtain the price valuation of the product. And taking the issued price of the product as a basic price, performing price balancing discount on each cash flow path in a static interest difference mode, and calculating the average value of all static interest differences to further obtain a discount rate curve of the product. And then, based on the discount rate curve, discounting the final predicted value of the cash flow to obtain the price estimation value of the product.

The embodiment has controllable errors of future interest rate and cash flow prediction results, and can be used for internal credit management of enterprises; moreover, a discount rate curve of the product is constructed by adopting a Monte Carlo method through dynamic simulation, and the method has compliance; meanwhile, pricing of products issued by loan asset securitization is achieved, the pricing error is small, the method has guiding significance for pricing existing products, and the method has reference for second-level market trading.

Taking RABS product pricing as an example, the cash flow of RABS products is derived from payback of underlying property (personal loans), and the different performance of underlying properties (e.g., advanced repayment) directly leads to greater uncertainty in the product's future cash flow. Thus, the core of the pricing of the RABS product is to predict the future cash flow of the product.

In the embodiment, the memory amount field of the personal loan database of company A is used for data mining, the general rule of early payment and default of the personal loan is explored and found, and the conduction relationship between the future loan cash flow and relevant factors such as interest rate, region and credit characteristics of borrowers is established. The method is suitable for cash flow analysis of a property pool taking personal loan as underlying property and pricing of related securities and derivative tools. Wherein, the pricing process comprises three parts: loan early-payment and default analysis, asset pool cash flow prediction, and asset securitization pricing. In an embodiment, the pricing process can be analyzed and evaluated using the earnings cash flow and release interest rate of the new RABS product.

Fig. 2 is a schematic main flow diagram of an asset securitization pricing method according to an embodiment of the invention. As shown in fig. 2, the asset securitization pricing method of the embodiment of the invention mainly comprises the following steps:

step S201: and obtaining model factors from the dimensions of the loan factors, the borrower factors, the interest rate factors and the season factors by taking the loan data as basic data. The loan data may include national loan opening rate and benchmark loan interest rate data corresponding to loan issuance, property pool information of the RABS, product issuance scale, nominal interest rate, term, collection data in each period, and the like.

The loan factors may include contract amount, outstanding principal balance, loan interest rate, repayment type, contract release date, account age and remaining term, loan city, house type (new/second-hand), mortgage value, monthly repayment payment data, and the like. The borrower factor may include the borrower's age, gender, income, occupation, etc.

The interest rate factor can comprise a set first time period reference loan interest rate and a set second time period national debt exploitation rate corresponding to the contract issuing date, and the current first time period reference loan interest rate and the current second time period national debt exploitation rate. The first time period and the second time period can be set by users, for example, both can be 5 years or more. The seasonal factor may include a day of loan issuance for a month and a day of repayment per period for a month.

Step S202: inputting the model factors into a machine learning algorithm to carry out model training to obtain an early-paid and default model, and predicting the occurrence probability of the early-paid event and the default event and the early-paid result by using the early-paid and default model obtained by training. The following are defined for early-paid and default events, respectively:

according to the relevant terms in the loan contract, the lender applies for an advance repayment to the borrowing line within the loan duration, and the repayment amount can be partial or complete, and the behavior is defined as the early payment event of the loan.

Under normal circumstances, the borrower should pay the loan interest to the borrower on time according to the repayment schedule. If the borrower does not pay the loan interest by the deadline, the loan is a default. Considering that most non-borrower defaults are subjectively willing and are complemented in a short period in the future without influencing the actual credit situation, the non-borrower defaults are defined as technical defaults. In the present embodiment, a substantial default event is defined as "accumulating unpaid events for 3 months and more consecutively", and such behavior is defined as a default event of the loan.

The individual early compensation events and default events are driven by the behavior of the borrower, have the characteristic of random and sporadic occurrence and cannot be reliably predicted. However, statistically, the occurrence probability has a certain conductive relationship with objective factors such as credit characteristics, interest rate level, region and the like of the borrower. The step is to analyze and establish the relation between the probability of the occurrence of the early-paid event and the default event and the objective factors.

In order to realize pricing of products issued by securitization of loan assets, qualified loan data is required to be screened according to preset standards and is included in analysis. The raw data used in the examples of the present invention are shown in table 1, company a being a trusted authority that issues securities products, and company B being a capital authority.

Table 1 shows the raw data of the individual loan database of company A

According to the above raw data, in the embodiment, 10147838 loan data are used in the step, the loan repayment record interval is between 03 and 04 months in 2010 and 2018, and the loan data is included in the loan repayment record interval with at least one repayment record. It should be noted that the loan date of 1378096 loans (about 13% of data) in the raw data is before the 03-2010 month period, but for this part of data we have collected only data after the 03-2010 year period, which may cause some survivor deviation and is reflected in the loan date factor.

In addition, according to the screening criteria, all loan data that leads to underwriting after a default do not appear in the original data, and the distribution of the interception has a large influence on the default rate, but if the proportion of the interception is small, the influence on the early-payment rate is limited. Therefore, in the embodiment, the default rate is not measured, the default probability of the personal housing loan of company A is directly used as the probability of the occurrence of the default event, and the historical average value of the default loss rate is used as the default result caused after the occurrence of the default event.

The early compensation comprises three service scenes of no early compensation, total early compensation and partial early compensation. Under the scene of partial early compensation, the method comprises the reduced amount early compensation and the reduced period early compensation. In the embodiment, a neural network model mode is adopted to judge whether early-compensation and early-compensation situations occur. When the probability of the occurrence of the early compensation event and the early compensation result are predicted, the format of data needs to be converted by using the loan repayment record, and 4.89 hundred million loan repayment records are formed, according to 60%: 20%: the 20% ratio is randomly distributed to generate a training set, a validation set and a test set. And then, selecting a proper machine learning algorithm to train the model, and predicting the occurrence probability of the early compensation event and the early compensation result by using the trained model. A detailed description of how the machine learning algorithm is selected follows.

According to a data structure of a loan repayment record and an internal SAS (Statistical Analysis System) module, in the embodiment, a decision tree, a logistic regression (Log regression), a neural network, an HP nerve, an HP regression and other machine learning algorithms are selected for model training, and prediction results are compared. The HP model and the original model are the same in nature, the difference is that the algorithm and the optimization condition are different, and the result can be used for cross validation.

