CN111192129A - Method and device for obtaining zero interest rate of multiple nodes on interest rate time limit structure curve - Google Patents

Method and device for obtaining zero interest rate of multiple nodes on interest rate time limit structure curve Download PDF

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CN111192129A
CN111192129A CN201811350531.8A CN201811350531A CN111192129A CN 111192129 A CN111192129 A CN 111192129A CN 201811350531 A CN201811350531 A CN 201811350531A CN 111192129 A CN111192129 A CN 111192129A
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诸定秋
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Yansheng Technology Shanghai Co Ltd
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Abstract

One or more embodiments of the present specification provide a method and apparatus for obtaining zero interest rate of a multi-term node on an interest rate term structure curve, the method including: obtaining market quotation Q of the interest rate product at a multi-term node1，Q2...QNAnd an expiration period T1，T2...TN(ii) a Establishing the value F of the interest rate product at the multi-term node based on the selected value function model1，F2...FNMarket quote Q at a multi-term node for the interest rate product1，Q2...QNExpiration period T1，T2...TNAnd zero interest rate R1，R2...RNA non-linear system of (3); performing equation solution calculation based on the nonlinear system to obtain the zero interest rate R of the multi-term node1，R2...RN。

Description

Method and device for obtaining zero interest rate of multiple nodes on interest rate time limit structure curve
Technical Field
The specification relates to the field of financial science and technology, in particular to a method and a device for obtaining zero interest rate of multiple nodes on an interest rate limit structure curve.
Background
The interest rate term structure refers to the relationship between interest rates (generally, spot interest rates) and expiration terms at different time points and the change rule, and is generally determined by the actual trading price of the bond market. In a mature financial market, the interest rate period structure of the bond can reflect the supply and demand relationship of the market, the overall level and the change direction of the market interest rate, and is an important basis for scientifically making financial and currency policies and perfecting bond issuing and management. Regarding the construction method of the existing interest rate term structure curve, the Bootstrapping method is generally used to solve the corresponding interest rate of zero interest rate by solving each interest rate product price on the term structure. Because market data usually contains noise, the simple method is difficult to filter out real noise signals, and a real arbitrage-free rate curve cannot be constructed in many cases; meanwhile, due to the special structure of the high-mobility interest rate derivative for constructing the curve in the market, the interest rate limit structure curve is constructed by solving the zero interest rates of multiple points on the interest rate curve at the same time, but the simple Bootstrapping method cannot solve the problem.
Disclosure of Invention
Based on the above-mentioned problems, the present specification provides a method for obtaining interest rate zero of a multi-term node on an interest rate term structure curve, comprising:
obtaining market quotation Q of the interest rate product at a multi-term node1，Q2…QNAnd an expiration period T1,T2…TN；
Establishing the value F of the interest rate product at the multi-term node based on the selected value function model1，F2…FNMarket quote Q at a multi-term node for the interest rate product1，Q2…QNExpiration period T1,T2…TNAnd zero interest rate R1，R2…RNThe non-linear system of (2):
F1(Q1；R1,R2,…,RN；T1,T2,…,TN)＝0
F2(Q2；R1,R2,…,RN；T1,T2,…,TN)＝0
…
FN(QN；R1,R2,…,RN；T1,T2,…,TN)＝0
；
performing equation solution calculation based on the nonlinear system to obtain the zero interest rate R of the multi-term node1，R2…RN。
In yet another illustrative embodiment, the method further comprises:
zero interest rate R based on the obtained multi-term nodes1，R2…RNAnd said expiration period T1,T2…TNAnd constructing a interest rate period structure curve of the interest rate product.
In yet another illustrative embodiment, the method further comprises:
market quotation Q at multi-term node based on the obtained interest rate product1，Q2…QNAnd an expiration period T1,T2…TNObtaining the discount rate P of the interest rate product at the multi-term node1，P2…PN。
In yet another illustrative embodiment, the equation solving calculation based on the nonlinear system is performed to obtain the interest rate of zero R of the multi-term node1，R2…RNThe method comprises the following steps:
constructing a Jacobian matrix of the nonlinear system:
Figure BDA0001864755160000021
establishing the interest rate R of the multiple nodes according to a preset algorithm model1，R2…RNValue F of said known interest rate product1，F2…FNThe Jacobian matrix JFThe calculated relationship of (1);
iterative computation of the Jacobian matrix J based on an adjoint difference methodFWhen the interest rate R of zero interest of the multi-term node is obtained based on the calculation relationship1，R2…RNWhen the value of (A) is converged, outputting the interest rate R of the multiple nodes1，R2…RN。
In yet another illustrated embodiment, the predetermined algorithm model is a Levenberg-Marquardt algorithm model.
