CN106485036A - Based on the method graded to asset securitization Assets Pool by Survival Models - Google Patents
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Abstract
A kind of method that asset securitization Assets Pool is graded based on Survival Models, the method can utilize Survival Models, and the more accurate and effective Assets Pool to magnanimity assets is graded.Compared with prior art, present invention utilizes a kind of new Survival Models are grading to Assets Pool, the Survival Models are intended to seek event of default（Unconditional）Probability of happening, in data deficiency, builds possible analogy method in the case of structure is incomplete.Survival Models are when time series analysis is carried out（Such as it is desirable that understanding impact of the time to rate of violation）And it is very outstanding for performance during Monte Carlo simulation.Based on the model, present invention also offers a kind of corresponding hardware device, the hardware device has all carried out the optimization of high degree to the storage mode of data, access efficiency and algorithm so that the process of mass data, access and storage sexual function are all greatly improved in ranking process.
Description
Technical field
The present invention relates to assets rating technique field, more specifically, more particularly to a kind of based on Survival Models to assets
The method graded by securitization assets pond.
Background technology
1st, asset securitization, such as with civilian housing loan as the asset securitization of mortgage；2nd, pledge, for example automobile
Asset securitization based on loan, equipment credit；3rd, mortgage loan credits, are the extensive property financing means of main at present three,
The balance sheet that above-mentioned three kinds of financing methods can help bank to come management bank, it is also possible to make financial company would be impossible to stream
Dynamic property assets are converted into current assets.Asset securitization can make financial institution obtain more cheap fund, can make gold
Melt the financing means more horn of plenty of mechanism.
Issuer generally requires historical data and the characteristic decision according to Assets Pool when Assets Pool grading is carried out
The rate of violation of Assets Pool is grading to products of securities.So, how to provide one can be to Assets Pool, particularly comprising sea
The Assets Pool (hundreds of to million) of amount asset data carries out accurate, effective grading, is just particularly important.
Content of the invention
(1) technical problem
Following challenge is faced in Assets Pool ranking process：
The limitation of the log-normal distributed model for the 1st, commonly using at present：
Log-normal is distributed the distribution of description loss late that can not be perfect, and lacks in the selection of variance credible
Degree.In addition, the model is relative efficiency when information content is relatively low, it can be difficult to extend on this basis.Log-normal divides
Cloth model parameterizes the distribution for describing true loss late it is assumed that can not be perfect with stronger, particularly in multimodal and thick tail
In the case of can deviate that truth is more, can cause to underestimate risk during the scene for being applied to loss late prediction.Separately
Outward, the model is applied to and is efficiently simulated when historical data is less relatively, but is difficult to promote the number for more enriching
According to.
2nd, rate of violation analysis, the not competent mass data of speed of ranking process are calculated：
The Assets Pool of financial institution is often mass data.Data-level is recorded in million, ten million bar.How very short
Time in carry out mass data grading be also a huge challenge.
(2) technical scheme
The invention provides a kind of method that asset securitization Assets Pool is graded based on Survival Models, the method tool
Body includes：
Step one, structure Survival Models：
The illegal building time provide a loan for T；
Having cumulative probability density function is：
FT(t)=P (T≤t):R → [0,1]
Probability density function is：
T of providing a loan Default Probability calculate survival function be：
S (t)=1-FT(t)
The dangerous function that default probability density is calculated is occurred within the one minimum time at moment t to be：
Can be obtained by above-mentioned function：
I.e.：
Step 2, carry out promise breaking simulation：
After S (t) function is obtained, Assets Pool is carried out by pen in time series using Monte-carlo Simulation Method
Grading is simulated and is obtained in promise breaking, and wherein S (t) samples for Monte Carlo and provides probability benchmark.
Preferably, S (t) is obtained by historical data fitting h (t)；
H (t) function is obtained with approximating method：
Observing time in Survival Models and promise breaking record, and determine function：
Wherein TiIt is life span, CiIt is observing time (loan expiration time)；
In the event of breaking a contract, Δ i=1 is remembered, otherwise remember Δ i=0；
For the loan sample i for not occurring to break a contract in the survival phase, meeting joint probability on time shaft t is：
P(Ci=ti)P(Ti＞ ti)
For the sample i for occurring to break a contract in the survival phase, meeting joint probability on a timeline is：
P(Ci＞ ti)P(Ti=ti)
All assets in static pond, likelihood function is：
Wherein P (Ti=ti)=f (ti)=h (ti)S(ti), therefore draw as minor function：
Wherein G (ti) and g (ti) it is observation time CiCDF and PDF, to G (ti) and g (ti) constant is carried out, therefore
Go out as minor function：
Wherein log-likelihood function is：
The estimated value of h (t) is obtained by Maximum-likelihood estimation, determines the probability for occurring to break a contract in very short time not because seeing
Survey time point and change, be i.e. h (t)=λ is S (t)=e-λt.