The target variable prepray _ prob is a binary variable representing whether or not early-compensation occurs. In consideration of the fact that the occurrence of the early compensation event has large subjectivity, the occurrence of the individual event is difficult to predict, and meanwhile, according to data statistics and exploration, the early compensation is a very small probability event, and the early compensation proportion in average repayment in each period is only 0.015%. Thus, rather than predicting a binary classification of an early-compensation event, the probability of the occurrence of an early-compensation event under different characteristics can be predicted.

Accordingly, the optimization objective function may be defined as: in any probability interval, the number of observations with the prediction probability falling into the probability interval multiplied by the median of the probability interval is consistent with the actual number of occurrences of the event in the corresponding observation. The mathematical expression is:

in the formula (I), the compound is shown in the specification,

a prediction function from event space to probability space, namely an optimization objective;

is the substantial occurrence of an early-paid event (event space subset); card (x) is a count function; q is a partition of the probability space; q is the median of the segmented probability interval.

FIG. 3 is a flow chart of a framework for predicting prediction _ prob using different algorithms in an embodiment of the present invention. As shown in fig. 3, when prediction is performed by using a decision tree, Log regression, and neural network algorithms, input data needs to be preprocessed and then input into the algorithms for prediction. When the decision tree is used for prediction, data partitioning needs to be performed on input data in advance; when prediction is performed by using Log regression and neural network algorithms, data partitioning needs to be performed on input data in advance, and then data vacancy filling is performed.

The target variable prefix _ type is an ordinal variable, which represents the type of early-paid event, and the meaning of the specific ordinal map is as shown in table 2:

table 2 shows ordinal number mapping meanings of embodiments of the present invention

Ordinal number types	Means for
		0	Without early compensation
1	All morning compensation
		2	Partial morning compensation (shrinkage)
3	Partial early compensation (shrinkage period)
		42	Partial early compensation (shrinkage period, the percentage of shrinkage is bigger)
43	Partial early payment (shrinkage period, the period is bigger)

Ordinal types 42 and 43 are less dominant than 1% of

ordinal types

2 and 3 based on observations of the data, so ordinal types 42 and 2 are merged and ordinal types 43 and 3 are merged. The optimization objective function definition is the same as prediction _ prob, and the predicted frame flow is similar to prediction _ prob, see fig. 4 in detail.

The target variable prepray _ ratio is a continuous variable representing the ratio of the amount of the early-paid money to the remaining principal in the beginning in the case of the occurrence of early-paid money, and is observable if and only if the value of prepray _ type is 2, 3, 42, 43, and its optimization objective function is defined as a probability-weighted least-squares method. The mathematical expression is:

in the formula (I), the compound is shown in the specification,

the optimization result function of prefix _ prob, g is the actual prefix _ ratio,

is a prediction function of prediction _ ratio, g,

Are all event space to probability space mapping functions.

Fig. 5 is a flow chart of a framework for predicting a prediction _ ratio using different algorithms in an embodiment of the present invention. As shown in fig. 5, the prediction can be performed by using linear regression, neural network, HP neural, and HP regression algorithms. When linear regression and neural network are used for prediction, input data needs to be subjected to data screening, data partitioning and data vacancy preprocessing and then input into an algorithm for prediction.

The following describes the process of model training using a machine learning algorithm.

(1) And determining a group of hyper-parameters of the machine learning algorithm, inputting the training set into the machine learning algorithm for training, and obtaining an initial early-compensation and default model which enables the set target function to be minimum. Where a hyper-parameter is a parameter that is set to a value before the learning process is started, such as the degree of a polynomial in a polynomial regression, a regularization parameter.

(2) The performance of the initial early-compensation and violation model is verified using a verification set.

(3) And (3) repeating the step (1) and the step (2) until the specified hyper-parameter combination is searched.

(4) And selecting the initial early-compensation and default model with the minimum error on the verification set as an intermediate early-compensation and default model, and combining the training set and the verification set as a whole to train the intermediate early-compensation and default model to obtain an optimal function, namely the trained early-compensation and default model.

(5) Inputting the test set into the trained early-compensation and default model for prediction so as to measure the generalization performance of the model.

Step S203: and preprocessing the interest rate factor, inputting the preprocessed interest rate factor into the interest rate model, and performing parameter verification on the interest rate model so as to predict the future interest rate by using the verified interest rate model. The interest rate model adopts a Blake-Karasinsk model and uses a Monte Carlo method to predict the future interest rate. The model is used for both early-compensation rate simulation and future risk-free rate prediction.

In the early compensation rate simulation, the national debt development history distribution is directly used for parameter verification. When the risk-free interest rate is predicted in the future, the Gossanoff theorem is used for leveling the expected long-term interest rate center, and the risk-free arbitrage opportunity condition under the risk neutral measure is met.

After predicting the three target variables of prep _ prob, prep _ type, and prep _ ratio in step S202, the target variable correlation factors are classified into: static factors, deterministic factors, and stochastic factors. All factor classifications are given in table 3.

Wherein the static factors comprise occupation, birth date, first-level branch and the like, and the static factors are not changed in the cash flow prediction process. The determining factors comprise residual principal, current period number, residual period number and the like, and the determining factors evolve in the cash flow prediction process according to a determined process. The random factors comprise the current national debt 5-year instantaneous yield, the current 5-year benchmark interest rate and the like, and the random factors evolve following a random process in the cash flow prediction process. It should be noted that the mortgage property value and income are both data at the time of loan application and are determining factors.

Table 3 is the classification table of the related factors of the target variables

For the random factors, a 5-year-period benchmark interest rate model and a 5-year-period national debt immediate earning rate model are used in the embodiment for predicting future interest rates. The subsequent adjustment can be carried out according to the change of the market condition, and particularly after the marketization process of the interest rate in China is finished, the parameter verification method is converted into risk neutral measure instead of historical measure. The prediction processes of the above two models are explained below.

(1) 5-year benchmark interest rate model

The loan benchmark interest rate is a policy interest rate, and no market price is traded, so the historical data of the loan benchmark interest rate is used for modeling in the embodiment. The data source can be the official network of the Chinese people's bank. All interest rate adjustment data after 2000 years can be used for modeling in data selection, 43 effective data points are provided, and the data volume is small.

The model selected is the non-deviating GARCH (1,1) model. The main advantage of the GARCH (1,1) model is the fitting of the fluctuating accumulation phenomenon, and the model is a simple model with few model parameters, so that the parameters can be reasonably estimated under the condition of insufficient data volume, and meanwhile, the occurrence of the overfitting phenomenon is avoided. Among them, the GARCH model is called a generalized ARCH model, and is an extension of the ARCH model.