In yet another illustrative embodiment, the cost function model includes one or more of an inter-bank peer borrowing model function model, a forward interest rate agreement function model, a futures function model, and an interest rate interchange function model.
Accordingly, the present specification also provides an apparatus for obtaining interest rate of zero interest rate of a multi-term node on an interest rate term structure curve, comprising:
an acquisition unit for acquiring market quotation Q of the interest rate product at a multi-term node1，Q2…QNAnd an expiration period T1,T2…TN；
A function construction unit for constructing the value F of the interest rate product at the multi-term node based on the selected value function model1，F2…FNMarket quote Q at a multi-term node for the interest rate product1，Q2…QNExpiration period T1,T2…TNAnd zero interest rate R1，R2…RNThe non-linear system of (2):
F1(Q1；R1,R2,…,RN；T1,T2,…,TN)＝0
F2(Q2；R1,R2,…,RN；T1,T2,…,TN)＝0
…
FN(QN；R1,R2,…,RN；T1,T2,…,TN)＝0
；
a calculation unit for performing equation solution calculation based on the nonlinear system to obtain the interest rate R of zero interest of the multi-term node1，R2…RN。
In yet another illustrative embodiment, the apparatus further comprises:
a curve construction unit for obtaining zero interest rate R of the multi-term node1，R2…RNAnd said expiration period T1,T2…TNAnd constructing a interest rate period structure curve of the interest rate product.
In yet another illustrative embodiment, the computing unit is to:
constructing a Jacobian matrix of the nonlinear system:
Figure BDA0001864755160000041
establishing the interest rate R of the multiple nodes according to a preset algorithm model1，R2…RNValue F of said known interest rate product1，F2…FNThe Jacobian matrix JFThe calculated relationship of (1);
iterative computation of the Jacobian matrix J based on an adjoint difference methodFWhen obtaining the interest rate R of zero interest of said multiple nodes based on said calculation relationship1，R2…RNWhen the value of (A) is converged, outputting the interest rate R of the multiple nodes1，R2…RN。
Accordingly, this specification also provides a computer device comprising: a memory and a processor; the memory having stored thereon a computer program executable by the processor; when the processor runs the computer program, the method for acquiring the zero interest rate of the multi-term node on the interest rate term structure curve is executed.
Accordingly, the present specification also provides a computer readable storage medium having stored thereon a computer program which, when executed by a processor, performs the above-described method of obtaining interest rates of a multi-term node on an interest rate term structure curve.
By the method, the device, the computer equipment and the computer readable storage medium for acquiring the zero interest rate of the multiple term nodes on the interest rate term structure curve, the zero interest rate of the multiple term nodes on one interest rate term structure curve is calculated in real time without adding additional hardware accelerating equipment, so that the cost and the difficulty of development and maintenance are reduced. The implementation of the method provided by the specification can greatly reduce the calculation of interest rate products required in interest rate curve construction on zero interest rate risk sensitivity, the calculation amount can be reduced to one percent or even one thousandth of the original calculation amount, and meanwhile, the implementation of the technology also uses an accurate analytic solution to replace the previous approximate difference decomposition, so that the accuracy and the stability of the curve construction are improved.
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Fig. 1 is a flowchart of a method for obtaining interest rates of zero interest at a multi-term node on a graph of an interest rate term structure according to an exemplary embodiment of the present disclosure;
fig. 2(a) and (b) are diagrams of a process for obtaining values of a jacobian matrix based on a adjoint difference method according to an exemplary embodiment of the present specification;
FIG. 3 is a diagram illustrating an apparatus for obtaining interest rates of zero interest at a multi-term node on a graph of interest rate term structure according to an exemplary embodiment of the present disclosure;
fig. 4 is a hardware structure diagram of an embodiment of an apparatus for obtaining zero interest rate of a multi-term node on an interest rate term structure curve provided in the present specification.