Preferably, S (t) is obtained by historical data fitting h (t)；
H (t) is estimated divided by total open-assembly time by total promise breaking quantity, is obtained as minor function in conjunction with Weibull model：
H (t)=λ α (λ t) α -1, wherein α, λ>0；
H (t) analogue value is tried to achieve by segmentation, and takes MCMC methodology to be fitted its curve.
(3) beneficial effect
The invention provides a kind of method that credit assets securitization Assets Pool based on Survival Models is graded, the method can
To utilize Survival Models, the more accurate and effective Assets Pool to magnanimity assets is graded.Compared with prior art, this
Bright make use of a kind of new Survival Models to grade Assets Pool, the Survival Models be intended to seek event of default (nothing bar
Part) probability of happening, in data deficiency, in the case of structure is incomplete, build possible analogy method.Survival Models are being carried out
During time series analysis (impact such as in the time that wants to know about to rate of violation) and for Monte Carlo simulation when show non-
Chang Youxiu.Based on the model, present invention also offers a kind of corresponding hardware device, storage of the hardware device to data
Mode, access efficiency and algorithm have all carried out the optimization of high degree so that process, the visit in ranking process to mass data
Ask and store sexual function all greatly to improve.
Description of the drawings
Fig. 1 is the estimation of dangerous function and the fitting comparison diagram of nonlinear curve in the present invention；
Fig. 2 is 10000 yearling loss late (Loss Rate) estimations and log-normal distribution in the present invention
Comparison diagram；
Fig. 3 is the flow chart of the credit assets securitization Assets Pool rating model based on Survival Models of the present invention.
Specific embodiment
With reference to the accompanying drawings and examples embodiments of the present invention are described in further detail.Following examples are used for
The present invention is described, but can not be used for limiting the scope of the present invention.
In describing the invention, unless otherwise stated, " multiple " are meant that two or more；Term " on ",
The orientation of instruction such as D score, "left", "right", " interior ", " outward ", " front end ", " rear end ", " head ", " afterbody " or position relationship are
Based on orientation shown in the drawings or position relationship, it is for only for ease of the description present invention and simplifies description, rather than indicate or dark
Show that the device of indication or element must be with specific orientation, with specific azimuth configuration and operation, therefore it is not intended that right
The restriction of the present invention.Additionally, term " first ", " second ", " the 3rd " etc. be only used for describe purpose, and it is not intended that indicate or
Hint relative importance.
In describing the invention, it should be noted that unless otherwise clearly defined and limited, term " being connected ", " company
Connect " should be interpreted broadly, for example, it may be being fixedly connected, or being detachably connected, or it is integrally connected；It can be machine
Tool connection, or electrical connection；Can be joined directly together, it is also possible to be indirectly connected to by intermediary.For this area
For those of ordinary skill, above-mentioned term concrete meaning in the present invention can be understood with concrete condition.
Fig. 1 to Fig. 3 is refer to, wherein, Fig. 1 is the estimation of dangerous function and the fitting of nonlinear curve contrast in the present invention
Figure；Fig. 2 is the contrast that 10000 yearling loss late (Loss Rate) estimations are distributed with log-normal in the present invention
Figure；Fig. 3 is the flow chart of the credit assets securitization Assets Pool rating model based on Survival Models of the present invention.
Can be in the such as computer system of one group of computer executable instructions the step of the flow process of accompanying drawing is illustrated
Execute.And, although show logical order in flow charts, but in some cases, can be suitable be different from herein
Sequence executes shown or described step.
Survival Models
The invention provides a kind of method that the Assets Pool of large data capacity is graded based on Survival Models, at this
Bright in Survival Models, if necessary to study assets when break a contract, then sets first provide a loan to the illegal building time as
T, T are a stochastic variable.
Having cumulative probability density function (CDF) is：
FT(t)=P (T≤t)：R → [0,1]
Probability density function (PDF) is：
Define survival function (survival function)：S (t)=1-FT(t)
The probability that i.e. loan is not broken a contract to t.