The SDE equation for the GARCH model is as follows:

the GARCH (1,1) model assumes that the raw data are equidistant data points, whereas the interest rate adjustment depends on the policy at the central row, being non-equidistant data points. So the unity rate adjustment margin (in years) is needed first. According to the SDE equation, volatility (or interest rate change itself) is directly proportional to the evolution of time, thus:

in the formula,. DELTA._tThe interval time is adjusted for the distance from the last interest rate.

Thereby generating an adjusted time series

As input conditions for the model. And then parameter verification can be carried out.

The parameter verification uses a garchfit method in a built-in fGarch library of the calculation software R. The essence of this method is the Maximum likelihood estimation method (Maximum)The Likelihood Method). In addition, the verification result needs to be calculated in addition to the parameter output

And

as an initial volatility in future simulations. The predictive simulation can then be performed.

Since the GARCH (1,1) model is a single factor model, the predictive simulation is simpler. In the embodiment, the unit of month is selected, and 120-period prediction (10 years) is carried out to meet the requirement. The following discretized SDE equation was used in the simulation:

in the formula (I), the compound is shown in the specification,

and

in checking directly selected parameters

And

(terminal volatility vs. terminal difference).

(2) 5-year-period national debt on-demand profitability model

The national debt development has active trading market and daily measuring and calculating curves of institutions such as middle debt and middle certificate. However, the derived varieties are relatively deficient, and the trading and fair value of non-linear derived products such as options and the like is not available. Thus, embodiments use both their historical data and current profitability curves for modeling. The data source can be a financial terminal, such as a Wande terminal, and a debt on-demand profitability curve of middle-debt countries.

Model selection we used a BK model, which included predictions of both short-term volatility and long-term regression. Among them, the BK model was created by Beaudry and Koop in 1993, and its main idea is: due to the asymmetry of the economic cycle, asymmetric terms and nonlinear components must be introduced when constructing a model of the economic cycle, and the BK model is actually an expression based on an ARMA model.

SDE equation for BK model

d(ln y_t)＝κ(θ_t-ln y_t)dt+σdW_t

Equation 6

In the formula, y_tThe distribution is Log-Normal distribution under the prediction of the random process as a simulation variable, negative values are not allowed to appear, and the reasonable assumption is made according to the current market interest rate environment; kappa is the regression rate parameter, with larger kappa meaning that the simulation variable y is off when short term fluctuations lead to deviations_tThe faster the regression to the target mean can be made; theta is a target mean parameter and is an assumption of the model for future expectation; σ is a short term volatility parameter. The model collectively expresses a time variation curve of fluctuation by κ and σ (autoregressive model, fluctuation is a descending curve).

In the embodiment, the financial terminal is used for 'Chinese debt country debt on-demand earning rate curve', actual measurement and demand are considered, the future 10 years are predicted by taking months as units, the time span is long, and the emphasis of the model is to evaluate medium and long term volatility and trend of interest rate. To remove microscopic perturbations, we used the end-of-month time node data as model input. And then parameter verification can be carried out.

Target mean value θ_tA 5-year fixed-term curve (consistency), i.e., market expectation under risk neutral measure, generated using the last year "debt national debt on demand profitability curve".

In the formula, y_tAnd (5) opening the debt on-demand earning rate (with the term t) for the debt country in the latest period.

Due to the lack of non-linear interest derivatives, market expectations for fluctuating curve structures cannot be achieved. In this case, the parameter estimation is performed using the history data. Where σ uses sample volatility.

κ is estimated based on the boundary conditions. Defining the interval W as y₅The difference between the 5% confidence interval and the 95% confidence interval is distributed, then

In general, e^-2κTSmaller, negligible, yields:

and after the parameter verification is finished, the model prediction can be carried out. The BK model is a single factor model, and the prediction simulation is simpler. The requirement can be met by selecting the unit of month for 120-period prediction (10 years). The following discretized SDE equation was used in the simulation:

y_5,t+Δt＝y_5,texp(κ(θ_t-ln y_5,t)Δt+σN(0,Δt))

equation 11

Step S204: and updating the loan data according to the predicted probability, the early-compensation result and the future interest rate, and predicting the future cash flow of the product by using a Monte Carlo method. Affected by early compensation and default, the repayment schedule needs to be dynamically updated in the simulation process. For the case of a current loan default, the current unpaid principal and the current amortization principal for which the loan data is updated are both 0. For the early compensation of the current loan, the actual calculation has more variables and more complex flow, so the embodiment is simplified to a certain extent. The simplified formula is as follows:

for the reduced amount early compensation type, the outstanding compensation period number does not need to be updated additionally. For the contracted early-paid type, the unreturned number needs to be updated first:

under "equal principal of money":

under "equal amount rest":

since the number of the period is required to be a positive integer, rounding processing is required, and the early compensation amount is updated after rounding, wherein the rounding rule is as follows:

number of outstanding future (new) ═ Round (number of outstanding future (new))

Equation 14

Under "equal principal of money":

under "equal amount rest":

wherein:

and then updating the repayment schedule (including default, early payment, normal payment):

unreturned principal (the next period) is the unreturned principal (the current period) and the principal repayment proportion (the current period)

Equation 18

Wherein, under "equal principal of money":

under "equal amount rest":

proportionality coefficient ═ (1+ current interest rate/12)^{Number of unrendered periods}

Equation 22

The current period should be paid again-the current interest rate/12

Equation 24

With the above, the prediction and decomposition of the cash flow are performed by using the monte carlo method, and the specific calculation flow is as follows. In the process of generating the flow, the priority discount value before the risk premium is not considered is also obtained at the same time.