Detailed Description
Interest rate period structure is the benchmark of asset pricing, financial product design, insurance value, risk management and the like, so the interest rate period structure model and the characteristics of interest rate behaviors are the key points of the research of finance. The construction of interest rate curves is one of the most important items in financial engineering. For practitioners in the financial industry, the level of interest rate curve construction directly affects the performance of financial product traders, and the capacity of risk management of financial institutions is also considered.
The Bootstrapping method commonly used in the market at present solves the corresponding interest rate of zero interest by solving the price quoted for each interest rate product on the term structure. Because market data usually contains noise, the simple method is difficult to filter out real noise signals, and a real arbitrage-free rate curve cannot be constructed in many cases; meanwhile, due to the special structure of the high-mobility interest rate derivative for constructing the curve in the market, the interest rate limit structure curve is constructed by solving the zero interest rates of multiple points on the interest rate curve at the same time, but the simple Bootstrapping method cannot solve the problem.
To solve the above problems, the present specification provides a method for zero interest rate of a multi-term node on an interest rate term structure curve, as shown in fig. 1, the method comprising:
102, obtaining the market quotation Q of the interest rate product at the multi-term node1，Q2…QNAnd an expiration period T1,T2…TN。
The quoted price of the interest rate product refers to the price quotation of the interest rate product on the market, such as the same industry borrowing, the interest rate futures, the forward period, the interest rate interchange and the like, such as the industry borrowing rate, the forward period interest rate, the swap period interest rate and the like. The interest rate product market has many offers for interest rate products with different expiration periods, and for the same interest rate product, such as national debt, it is possible to collect information about its offers in different expiration periods, such as 0.5 years, 1 year, 2 years, etc., usually considering the whole period structure in the range of 0 to 30 years or even 60 years. Since different types of interest rate products will typically cover various time periods, the expiration periods of the selected interest rate products need not coincide with each other. Preferably, interest rate products (with a smaller spread in buy and sell quotes) that are well-distributed in the market can be selected because they are best suited for market risk hedging.
The value of the interest rate product is the current estimate of the interest rate product, and can be converted into a value according to all cash flows of the interest rate product. Since the value of interest rate products is typically converted based on future interest rate cash flows, in an illustrative embodiment, the expiration period T is based on the same interest rate product obtained from the market as described above1,T2…TNAnd quoted price Q at the corresponding deadline1，Q2…QNGenerating future interest rate cash flow discount rate P of the interest rate product1，P2…PN。
104, based on the selected valueFunction model, value F of interest rate product in multi-term node1，F2…FNMarket quote Q at a multi-term node for the interest rate product1，Q2…QNExpiration period T1,T2…TNAnd zero interest rate R1，R2…RNThe non-linear system of (2):
F1(Q1；R1,R2,…,RN；T1,T2,…,TN)＝0
F2(Q2；R1,R2,…,RN；T1,T2,…,TN)＝0
…
FN(QN；R1,R2,…,RN；T1,T2,…,TN)＝0
。
the cost function model of the known interest rate product is generally a risk neutral linear non-arbitrage rate model, and specifically, different cost function models can be selected according to the type of the interest rate product. Different types of interest rate products may be used to generate the interest rate term structure curve, and the expiration terms of the selected interest rate products need not coincide with each other, and it is generally contemplated that the entire term structure is selected in the range of 0 to 30 years, or even 60 years. As will be appreciated by those skilled in the art, the first point on the interest rate term structure curve for a known interest rate product is the reference date T of the curve0And at the reference date T0The discount rate of interest rate product should be 1, i.e. { T }0,Px(T0,T0)＝1}。
In an illustrative embodiment, when the interest rate product is an inter-bank industry loan interest rate product, the cost function model for the interest rate product may be expressed in a DEPO model. DEPO is a standard interest-bearing contract on the money market, typically with a start date on the day or due date, defined as
DEPO(Ti)＝N[1+L(Tf,T0,Ti)*τ(T0,Ti)](1)
N is the nominal amount of the contract; t isfSetting time for interest rate, typically the day of the transaction; t isiIs due date; tau (T)0,Ti) Is the length of the rest interval.
Accordingly, its value at time t is:
DEPO(t；Ti)＝Px(t,Ti)N[1+R(Tf,T0,Ti)*τ(T0,Ti)](2)
wherein
Figure BDA0001864755160000071
The discount rate, R, of future interest rate cash flow for the interest rate productx(T, T) is the zero interest rate at the time of the term T.