Dangerous function (hazard function) is defined, dangerous function is occur within the one minimum time at moment t
The probability density of promise breaking.
Therefore above-mentioned survival function and dangerous function are combined
Can be obtained by above-mentioned formula：
In practical operation, due to the restriction of observation time, complete promise breaking distribution f cannot be typically obtainedT(t), therefore,
The present invention is fitted h (t) by historical data to obtain S (t).After S (t) is obtained, the present invention is using Monte Carlo simulation
Method is simulated come a promise breaking Assets Pool carried out in time series by pen, and S (t) will sample for Monte Carlo and provide probability
Benchmark.
As follows to the approximating method of h (t) using historical data：
For Survival Models in order to estimate h (t), first have to obtain sample life in the likelihood function of the model, i.e. Assets Pool
Deposit the joint probability distribution of time.Following data are needed for assets in Survival Models：Observing time and promise breaking note
Record, and be designated as：
In above-mentioned formula, TiIt is life span, CiIt is observing time (loan expiration time).In the event of breaking a contract, Δ i is remembered
=1, otherwise remember Δ i=0.For the loan sample i for not occurring to break a contract in the survival phase, on time shaft t, meet joint probability：
P(Ci=ti)P(Ti＞ ti)
And the sample i for occurring within the survival phase to break a contract, meet joint probability on a timeline：
P(Ci＞ ti)P(Ti=ti)
Therefore, for all assets in static pond, likelihood function is：
Wherein P (Ti=ti)=f (ti)=h (ti)S(ti), therefore obtain equation below：
Wherein G (ti) and g (ti) it is observation time CiCDF and PDF, to h (ti) maximum likelihood value is when producing impact
Constant can be reduced to, obtain as minor function：
Its log-likelihood function is：
Parameter is assumed
H (t) is carried out it is assumed that and obtaining h (t) most likely value by Maximum-likelihood estimation.Simplest parameter model
, we assume that there is the probability that breaks a contract in very short time not because of observation time in the model in exponential model (exponential)
Put and change, i.e. h (t)=λ, therefore S (t)=e-λt.
Now likelihood function develops into：
For obtain λ maximum value possible, to λ derivation and make result be equal to 0：
Equation abbreviation is：
As can be seen from the above equation, we can estimate h (t) by total promise breaking quantity divided by total open-assembly time, wherein total sudden and violent
The dew time does not repay stroke count for the moon and is multiplied by that monthly observation time is cumulative to be obtained.
The advantage of exponential model is to be easily obtained data, and required amount of calculation is less, but exponential model also therefore suffers from being permitted
Multifactor restriction：Lack the lever of regulation and control relative risk and loan time.Therefore, the present invention is it is further contemplated that adopt
Weibull model, i.e.,：H (t)=λ α (λ t) α -1, wherein α, λ ＞ 0.
Weibull model increased variable α and can regulate and control risk function with time (monotonously) growth/minimizing, when α=1
When the model be exponential model, as α ＞ 1, risk function increases with the growth of time.Weibull distribution in practical operation
Likelihood function be difficult to seek maximum likelihood estimator.H (t) analogue value is tried to achieve by segmentation, and takes MCMC or additive method to intend
Close its curve.
Can see that the numeric distribution that Weibull is obtained has higher conjunction to the fitting of the data in the static pond by Fig. 1
Reason degree (some months is due to the less deflection curve of sample afterwards).
Realize step
If necessary to assess a combination investment (X, W), wherein X ∈ Rn is expiration time, and W ∈ Rn is weight, can make
Sampled with Monte Carlo simulation algorithm：
U～U (0,1), Amount～LN (μ, σ 2),
Wherein μ, σ 2 is the average of per loan and variance in static pond.T～U (0,1), here t be the repayment time divided by
The distribution of loan expiration time, it is stipulated that refund and be evenly distributed, therefore can be replaced with other distributions.
To i=1,2 ..., n, if ui＞ S (Xi×ti), then remember Δ i=1, otherwise remember Δ i=0, then obtain loss
Rate：
Repeat above step 10000 times, obtain the experience distribution of loss late.It is assumed here that the assets in Assets Pool do not have phase
Guan Xing.If it is known that the assets in Assets Pool have with certain correlation (setting correlation matrix as ∑), then the first step can be changed
For the u0～MN (0, ∑) that samples, the CDF of u=Φ (u0), wherein Φ (.) for normal distribution is taken.For exponential distribution,Weibull is distributed,
With for the example that most simplifies, it is assumed that there is 10 loan data (upper limit is 12 months)
According to above table, total outstanding quantity 4 is measured using dangerous function, total open-assembly time is
3+5+11+8+12*6=99, therefore h (t)=4/99
So loan life span-probability be distributed as e-(4/99)t, t is the time.