The cash flow prediction calculation process comprises the following steps:

→ independent generation of N interest rate simulation paths

→ reservation of Ns priority cash flow paths (s is the number of priorities)

Reserved N x s priority discount value

→ i from 1 to N: selecting the ith interest rate path for calculation

→ T from 0 to T: selecting interest rate in the t period for calculation

→ → judgment: whether a new year

→ → is: adjusting the interest rate of the bottom layer

→ → k from 1 to M: selecting the kth loan to calculate

→ → random generation of default events according to the default rate

→ → judgment: breach of contract event occurrence

→ → → → → → → → → → → → → → → yes: update the unreturned principal to 0

→ → → → → → → → → → → → → → → yes: calculate the instinct repayment to 0

→ → → → → → → → → → → → → → → yes: jumping out of the current cycle and executing the next cycle

→ → calculate the instinct and the rest of the information

→ → generation of morning events randomly according to the morning rate

→ → judgment: early event occurrence

→ → → → → → → → → → → → → → → yes: judging early compensation type and calculating early compensation proportion and early compensation amount

→ → → → → → → → → → → no: the early compensation amount is 0

→ → update the underlying loan unpaid principal

→ → calculating the instinct repayment + the earliness repayment

→ → k end of the cycle

→ → property pool unreturned principal ═ total (bottom loan unreturned principal)

→ → money back in this period is total (bottom loan repayment)

→ → collection of interest ═ total (bottom loan interest repayment)

→ → calculating the cost of the recovery

→ → judgment: whether first term payment

→ → is: calculating the first cost

→ → no: initial cost of 0

→ → judgment: whether or not it is late year

→ → is: calculating the end-of-year cost

→ → no: the end-of-year cost is 0

→ → calculation of cost per phase

→ → calculation of the amount of available charge before redemption ═ this period of money return-money recovery charge-first period charge-end of year charge-per period charge

→ → calculation of the actual cash sum which is the disposable sum before cash/(1 + cash rate)

→ → exchange priority interest

→ → exchange priority principal (in order)

→ → update priority residual principal

→ → update of residual principal fund of securities

→ → update ith priority route stage t principal repayment amount

→ → judgment: priority residual principal of 0

→ → is: terminate the t-cycle

→ t end of the cycle

→ update the ith priority discount value

End of the → i cycle

→ expected cash flow path-average (priority cash flow path)

→ expected discount value-average (priority discount value)

In the process, the recovery cost is the execution cost generated by the recovery, the first-stage cost is the cost needing to be paid in the first stage, the annual end cost is the cost paid in the last K years each year, the annual end cost can be calculated by the outstanding repayment fund of the asset pool, and the exchange rate is the service cost paid by the trust. In addition, the bond is layered and divided into a priority and a secondary, the priority is paid first, and the secondary is paid after the payment is finished.

The early-compensation and default calculation method uses the cash flow of the loan level for calculation, and in special cases, the cash flow of the loan level may not be obtained, but only the cash flow of the property pool (including the cash flow of the principal, the cash flow of interest, and the like). In a preferred embodiment, another approximate early-compensation effect is given below. This approximation is equivalent to preemptively earning out a long-lived cash flow.

Then

The current time of the gold

Cash flow of principal fund (current stage) + shrinkage early repayment amount + shrinkage early compensation amount-default amount

Equation 28

Interest cash flow (current period) ═ interest cash flow (current period) (1-default proportion)

Equation 29

The cash flow (future) is the cash flow (future) (1-proportion of reduction-default proportion)

Equation 30

Interest cash flow (future)

Interest cash flow (future) 1-shrinkage proportion-default proportion)

Equation 31

Under the assumption that the reduction proportion is 0, the default proportion is 0 and the total early-compensation amount is the reduction early-compensation, the cash flow shows an obvious phenomenon of 'tail-chopping', also called 'tail-chopping' early-compensation, and the early-compensation cash flow is generally calculated by using the method in the report of the dealer facilitator at present.

Step S205: and (4) pricing the product by using a relative pricing method based on a principle of no arbitrage. According to the basic price of the product issued by the loan asset securitization, the steps are used for discounting a plurality of cash flow paths to obtain a discount rate curve of the product. And then combining the discount rate curve with the final predicted value of the cash flow in the step S204 to obtain the price estimation value of the product.

Because of the current secondary market trade of products being low, only the release price of newly released products per month is taken as a fair value reference. Meanwhile, considering that the difference between the property securitized products is obvious, the home mortgage securitized products issued by other banks cannot penetrate through to obtain the bottom layer loan data, so that the method is difficult to be used for pricing the products in the embodiment. Therefore, the issuance price of the new issuance product is the base price. In the embodiment, the nominal interest rate of the securities end is taken as the issued price of the product in each period as a fair price, and the base price is calculated by taking the nominal interest rate of the latest product in the first period as a base price.

The following describes product pricing in terms of both specific time point (release date) pricing and general time point (non-release date) pricing. For pricing at a specific time point (release date), on the release date of a new product, the risk premium of the product on debt of the state can be calculated according to the bookkeeping interest rate and the cash flow prediction result. Further, estimates may be made for inventory products or other products to be released based on their discount rate curves and their cash flow forecasts.

For general time point (non-release day) pricing, on the non-new product release day, due to the fact that no market price exists, the risk premium of the product is considered to be the same as that of the previous specific time point, and the discount rate curve is adjusted according to the relative change of a selected comparison reference (such as national debt) to estimate.

FIG. 6 is a schematic diagram of a product pricing flow according to an embodiment of the invention. As shown in fig. 6, the discount rate is obtained based on the new product and the new product cash flow, and then the product inventory evaluation and the future product evaluation are performed in combination with the product inventory cash flow and the future product cash flow, respectively.

In the embodiment, for different cash flow paths of the product which is not obtained in S204, the price per cash flow path is discounted, and the static interest difference under each cash flow path is calculated by adopting the discount rate in a mode of national debt (or national debt) + static interest difference. And taking the average value of the static difference, namely the static difference of the RABS relative to the national development bond (or national bond) interest rate curve, and further obtaining the reduction rate curve of the product.

The calculation of the risk premium is explained below. Risk premiums include OAS premiums, liquidity premiums, credit premiums, and the like. Among them, liquidity price premium occupies a large proportion, but it is difficult to analyze it by price difference of business, market depth, etc. due to the lack of active market trading at present. The credit premium is limited by the large percentage of inferior security pads. Therefore, in this embodiment, OAS premium is mainly analyzed.

In a personal loan contract, the borrower may earn out some or all of the current unreturned principal at a future point in time. Therefore, when the benchmark interest rate rises or the market investment interest rate (discount rate) falls, the borrower has more early compensation impulses, and the cash flow distribution of the product is influenced. This is the cause of OAS premium. FIGS. 7(a) to 7(c) show the distribution of cash flow in the case of three types of increase and decrease in the discount rate, which are the standard cases of the embodiment of the present invention.