DEPO can generally be used to construct a short-term portion of an interest rate duration structure curve, and a duration T on the curveiThe reduction ratio value is:
Figure BDA0001864755160000072
according to the principle of contract flat value, can obtain
Px(t,T0)-Px(t,Ti)[1+L(t,T0,Ti)τ(T0,Ti)]＝0 (7)
Wherein, L (T, T)0,Ti) For the interest rate product at the time limit TiThe quote of (1).
In yet another illustrative embodiment, the interest rate product is a forward interest rate product (FRA), which, as will be appreciated by those skilled in the art, is similar to an inter-bank industry loan rate product, but the start time is not present, but rather at some future day. The forward interest rate product value agreement on the market is typically such that the actual payment date is the time of day, not the due date, and the forward interest rate product value function model may be defined as
Figure BDA0001864755160000073
The long term interest rate agreement on the market can be used to construct the short term part on the interest rate curve, and the trade time of the agreement is a flat value to obtain the long term interest rate as
Figure BDA0001864755160000074
Thus, it is finally obtained:
P(t,Ti-1)-P(t,Ti)[1+L(t,Ti-1,Ti)τ(Ti-1,Ti)]＝0 (10)
in yet another illustrative embodiment, the interest rate products are futures products, and the futures interest rate is generally a deposit-type contract traded at the exchange, equivalent to an off-site traded future interest rate contract, with the interest rate product value function modeled as
Future(Ti-1,Ti)＝N[1-F(Ti-1,Ti)](11)
Similarly, the forward contract and the forward interest rate in futures can also conform to the above formula (9), and thus can obtain:
P(t,Ti-1)-P(t,Ti)[1+F(t,Ti-1,Ti)τ(Ti-1,Ti)]＝0 (12)
wherein F (T, T)i-1,Ti) Is the forward interest rate corresponding to the futures contract.
Futures contracts are also typically short term portions that are used to construct interest rate curves.
In yet another illustrated embodiment, the interest rate product is an interest rate interchange product. Interest rate interchange contract is a contract for conducting transaction outside the field, and usually two parties of the transaction exchange a series of cash flows with each other, and the trade is generally based on the floating interest rate L (T) of the inter-bank industry borrowingi-1,Ti) And cash flow based on a fixed interest rate S. An interest rate interchange contract is typically represented by the following cash flow table
Figure BDA0001864755160000081
Floating interest rate cash flow table
Figure BDA0001864755160000082
Cash flow table with fixed interest rate
And is
Figure BDA0001864755160000083
For each cash flow table, the interest rate coupon value of each corresponding interest counting interval is
Figure BDA0001864755160000084
Figure BDA0001864755160000085
Then the value function model for the interest rate product is
Figure BDA0001864755160000086
Where ω denotes whether a fixed interest (-1) is paid or received in the contract (+1), Pd(T, T) represents the discount rate, from the discount rate curve specified by contract pricing, and
Figure BDA0001864755160000087
wherein P isx(T, T) is obtained from the target profitability curve.
According to the market quotation flat value principle, the method can obtain
Figure BDA0001864755160000088
Market rate interchange contracts are typically used to construct the medium and long term portions of the rate of return curve.
The above embodiments illustrate the process of selecting a cost function model of a corresponding interest rate product according to the type of the known interest rate product. Based on the above selectionSelecting a value function model of interest rate products, and constructing the value F of the interest rate products at multi-term nodes1，F2…FNMarket quote Q at a multi-term node for the interest rate product1，Q2…QNExpiration period T1,T2…TNAnd zero interest rate R1，R2…RNThe non-linear system of (2):
F1(Q1；R1,R2,…,RN；T1,T2,…,TN)＝0
F2(Q2；R1,R2,…,RN；T1,T2,…,TN)＝0
…
FN(QN；R1,R2,…,RN；T1,T2,…,TN)＝0
。
wherein Fk(k-1, … N) is derived from equations (7), (10), (12) and (17) above, Qk(k-1, … N) L (T, T) from equations (7), (10), (12) and (17)0,Ti),F(t,Ti-1,Ti),
Figure BDA0001864755160000091
And the like.