Lose exposed experience and be distributed as X=800,1300,2000,5000 (each 1/4).
The experience of the rate of recovery is distributed as R=0 (p=3/4), 3/4 (p=1/4)
Fig. 2 shows compared with the result that above-mentioned model is obtained with log-normal method using the result of Monte Carlo simulation
Relatively.Thus verify：When Assets Pool is sufficiently large, log-normal distribution is met with the result of present invention simulation very much.
The application can be graded to the Assets Pool of magnanimity assets, be rapidly performed by calculating, typically in 5 minutes, energy
Complete the grading of million data ranks.
Embodiments of the invention in order to example and description for the sake of and be given, and be not exhaustively or by this
Bright it is limited to disclosed form.Many modifications and variations are obvious for the ordinary skill in the art.Choosing
It is in order to the principle of the present invention and practical application are more preferably described to select and describe embodiment, and makes one of ordinary skill in the art
It will be appreciated that the present invention is so as to design the various embodiments with various modifications for being suitable to special-purpose.
Claims (3)
1. a kind of method that asset securitization Assets Pool is graded based on Survival Models, it is characterised in that include：
Step one, structure Survival Models：
The illegal building time provide a loan for T；
Having cumulative probability density function is：
FT(t)=P (T≤t)：R → [0,1]
Probability density function is：
T of providing a loan Default Probability calculate survival function be：
S (t)=1-FT(t)
The dangerous function that default probability density is calculated is occurred within the one minimum time at moment t to be：
Can be obtained by above-mentioned function：
I.e.：
Step 2, carry out promise breaking simulation：
After S (t) function is obtained, the promise breaking by pen is carried out to Assets Pool in time series using Monte-carlo Simulation Method
Grading is simulated and obtains, wherein S (t) samples for Monte Carlo and provides probability benchmark.
2. the method that asset securitization Assets Pool is graded based on Survival Models according to claim 1, its feature
It is,
H (t) is fitted by historical data to obtain S (t)；
H (t) function is obtained with approximating method：
Observing time in Survival Models and promise breaking record, and determine function：
Wherein TiIt is life span, CiIt is observing time (loan expiration time)；
In the event of breaking a contract, Δ i=1 is remembered, otherwise remember Δ i=0；
For the loan sample i for not occurring to break a contract in the survival phase, meeting joint probability on time shaft t is：
P(Ci=ti)P(Ti＞ ti)
For the sample i for occurring to break a contract in the survival phase, meeting joint probability on a timeline is：
P(Ci＞ ti)P(Ti=ti)
All assets in static pond, likelihood function is：
Wherein P (Ti=ti)=f (ti)=h (ti)S(ti), therefore draw as minor function：
Wherein G (ti) and g (ti) it is observation time CiCDF and PDF, to G (ti) and g (ti) carry out constant, therefore draw as
Minor function：
Wherein log-likelihood function is：
The estimated value of h (t) is obtained by Maximum-likelihood estimation, determines the probability for occurring to break a contract in the very short time not because during observation
Between point and change, i.e. h (t)=λ is S (t)=e-λt.
3. the method that asset securitization Assets Pool is graded based on Survival Models according to claim 1, its feature
It is,
H (t) is fitted by historical data to obtain S (t)；
H (t) is estimated divided by total open-assembly time by total promise breaking quantity, is obtained as minor function in conjunction with Weibull model：
H (t)=λ α (λ t) α -1, wherein α, λ>0；
H (t) analogue value is tried to achieve by segmentation, and takes MCMC methodology to be fitted its curve.
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| CN111985773A (en) * | 2020-07-15 | 2020-11-24 | 北京淇瑀信息科技有限公司 | User resource allocation strategy determining method and device and electronic equipment |
| CN113590629A (en) * | 2021-08-09 | 2021-11-02 | 马上消费金融股份有限公司 | Data processing method, default probability model training method and related equipment |
| CN113590629B (en) * | 2021-08-09 | 2024-05-24 | 马上消费金融股份有限公司 | Data processing method, default probability model training method and related equipment |
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