The core of the evaluation of OAS overflow price is to calculate the cash value of the implied early-payment right, the implied fluctuation rate of the required interest rate and other parameters, which cannot be obtained under the condition of market loss of the current interest rate nonlinear derivatives. Therefore, the embodiment utilizes the relation between the predicted cash flow and interest rate to construct the implicit form of the early-stage compensation right so as to estimate the model price of the early-stage compensation right. The specific calculation method is as follows: OAS is a unique solution to the zero of the following function.

In the formula, CF_i,tPredicting cash flow at the moment t under the ith simulation scene; r is_i,tThe predicted interest rate at the moment t under the ith simulation scenario; n is the total number of simulated scenes.

It is worth noting that the model prices above are more of what is expected from the use of historical data than from the market under risk neutral measures. After the market for non-linear interest rate derivative instruments (treasury options, interest rate tips, interest rate interchange options, etc.) is built up gradually, or after trading of asset securitized products is more active, a modeling estimate can be made using market trading prices.

In another embodiment, other models may be used to make predictions of the cash flow of a product. The details will be described below. Because the RABS bottom-layer assets are composed of fully dispersed personal loans, the default rate of the bottom-layer assets is low under the condition that no systematic risk occurs, the influence on the product cash flow is small, and the international research on the product cash flow mainly focuses on the prediction of the early compensation condition of the bottom-layer assets. The models used were: the early-compensation model is provided by a supervisory institution, the early-compensation model is provided by a professional loan institution and the early-compensation model is provided by a transaction platform.

An early compensation model proposed by a regulatory body is typically an OTS model of the U.S. department of stock and loan administration (Office of sales Supervision), and the model considers that the annual early compensation rate (hereinafter referred to as "CPR") of loans is influenced by three factors, namely the loan account age, the season, the refinancing cost and the like, and the three factors are multiplied by each other. The OTS model is popular and easy to understand, is convenient for practical operation, and has lower prediction accuracy.

The earnings model proposed by the professional lending institution is typically a mixed distribution parameter model of Andrew Davison & Co. The model distinguishes borrowers as price sensitive and price mahogany. The early compensation rates of the two types of borrowers are influenced by factors such as season circulation factors, re-financing factors, income factors and historical early compensation times, but the early compensation behaviors of the price sensitive borrowers are influenced more by market interest rates and house price changes, and all the factors in the model are in an addition relation. The weighted average of the early compensation rates of the two types of borrowers is the early compensation rate of the loan combination. The model is optimized for the OTS model, and the accuracy of model prediction is improved to a certain extent.

The early compensation model provided by the trading platform is typically the early compensation model of the Penbo terminal. Compared with the OTS model, the Pengbo model enriches the factor structure, and the used factors mainly comprise a re-financing factor, a circulation factor, a cash register factor, an account age factor and a passive factor (for example, the divorce causes the property change), and the factors are in an addition relationship. Based on the powerful data support of the Pengbo terminal, the coefficients of all factors of the model are continuously adjusted and perfected, the prediction accuracy is superior to that of other models, and the model is one of the mainstream models used by the American trading desk.

In another embodiment, when the secondary market is actively trading, products of different duration and different characteristics can find corresponding trading prices, and the discount rate is determined based on the secondary trading prices. When no second-level market transaction exists or the transaction amount is low, the counterparty cannot directly capture factors such as transaction price from the market, and the discount rate is generally determined by means of the first-level issue price. In this case, the applicable models include a static discount rate model, a static difference of interest model, and a monte carlo simulation dynamic model.

Wherein, the static discount rate model is used for discounting cash flow of each period on the assumption that the yield rate is unchanged in the product storage period; the static interest difference model is to discount cash flow of each period on the assumption that the yield rate is relatively unchanged relative to the risk-free interest rate benchmark interest difference in the product storage period; the Monte Carlo simulation dynamic model simulates different cash flow paths, and a static difference method is adopted for each path to discount the cash flow of the product and calculate the mean value of the static difference.

In addition to the above, RABS products can be priced from the perspective of age and convexity, from the perspective of option risk premium, from the perspective of economics, from the perspective of credit risk density functions, and from the perspective of using Bayesian distributions in the hybrid density functions.

The effect of the asset securitization pricing method according to the embodiment of the invention will be described below with reference to the test data. Through actual product verification, in the aspect of early-compensation result prediction, the error between the predicted value and the actual value of the single-month early-compensation rate of the RABS product is about 0.1%, and the maximum error value is 0.37%. In the aspect of cash flow prediction results, the error ratio of the predicted value to the actual value of the cash flow of the RABS product in a single month is about 4.67%, and the maximum error ratio is 14.98%. The error ratio of the predicted value and the actual value of the total cash flow of each single product is about 2.45% and the maximum error ratio is 5.26% by 8 months after the product is established in 2018. In general, the pricing method of the embodiment of the invention has controlled the error within a small range except for individual months.

In the example, the data of loan between 1 month and 9 months of 2017 is used for pricing products, and the early payment rate and cash flow error results are shown in table 4, and the error unit is%.

Table 4 shows the results of the early compensation rate and cash flow error

The embodiment of the invention originally completes valuation prediction of securitization pricing of the property of the full-flow personal loan, designs and realizes the processes of loan early compensation and default analysis, property pool cash flow prediction and property securitization pricing. Through actual product verification, the error ratio of the predicted value to the actual value of the total cash flow of each single product is about 2.45%, the maximum error ratio is 5.26%, and the error can be controlled in a small range.

The embodiment of the invention designs the model factors required by cash flow prediction autonomously, obtains the model factors from the loan factors, the borrower factors, the interest rate factors and the season factors through asset analysis and expert experience, and screens out the effective cash flow model factors through 8-year repeated optimization and retest of actual data.

The embodiment of the invention is based on early compensation and default analysis, interest rate model and RABS initial asset pool list, iterative calculation is carried out stage by stage to obtain the predicted value of cash flow of each stage of basic assets, and a plurality of cash flows are simulated by a Monte Carlo method and the average value of the cash flows is taken, thereby realizing the prediction of future cash flow.

The embodiment of the invention applies various machine learning algorithms to the asset securitization pricing, and the optimal machine learning algorithm is found out by comparing the prediction effects of different models. Through verification and comparison, a neural network algorithm is finally selected to realize valuation prediction of asset securitization pricing, so that the error between a prediction result and an actual value is the lowest.