106, carrying out equation solution calculation based on the nonlinear system to obtain the zero interest rate R of the multi-term node1，R2…RN。
Here by CxContinuous term structure yield curve representing a certain rate product:
Figure BDA0001864755160000092
where the subscript x represents the interest-bearing interval of the target product interest rate corresponding to the curve, e.g., x ═ { ON,1M,3M,6M,12M }, t represents the reference time (e.g., today or due date) of the curve, and the zero interest rate in the curve is initialized to the value of interest rate of the target product0. Continuous type of interest-free rate Rx(T, T) and the reduction ratio Px(T, T) is in the relationship
Figure BDA0001864755160000093
According to (1) and (2), the above zero interest rate curve can be described as:
Figure BDA0001864755160000094
in an embodiment, the equation solving calculation based on the nonlinear system is performed to obtain the interest rate R of zero interest of the multi-term node1，R2…RNThe process comprises the following steps:
constructing a Jacobian matrix of the nonlinear system:
Figure BDA0001864755160000101
establishing the interest rate R of the multiple nodes according to a preset algorithm model1，R2…RNA cost function F of the known interest rate product and the Jacobian matrix JFBased on the adjoint difference method to obtain the Jacobian matrix JFAnd a cost function F of said converged interest rate product, based on said predetermined algorithm model and said Jacobian matrix JFValue of (d), a cost function F of the converged interest rate product to solve the zero interest rate R of the multiple nodes1，R2…RN。
In an illustrative embodiment, the predetermined algorithm model is a Levenberg-Marquardt algorithm, so solving the nonlinear system finds the corresponding interest rate of zero to minimize the sum of the squares of the following equations:
Figure BDA0001864755160000102
assume multiple deadlines on the current interest rate curveThe value of a node is
Figure BDA0001864755160000103
For the product with J cash flows, the corresponding discount rate is set as { P }1,P2,…,PJThe zero interest rate corresponding to it is { r }1,r2,…,rJ}, then FkCan be obtained by calculation as shown in fig. 2(a) below.
In an illustrative embodiment, the Jacobian matrix J is calculated according to the adjoint difference method by taking the interest rate interchange product as an exampleFThe procedure for the values of (c) is as follows:
as shown in the formula (17) in the above embodiment,
Fk(Qk；R1,R2,…,RN；T1,T2,…,TN)＝IRS(t；TL,TS,Lx,S,ω)
wherein Qk＝S,Pd(T, T) is derived from a known reduction curve, and if it is known, then there may be a value according to equation (17)
ri＝r(t,Ti L)＝gi(R1,R2,…,RN；T1,T2,…,TN) I is 1, …, and n, g is an interpolation function. If T isk-1≤Ti L<TkK is 1, …, N, then
Figure BDA0001864755160000104
Figure BDA0001864755160000111
Figure BDA0001864755160000112
Figure BDA0001864755160000113
Figure BDA0001864755160000114
Fk＝TCFL-TCFSWherein
Figure BDA0001864755160000115
Are known.
Solve to F in the forward directionkThen, F is solved reverselykIs accompanied by
Figure BDA0001864755160000116
To obtain
Figure BDA0001864755160000117
Wherein k, l ═ 1, … N; as shown in FIG. 2 (b);
Figure BDA0001864755160000118
Figure BDA0001864755160000119
Figure BDA00018647551600001110
Figure BDA00018647551600001111
Figure BDA00018647551600001112
Figure BDA00018647551600001113
Figure BDA00018647551600001114
Figure BDA00018647551600001115
Figure BDA00018647551600001116
from this it can be derived
Figure BDA00018647551600001117
That is to say
Figure BDA00018647551600001118
And finally obtaining a Jacobian matrix JFThe value of (c).
Repeatedly iterating the forward solution FkAnd from FkIs accompanied by inverse solution
Figure BDA00018647551600001119
Up to a zero interest rate R of said multi-term node1，R2…RNThe resulting interest rate time limit structure curve
Figure BDA0001864755160000121
The above system equation (18) can be satisfied.
In yet another illustrative embodiment, the interest rate R of the multi-term node is zero interest rate based on the above-mentioned interest rate term structure curve1，R2…RNAnd said expiration period T1,T2…TNAnd constructing a interest rate period structure curve of the interest rate product.