FIG. 8 is a schematic diagram of the main modules of an asset securitization pricing apparatus according to an embodiment of the invention. As shown in fig. 8, an asset securitization pricing apparatus 800 of the embodiment of the present invention mainly includes:

the early-payment default prediction module 801 is configured to obtain a model factor from the multiple loan data according to the set dimension, input the model factor into a machine learning algorithm, and perform model training, so as to predict the occurrence probability of the early-payment event and the default event and the early-payment result by using the early-payment and default model obtained by training. And mining the loan data from the loan factor, the borrower factor, the interest rate factor and the season factor by utilizing a big data technology to obtain a model factor.

The interest rate prediction module 802 is configured to input an interest rate model after preprocessing the interest rate factors in the model factors, and perform parameter verification on the interest rate model to predict a future interest rate by using the verified interest rate model. The interest rate model is a benchmark interest rate model or a national debt on-demand earning rate model. In the examples, the reference interest rate model uses the GARCH model, and the national debt on-demand profitability model uses the BK model.

And the cash flow prediction module 803 is used for updating the loan data according to the predicted probability, the early compensation result and the future interest rate, obtaining an initial prediction value of the multi-period cash flow through iterative calculation stage by stage, simulating a plurality of cash flow paths by using a Monte Carlo method, and determining a final prediction value of the multi-period cash flow. Under the influence of early compensation and default, before the cash flow is predicted, loan data needs to be dynamically updated, and a plurality of cash flow paths are simulated by combining a Monte Carlo method so as to ensure the accuracy of the predicted cash flow.

And the product pricing module 804 is used for discounting the plurality of cash flow paths according to the basic price of the product issued by securitization of the loan assets to obtain a discount rate curve of the product, so as to obtain the price valuation of the product by combining the discount rate curve and the final forecast value. And taking the issued price of the product as a basic price, performing price balancing discount on each cash flow path in a static interest difference mode, and calculating the average value of all static interest differences to further obtain a discount rate curve of the product. And then, based on the discount rate curve, discounting the final predicted value of the cash flow to obtain the price estimation value of the product.

In addition, the asset securitization pricing apparatus 800 of the embodiment of the present invention may further include: an early-compensation approximation module (not shown in fig. 8). The module is used for respectively calculating a shrinkage proportion, a shrinkage proportion and a default proportion, wherein the shrinkage proportion, the shrinkage proportion and the default proportion are respectively the ratios of the shrinkage early-paid amount, the default amount and the current unrepension principal; calculating the cash flow of the current principal fund according to the reduced amount early-payment amount, the reduced period early-payment amount and the default amount; calculating future principal cash flow according to the reduction proportion and the default proportion; calculating the cash flow of interest in the current period according to the default proportion; and calculating the future interest cash flow according to the shrinkage proportion, the shrinkage proportion and the default proportion.

From the above description, it can be seen that the model factors are obtained from the set dimensions, the probability and early-compensation result of the early-compensation event and the default event are predicted by combining the machine learning algorithm, the future interest rate is predicted by combining the interest rate model, the initial predicted value of the multi-stage cash flow of the basic asset is further calculated by iterative calculation on a period-by-period basis, the final predicted value of the multi-stage cash flow is determined by the Monte Carlo method, the cash flow prediction accuracy is improved, and the price estimation of the product is realized.

Fig. 9 illustrates an exemplary system architecture 900 of an asset securitization pricing method or asset securitization pricing apparatus to which embodiments of the invention may be applied.

As shown in fig. 9, the system architecture 900 may include

end devices

901, 902, 903, a network 904, and a server 905. Network 904 is the medium used to provide communication links between

terminal devices

901, 902, 903 and server 905. Network 904 may include various connection types, such as wired, wireless communication links, or fiber optic cables, to name a few.

A user may use the

terminal devices

901, 902, 903 to interact with a server 905 over a network 904 to receive or send messages and the like. The

terminal devices

901, 902, 903 may have various communication client applications installed thereon, such as a shopping application, a web browser application, a search application, an instant messaging tool, a mailbox client, social platform software, and the like.

The

terminal devices

901, 902, 903 may be various electronic devices having a display screen and supporting web browsing, including but not limited to smart phones, tablet computers, laptop portable computers, desktop computers, and the like.

The server 905 may be a server that provides various services, such as a back-office management server that analyzes loan data acquired by an administrator using the

terminal apparatuses

901, 902, 903. The back-office management server can perform early-payment and default analysis, interest rate prediction, cash flow prediction, product valuation and other processing on the received loan data, and feed back a processing result (such as the price valuation of the product) to the terminal equipment.

Note that, the asset securitization pricing method provided in the embodiment of the present application is generally executed by the server 905, and accordingly, the asset securitization pricing device is generally provided in the server 905.

It should be understood that the number of terminal devices, networks, and servers in fig. 9 is merely illustrative. There may be any number of terminal devices, networks, and servers, as desired for implementation.

The invention also provides an electronic device and a computer readable medium according to the embodiment of the invention.

The electronic device of the present invention includes: one or more processors; a storage device for storing one or more programs which, when executed by the one or more processors, cause the one or more processors to implement a method for securitization pricing of assets of an embodiment of the invention.

The computer readable medium of the present invention has stored thereon a computer program that, when executed by a processor, implements a method of securitized pricing of assets of embodiments of the present invention.

Referring now to FIG. 10, shown is a block diagram of a computer system 1000 suitable for use in implementing an electronic device of an embodiment of the present invention. The electronic device shown in fig. 10 is only an example, and should not bring any limitation to the functions and the scope of use of the embodiments of the present invention.

As shown in fig. 10, the computer system 1000 includes a Central Processing Unit (CPU)1001 that can perform various appropriate actions and processes according to a program stored in a Read Only Memory (ROM)1002 or a program loaded from a storage section 1008 into a Random Access Memory (RAM) 1003. In the RAM 1003, various programs and data necessary for the operation of the computer system 1000 are also stored. The CPU 1001, ROM 1002, and RAM 1003 are connected to each other via a bus 1004. An input/output (I/O) interface 1005 is also connected to bus 1004.

The following components are connected to the I/O interface 1005: an input section 1006 including a keyboard, a mouse, and the like; an output section 1007 including a display such as a Cathode Ray Tube (CRT), a Liquid Crystal Display (LCD), and the like, and a speaker; a storage portion 1008 including a hard disk and the like; and a communication section 1009 including a network interface card such as a LAN card, a modem, or the like. The communication section 1009 performs communication processing via a network such as the internet. The driver 1010 is also connected to the I/O interface 1005 as necessary. A removable medium 1011 such as a magnetic disk, an optical disk, a magneto-optical disk, a semiconductor memory, or the like is mounted on the drive 1010 as necessary, so that a computer program read out therefrom is mounted into the storage section 1008 as necessary.