The interest rate duration structure curve described in the above embodiment is generally the relationship between the yield rate and the remaining duration of the bond with the same credit level/the same issuer for the consecutive remaining duration days, and may be either an interest rate immediate curve or an interest rate due curve, and may be determined according to the selected interest rate duration structure model.
The interest rate time limit structure model described in the above embodiment may generally have a linear interest rate model without arbitrage. As can be seen from the above embodiments, when a linear no-arbitrage model is used, the user should also select the linear interpolation function g used in the linear no-arbitrage model.
The value of the known interest rate product described in the above embodiments refers to the current estimate of the product, and the value of the product is discounted based on all cash flows of the product. By the aid of the construction method of the interest rate time limit structure curve, zero interest rates of multiple nodes on one interest rate time limit structure curve can be calculated simultaneously, and an inefficient construction mode that the zero interest rates are solved for the single nodes in the interest rate time limit structure curve one by one in a Bootstrapping method is avoided. Meanwhile, because the invention does not need to add extra hardware accelerating equipment, the cost and the difficulty of development and maintenance are reduced. The implementation of the AAD technique can greatly reduce the calculation of interest rate product sensitivity to zero interest rate risk required in the construction of the interest rate curve, which can be reduced to one percent or even one thousandth of the original calculation amount. Meanwhile, the invention also uses accurate analytic solution to replace the prior approximate difference decomposition, thereby improving the accuracy and stability of curve construction.
Corresponding to the implementation of the above flow, the embodiments of the present specification further provide a device for constructing an interest rate duration structure curve. The apparatus may be implemented by software, or by hardware, or by a combination of hardware and software. Taking a software implementation as an example, the logical device is formed by reading a corresponding computer program instruction into a memory for running through a Central Processing Unit (CPU) of the device. In terms of hardware, the device in which the data processing apparatus is located generally includes other hardware such as a chip for transmitting and receiving wireless signals and/or other hardware such as a board for realizing a network communication function, in addition to the CPU, the memory, and the storage shown in fig. 4.
Fig. 3 is a device 30 for obtaining interest rate of zero interest at a multi-term node on a graph of an interest rate term structure according to the present disclosure, including:
an obtaining unit 302 for obtaining the market quotation Q of the interest rate product at the multi-term node1，Q2…QNAnd an expiration period T1,T2…TN；
A function construction unit 304, which constructs the value F of the interest rate product at the multi-term node based on the selected value function model1，F2…FNMarket quote Q at a multi-term node for the interest rate product1，Q2…QNExpiration period T1,T2…TNAnd zero interest rate R1，R2…RNThe non-linear system of (2):
F1(Q1；R1,R2,…,RN；T1,T2,…,TN)＝0
F2(Q2；R1,R2,…,RN；T1,T2,…,TN)＝0
…
FN(QN；R1,R2,…,RN；T1,T2,…,TN)＝0
；
a calculating unit 306 for performing equation solution calculation based on the nonlinear system to obtain the interest rate R of zero interest of the multi-term node1，R2…RN。
In yet another illustrated embodiment, the apparatus 30 further comprises:
a curve construction unit 308 for obtaining a zero interest rate R of the multi-term node1，R2…RNAnd said expiration period T1,T2…TNAnd constructing a interest rate period structure curve of the interest rate product.
In a further illustrated embodiment, the computing unit 306 is configured to:
constructing a Jacobian matrix of the nonlinear system:
Figure BDA0001864755160000131
establishing the interest rate R of the multiple nodes according to a preset algorithm model1，R2…RNValue F of said known interest rate product1，F2…FNThe Jacobian matrix JFThe calculated relationship of (1);
iterative computation of the Jacobian matrix J based on an adjoint difference methodFWhen obtaining the interest rate R of zero interest of said multiple nodes based on said calculation relationship1，R2…RNWhen the value of (A) is converged, outputting the interest rate R of the multiple nodes1，R2…RN。
The implementation processes of the functions and actions of each unit in the device are specifically described in the implementation processes of the corresponding steps in the method, and related parts are described in the partial description of the method embodiment, which is not described herein again.
The above-described embodiments of the apparatus are merely illustrative, and the units described as separate parts may or may not be physically separate, and parts displayed as units may or may not be physical modules, may be located in one place, or may be distributed on a plurality of network modules. Some or all of the units or modules can be selected according to actual needs to achieve the purpose of the solution in the specification. One of ordinary skill in the art can understand and implement it without inventive effort.
The apparatuses, units and modules illustrated in the above embodiments may be implemented by a computer chip or an entity, or by a product with certain functions. A typical implementation device is a computer, which may take the form of a personal computer, laptop computer, cellular telephone, camera phone, smart phone, personal digital assistant, media player, navigation device, email messaging device, game console, tablet computer, wearable device, or a combination of any of these devices.
Corresponding to the method embodiment, the embodiment of the present specification further provides a computer device, which includes a memory and a processor. Wherein the memory has stored thereon a computer program executable by the processor; the processor, when executing the stored computer program, performs the steps of a method of obtaining zero interest rates for multiple term nodes on a term structure curve of interest rates in the embodiments of the present specification. For a detailed description of each step of the method for obtaining zero interest rate of multi-term nodes on the interest rate term structure curve, please refer to the previous contents, which is not repeated.
Corresponding to the above method embodiments, embodiments of the present specification further provide a computer-readable storage medium, on which computer programs are stored, which, when executed by a processor, perform the steps of the method for obtaining zero interest rate of a multi-term node on an interest rate term structure curve in the embodiments of the present specification. For a detailed description of each step of the method for obtaining zero interest rate of multi-term nodes on the interest rate term structure curve, please refer to the previous contents, which is not repeated.
The above description is only a preferred embodiment of the present disclosure, and should not be taken as limiting the present disclosure, and any modifications, equivalents, improvements, etc. made within the spirit and principle of the present disclosure should be included in the scope of the present disclosure.
In a typical configuration, a computing device includes one or more processors (CPUs), input/output interfaces, network interfaces, and memory.
The memory may include forms of volatile memory in a computer readable medium, Random Access Memory (RAM) and/or non-volatile memory, such as Read Only Memory (ROM) or flash memory (flash RAM). Memory is an example of a computer-readable medium.
Computer-readable media, including both non-transitory and non-transitory, removable and non-removable media, may implement information storage by any method or technology. The information may be computer readable instructions, data structures, modules of a program, or other data.
Examples of computer storage media include, but are not limited to, phase change memory (PRAM), Static Random Access Memory (SRAM), Dynamic Random Access Memory (DRAM), other types of Random Access Memory (RAM), Read Only Memory (ROM), Electrically Erasable Programmable Read Only Memory (EEPROM), flash memory or other memory technology, compact disc read only memory (CD-ROM), Digital Versatile Discs (DVD) or other optical storage, magnetic cassettes, magnetic tape magnetic disk storage or other magnetic storage devices, or any other non-transmission medium that can be used to store information that can be accessed by a computing device. As defined herein, a computer readable medium does not include a transitory computer readable medium such as a modulated data signal and a carrier wave.
It should also be noted that the terms "comprises," "comprising," or any other variation thereof, are intended to cover a non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements does not include only those elements but may include other elements not expressly listed or inherent to such process, method, article, or apparatus. Without further limitation, an element defined by the phrase "comprising an … …" does not exclude the presence of other like elements in a process, method, article, or apparatus that comprises the element.
As will be appreciated by one skilled in the art, embodiments of the present description may be provided as a method, system, or computer program product. Accordingly, embodiments of the present description may take the form of an entirely hardware embodiment, an entirely software embodiment or an embodiment combining software and hardware aspects. Furthermore, embodiments of the present description may take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, and so forth) having computer-usable program code embodied therein.

Claims (10)

1. A method of obtaining interest rates of zero interest at a multi-term node on an interest rate term structure curve, comprising:
obtaining market quotation Q of the interest rate product at a multi-term node1，Q2…QNAnd an expiration period T1,T2…TN；
Constructing the interest rate product in multiple stages based on the selected cost function modelValue of finite Point F1，F2…FNMarket quote Q at a multi-term node for the interest rate product1，Q2…QNExpiration period T1,T2…TNAnd zero interest rate R1，R2…RNThe non-linear system of (2):
F1(Q1；R1,R2,…,RN；T1,T2,…,TN)＝0
F2(Q2；R1,R2,…,RN；T1,T2,…,TN)＝0
…
FN(QN；R1,R2,…,RN；T1,T2,…,TN)＝0；
performing equation solution calculation based on the nonlinear system to obtain the zero interest rate R of the multi-term node1，R2…RN。
2. The method of claim 1, further comprising:
zero interest rate R based on the obtained multi-term nodes1，R2…RNAnd said expiration period T1,T2…TNAnd constructing a interest rate period structure curve of the interest rate product.