In particular, the processes described above with respect to the main step diagrams may be implemented as computer software programs, according to embodiments of the present disclosure. For example, embodiments of the present disclosure include a computer program product comprising a computer program embodied on a computer readable medium, the computer program containing program code for performing the method illustrated in the main step diagram. In such an embodiment, the computer program may be downloaded and installed from a network through the communication part 1009 and/or installed from the removable medium 1011. The computer program executes the above-described functions defined in the system of the present invention when executed by the Central Processing Unit (CPU) 1001.

It should be noted that the computer readable medium shown in the present invention can be a computer readable signal medium or a computer readable storage medium or any combination of the two. A computer readable storage medium may be, for example, but not limited to, an electronic, magnetic, optical, electromagnetic, infrared, or semiconductor system, apparatus, or device, or any combination of the foregoing. More specific examples of the computer readable storage medium may include, but are not limited to: an electrical connection having one or more wires, a portable computer diskette, a hard disk, a Random Access Memory (RAM), a read-only memory (ROM), an erasable programmable read-only memory (EPROM or flash memory), an optical fiber, a portable compact disc read-only memory (CD-ROM), an optical storage device, a magnetic storage device, or any suitable combination of the foregoing. In the present invention, a computer readable storage medium may be any tangible medium that can contain, or store a program for use by or in connection with an instruction execution system, apparatus, or device. In the present invention, however, a computer readable signal medium may include a propagated data signal with computer readable program code embodied therein, for example, in baseband or as part of a carrier wave. Such a propagated data signal may take many forms, including, but not limited to, electro-magnetic, optical, or any suitable combination thereof. A computer readable signal medium may also be any computer readable medium that is not a computer readable storage medium and that can communicate, propagate, or transport a program for use by or in connection with an instruction execution system, apparatus, or device. Program code embodied on a computer readable medium may be transmitted using any appropriate medium, including but not limited to: wireless, wire, fiber optic cable, RF, etc., or any suitable combination of the foregoing.

The flowchart and block diagrams in the figures illustrate the architecture, functionality, and operation of possible implementations of systems, methods and computer program products according to various embodiments of the present invention. In this regard, each block in the flowchart or block diagrams may represent a module, segment, or portion of code, which comprises one or more executable instructions for implementing the specified logical function(s). It should also be noted that, in some alternative implementations, the functions noted in the block may occur out of the order noted in the figures. For example, two blocks shown in succession may, in fact, be executed substantially concurrently, or the blocks may sometimes be executed in the reverse order, depending upon the functionality involved. It will also be noted that each block of the block diagrams or flowchart illustration, and combinations of blocks in the block diagrams or flowchart illustration, can be implemented by special purpose hardware-based systems which perform the specified functions or acts, or combinations of special purpose hardware and computer instructions.

The modules described in the embodiments of the present invention may be implemented by software or hardware. The described modules may also be provided in a processor, which may be described as: a processor includes an early-payment default prediction module, an interest rate prediction module, a cash flow prediction module, and a product pricing module. For example, the early-payment default prediction module can be further described as a module for obtaining model factors from the multiple loan data according to the set dimension, inputting the model factors into a machine learning algorithm for model training, and predicting the probability of the early-payment event and the default event using the trained early-payment and default model and the early-payment result.

As another aspect, the present invention also provides a computer-readable medium that may be contained in the apparatus described in the above embodiments; or may be separate and not incorporated into the device. The computer readable medium carries one or more programs which, when executed by a device, cause the device to comprise: obtaining model factors from the multi-loan data according to the set dimensionality, inputting the model factors into a machine learning algorithm for model training, and predicting the probability of occurrence of early-paid events and default events and early-paid results by using early-paid and default models obtained by training; preprocessing the interest rate factors in the model factors, inputting the preprocessed interest rate factors into an interest rate model, and performing parameter verification on the interest rate model to predict future interest rate by using the verified interest rate model; updating the loan data according to the predicted probability, the early-compensation result and the future interest rate, obtaining an initial predicted value of the multi-stage cash flow by iterative calculation stage by stage, simulating a plurality of cash flow paths by using a Monte Carlo method, and determining a final predicted value of the multi-stage cash flow; and according to the basic price of the product issued by the loan asset securitization, performing discount on the plurality of cash flow paths to obtain a discount rate curve of the product, and combining the discount rate curve and the final predicted value to obtain the price valuation of the product.

The product can execute the method provided by the embodiment of the invention, and has corresponding functional modules and beneficial effects of the execution method. For technical details that are not described in detail in this embodiment, reference may be made to the method provided by the embodiment of the present invention.

The above-described embodiments should not be construed as limiting the scope of the invention. Those skilled in the art will appreciate that various modifications, combinations, sub-combinations, and substitutions can occur, depending on design requirements and other factors. Any modification, equivalent replacement, and improvement made within the spirit and principle of the present invention should be included in the protection scope of the present invention.

Claims

1. A method for securitized pricing of assets, comprising:

obtaining model factors from the multi-loan data according to the set dimensionality, inputting the model factors into a machine learning algorithm for model training, and predicting the probability of occurrence of early-paid events and default events and early-paid results by using early-paid and default models obtained by training;

preprocessing the interest rate factors in the model factors, inputting the preprocessed interest rate factors into an interest rate model, and performing parameter verification on the interest rate model to predict future interest rate by using the verified interest rate model;

updating the loan data according to the predicted probability, the early-compensation result and the future interest rate, obtaining an initial predicted value of the multi-stage cash flow by iterative calculation stage by stage, simulating a plurality of cash flow paths by using a Monte Carlo method, and determining a final predicted value of the multi-stage cash flow;

and according to the basic price of the product issued by the loan asset securitization, performing discount on the plurality of cash flow paths to obtain a discount rate curve of the product, and combining the discount rate curve and the final predicted value to obtain the price valuation of the product.

2. The method of claim 1, wherein iteratively calculating on a per-term basis yields initial predicted values for the multi-term cash flow, comprising:

generating a plurality of interest rate paths, wherein the interest rate paths comprise a plurality of interest rates in a plurality of periods, and calculating the interest rate in each period of each interest rate path as follows:

respectively summing up the bottom loan unpaid principal, the bottom loan principal repayment and the bottom loan interest repayment to correspondingly obtain an asset pool unpaid principal, a current repayment and an interest repayment;

calculating the cost of the recovery money according to the interest return payment, calculating the cost of each period according to the outstanding repayment fund of the asset pool, calculating the cost of the first period according to the priority scale and the asset pool scale under the condition that the first period payment is needed, and calculating the cost of the end of year under the condition that the current time is the end of year;

differentiating the sum of the current-period reimbursement fee, the current-period fee, the first-period fee and the last-year fee to obtain a pre-redemption disposable amount, and calculating an actual redemption amount in combination with a redemption rate;

and according to the priority order of product redemption, under the limit of the actual redemption amount, redeeming priority interest and priority principal, updating the priority residual principal, the security residual principal and the principal repayment amount of the current cash flow in the current period, and repeating the calculation process until the priority residual principal is 0.

3. The method of claim 1, wherein the model factors are derived from mining the loan data in four dimensions, a loan factor, a borrower factor, the interest rate factor, and a seasonal factor, using big data technology; wherein the content of the first and second substances,

the loan factors comprise contract amount, outstanding principal balance, loan interest rate, repayment type, contract release date, account age and remaining term, loan city, house type, mortgage value and monthly repayment payment data;

the borrower factors comprise the age, the sex, the income and the occupation of the borrower;

the interest rate factor comprises a first time period reference loan interest rate and a second time period national debt exploitation rate corresponding to the contract issuing date, and the first time period reference loan interest rate and the second time period national debt exploitation rate in the current period;

the season factor comprises a month corresponding to loan issuance days and a month corresponding to repayment days per period.

4. The method of claim 3, wherein inputting the model factors into a machine learning algorithm for model training comprises:

dividing model factors obtained from the plurality of loan data into a training set, a verification set and a test set;

training: determining a group of hyper-parameters of a machine learning algorithm, inputting the training set into the machine learning algorithm for training to obtain an initial early-compensation and default model which enables a set target function to be minimum;

and (3) verification: verifying the performance of the initial early-compensation and default model by using the verification set, and repeating the training step and the verification step until a specified hyper-parameter combination is searched;

selecting an initial early-compensation and default model with the minimum error on the verification set as an intermediate early-compensation and default model, combining the training set and the verification set as a whole, and training the intermediate early-compensation and default model to obtain a trained early-compensation and default model;

and inputting the test set into the early-compensation and default model for prediction.

5. The method of claim 1, wherein the interest rate model is any one of a benchmark interest rate model and a national debt on-demand rate model, wherein,

the reference interest rate model uses a GARCH model, correspondingly, the preprocessing comprises unitizing the adjustment amplitude of the interest rate, and the parameter verification uses a garchfit method;

the on-demand profitability model of the national debt uses a BK model, correspondingly, the preprocessing comprises data conversion, and the parameter verification is realized by calculating a confidence interval.

6. The method of claim 1, wherein the morning compensation result comprises a type of morning compensation at the occurrence of the morning compensation event, the type of morning compensation comprising a reduced amount morning compensation and a reduced period morning compensation;

updating the loan data based on the predicted probability, the early-compensation result, and the future interest rate, comprising:

judging whether the current loan is default or early-payment according to the predicted probability and judging the type of the early-payment when the early-payment occurs;

in the case of default of the current loan, updating the current non-repayment principal and the current amortization principal of the loan data to be both 0;

under the condition that the current loan is paid early and the early payment type is reduced early, calculating the next unreturned principal according to the current unreturned principal and the current principal repayment proportion, and respectively calculating the current due and the current due in two repayment modes of the equal-cost principal and the equal-cost;

under the condition that the current loan is compensated early and the early compensation type is the reduced early compensation, calculating the number of uncompensated remuneration dates in two compensation modes of equal principal and equal principal, and then calculating the current due and the current due principal in the two compensation modes according to the reduced early compensation mode;

and correspondingly updating the corresponding fields of the loan data according to the calculation results of different early compensation types.

7. The method of claim 1, wherein when the loan data is a pool of assets formed by securitization of loan assets, the method further comprises:

respectively calculating a shrinkage proportion, a shrinkage proportion and a default proportion, wherein the shrinkage proportion, the shrinkage proportion and the default proportion are respectively the ratios of the shrinkage early-paid amount, the default amount and the current unreturned principal;

calculating the cash flow of the current principal fund according to the reduced amount early-payment amount, the reduced period early-payment amount and the default amount; calculating future principal cash flow according to the reduction proportion and the default proportion;

calculating the cash flow of interest in the current period according to the default proportion; and calculating the future interest cash flow according to the shrinkage proportion, the shrinkage proportion and the default proportion.

8. The method of any of claims 1 to 7, wherein discounting the plurality of cash flow paths resulting in a discount rate curve for the product comprises:

respectively discounting the plurality of cash flow paths by adopting a static difference method to obtain static differences under the plurality of cash flow paths;

and calculating the average value of the plurality of static differences to obtain the discount rate curve of the product.

9. The method of claim 8, wherein respectively discounting the plurality of cash flow paths comprises:

and constructing an implicit form of the early-stage compensation right by utilizing the relationship between the final predicted value of the multi-stage cash flow and the future interest rate so as to estimate the cash value of the early-stage compensation right.

10. An asset securitization pricing apparatus, comprising:

the early-payment default prediction module is used for acquiring model factors from the multi-loan data according to the set dimensionality, inputting the model factors into a machine learning algorithm for model training, and predicting the probability of the occurrence of the early-payment events and default events and the early-payment result by using the early-payment and default models obtained by training;

the interest rate prediction module is used for preprocessing the interest rate factors in the model factors, inputting the interest rate models, and performing parameter verification on the interest rate models to predict future interest rates by using the verified interest rate models;

the cash flow prediction module is used for updating the loan data according to the predicted probability, the early-compensation result and the future interest rate, obtaining an initial prediction value of the multi-period cash flow by iterative calculation stage by stage, simulating a plurality of cash flow paths by using a Monte Carlo method, and determining a final prediction value of the multi-period cash flow;

and the product pricing module is used for discounting the plurality of cash flow paths according to the basic price of the product issued by loan asset securitization to obtain a discount rate curve of the product so as to obtain the price valuation of the product by combining the discount rate curve and the final predicted value.

11. An electronic device, comprising:

one or more processors;

a storage device for storing one or more programs,

when executed by the one or more processors, cause the one or more processors to implement the method of any one of claims 1-9.

12. A computer-readable medium, on which a computer program is stored, which, when being executed by a processor, carries out the method according to any one of claims 1-9.