3. The method according to claim 1 or 2, wherein the equation solving calculation is performed based on the nonlinear system to obtain a zero interest rate R of the multi-term node1，R2…RNThe method comprises the following steps:
constructing a Jacobian matrix of the nonlinear system:
Figure FDA0001864755150000011
establishing the interest rate of the multiple nodes according to a preset algorithm modelR1，R2…RNValue F of said known interest rate product1，F2…FNThe Jacobian matrix JFThe calculated relationship of (1);
iterative computation of the Jacobian matrix J based on an adjoint difference methodFWhen the interest rate R of zero interest of the multi-term node is obtained based on the calculation relationship1，R2…RNWhen the value of (A) is converged, outputting the interest rate R of the multiple nodes1，R2…RN。
4. The method of claim 3, wherein the predetermined algorithm model is a Levenberg-Marquardt algorithm model.
5. The method of claim 1, the cost function model comprising one or more of an inter-bank peer borrowing model function model, a forward interest rate agreement function model, a futures function model, an interest rate interchange function model.
6. An apparatus for obtaining interest rates of zero interest at a multi-term node on an interest rate term structure curve, comprising:
an acquisition unit for acquiring market quotation Q of the interest rate product at a multi-term node1，Q2…QNAnd an expiration period T1,T2…TN；
A function construction unit for constructing the value F of the interest rate product at the multi-term node based on the selected value function model1，F2…FNMarket quote Q at a multi-term node for the interest rate product1，Q2…QNExpiration period T1,T2…TNAnd zero interest rate R1，R2…RNThe non-linear system of (2):
F1(Q1；R1,R2,…,RN；T1,T2,…,TN)＝0
F2(Q2；R1,R2,…,RN；T1,T2,…,TN)＝0
…
FN(QN；R1,R2,…,RN；T1,T2,…,TN)＝0；
a calculation unit for performing equation solution calculation based on the nonlinear system to obtain the interest rate R of zero interest of the multi-term node1，R2…RN。
7. The apparatus of claim 6, further comprising:
a curve construction unit for obtaining zero interest rate R of the multi-term node1，R2…RNAnd said expiration period T1,T2…TNAnd constructing a interest rate period structure curve of the interest rate product.
8. The apparatus of claim 6 or 7, the computing unit to:
constructing a Jacobian matrix of the nonlinear system:
Figure FDA0001864755150000031
establishing the interest rate R of the multiple nodes according to a preset algorithm model1，R2…RNValue F of said known interest rate product1，F2…FNThe Jacobian matrix JFThe calculated relationship of (1);
iterative computation of the Jacobian matrix J based on an adjoint difference methodFWhen obtaining the interest rate R of zero interest of said multiple nodes based on said calculation relationship1，R2…RNWhen the value of (A) is converged, outputting the interest rate R of the multiple nodes1，R2…RN。
9. A computer device, comprising: a memory and a processor; the memory having stored thereon a computer program executable by the processor; the processor, when executing the computer program, performs the method of any of claims 1 to 5.
10. A computer-readable storage 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 to 5.
CN201811350531.8A 2018-11-14 2018-11-14 Method and device for obtaining zero interest rate of multiple nodes on interest rate time limit structure curve Pending CN111192129A (en)

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Publication number Priority date Publication date Assignee Title
CN112116429A (en) * 2020-09-28 2020-12-22 中国建设银行股份有限公司 Interest rate derivative product client quotation method and device

Citations (1)

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Publication number Priority date Publication date Assignee Title
CN102750651A (en) * 2012-05-31 2012-10-24 中国工商银行股份有限公司 Curve fitting-based device and method for processing data

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Publication number Priority date Publication date Assignee Title
CN102750651A (en) * 2012-05-31 2012-10-24 中国工商银行股份有限公司 Curve fitting-based device and method for processing data

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* Cited by examiner, † Cited by third party
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CN112116429A (en) * 2020-09-28 2020-12-22 中国建设银行股份有限公司 Interest rate derivative product client quotation method and device

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