CN106485036B - Method for grading asset securitization asset pool based on survival model - Google Patents

Abstract

A method for grading an asset securitization asset pool based on a survival model can be used for more accurately and effectively grading the asset pool of mass assets. Compared with the prior art, the invention utilizes a new survival model to rate the asset pool, the survival model aims to search the occurrence probability (unconditional) of the default event, and a possible simulation method is constructed under the conditions of data deficiency and incomplete structure. The survival model performs very well when subjected to time series analysis (e.g., we want to know the effect of time on the rate of violations) and when used in Monte Carlo simulation. Based on the model, the invention also provides a corresponding hardware device, and the hardware device optimizes the data storage mode, the access efficiency and the algorithm to a great extent, so that the functions of processing, accessing and storing mass data in the rating process are greatly improved.

Description

Method for grading asset securitization asset pool based on survival model

Technical Field

The invention relates to the technical field of asset rating, in particular to a method for rating an asset securitization asset pool based on a survival model.

Background

1. Securitization of assets, such as mortgage with civil housing loans; 2. mortgages, such as automotive loans, equipment loan-based securitization of assets; 3. mortgage credit right is the main three large-scale financing means at present, and the three financing means can help banks manage the liability statement of the banks and can enable financial enterprises to convert unlikely liquidity into liquidity. Securitization of assets can enable financial institutions to obtain cheaper funds, and can enable financing means of the financial institutions to be richer.

When an issuer performs asset pool ratings, it is often necessary to determine the rate of breach of an asset pool based on historical data and characteristics of the asset pool to rate a vouchered product. It is important to provide an accurate and efficient rating for asset pools, particularly those containing vast amounts of asset data (hundreds to millions).

Disclosure of Invention

First technical problem

The following challenges are faced in the asset pool rating process:

1. limitations of the log-normal distribution model currently in common use:

The log-normal distribution does not perfect describe the distribution of loss rates and lacks confidence in the selection of variances. In addition, the model is relatively efficient when the amount of information is low, but it is difficult to extend on this basis. The Log-normal distribution model has stronger parameterization assumption, cannot perfectly describe the distribution of the real loss rate, and particularly deviates more from the real situation in the case of multimodal and thick tail, and causes insufficient estimation of risk when applied to the scene of loss rate prediction. In addition, the model is suitable for relatively efficient simulation when there is less historical data, but is difficult to popularize for richer data.

2. The speed of the breach rate analysis and rating process is not adequate for mass data calculation:

the pool of assets for a financial institution is often a vast amount of data. Data levels are recorded in millions and tens of millions. How to rate the mass data in a very short time is also a great challenge.

(II) technical scheme

The invention provides a method for grading an asset securitization asset pool based on a survival model, which specifically comprises the following steps:

step one, building a survival model:

The time from loan to default distance is T;

the cumulative probability density function is:

F_T(t)＝P(T≤t):R→[0，1]

The probability density function is:

The survival function of the non-default probability calculation from the loan to the time t is as follows:

S(t)＝1-F_T(t)

the risk function for the occurrence of the calculation of the probability density of a violation in a very small time at the instant t is:

from the above functions, it is possible to:

Namely:

step two, performing default simulation:

After obtaining the S (t) function, a Monte Carlo simulation method is used to simulate the asset pool against violations on a time series and obtain a rating, where S (t) provides a probabilistic basis for Monte Carlo sampling.

Preferably, S (t) is obtained by fitting h (t) to historical data;

obtaining an h (t) function by a fitting method:

observation time and breach record in the survival model, and determine the function:

Where T _i is time-to-live and C _i is time-of-observation (loan expiration time);

if a violation occurs, note Δi=1, otherwise note Δi=0;

for a loan sample i for which no default occurs in the duration, the joint probability is satisfied on the time axis t as follows:

P(C_i＝t_i)P(T_i＞t_i)

for a sample i for which a violation occurs within a lifetime, the joint probability on the time axis is satisfied as:

P(C_i＞t_i)P(T_i＝t_i)

all assets in the static pool, likelihood functions are:

where P (T _i＝t_i)＝f(t_i)＝h(t_i)S(t_i) thus gives the following function:

Where G (t _i) and G (t _i) are CDF and PDF of observation time C _i, G (t _i) and G (t _i) are constants, thus yielding the following functions:

wherein the log likelihood function is:

the estimated value of h (t) is obtained by maximum likelihood estimation, and it is determined that the probability of occurrence of a violation in a very short time does not change depending on the observation time point, i.e., h (t) =λ, i.e., S (t) =e ^-λt.

Preferably, S (t) is obtained by fitting h (t) to historical data;

H (t) is estimated by dividing the total number of violations by the total exposure time, combined with the Weibull model to give the following function:

h (t) =λα (λt) α -1, where α, λ >0;

and h (t) analog values are obtained through segmentation, and an MCMC method is adopted to fit the curve.

(III) beneficial effects

The invention provides a method for grading a securitized asset pool of a credit asset based on a survival model, which can more accurately and effectively grade the asset pool of a mass asset by using the survival model. Compared with the prior art, the invention utilizes a new survival model to rate the asset pool, the survival model aims to search the occurrence probability (unconditional) of the default event, and a possible simulation method is constructed under the conditions of data deficiency and incomplete structure. The survival model performs very well when subjected to time series analysis (such as when one wishes to know the effect of time on the rate of violations) and when used in Monte Carlo simulation. Based on the model, the invention also provides a corresponding hardware device, and the hardware device optimizes the data storage mode, the access efficiency and the algorithm to a great extent, so that the functions of processing, accessing and storing mass data in the rating process are greatly improved.

Drawings

FIG. 1 is a graph showing a comparison of the estimation of a hazard function and the fit of a nonlinear curve in the present invention;

FIG. 2 is a graph comparing 10000 annual bond Loss Rate (Loss Rate) estimates with log-normal distribution in the present invention;

FIG. 3 is a flow chart of a credit asset securitization asset pool rating model based on a survival model of the present invention.

Detailed Description

Embodiments of the present invention are described in further detail below with reference to the accompanying drawings and examples. The following examples are illustrative of the invention but are not intended to limit the scope of the invention.

In the description of the present invention, unless otherwise indicated, the meaning of "a plurality" is two or more; the terms "upper," "lower," "left," "right," "inner," "outer," "front," "rear," "head," "tail," and the like are used as an orientation or positional relationship based on that shown in the drawings, merely to facilitate description of the invention and to simplify the description, and do not indicate or imply that the devices or elements referred to must have a particular orientation, be constructed and operated in a particular orientation, and therefore should not be construed as limiting the invention. Furthermore, the terms "first," "second," "third," and the like are used for descriptive purposes only and are not to be construed as indicating or implying relative importance.

In the description of the present invention, it should be noted that, unless explicitly specified and limited otherwise, the terms "connected," "connected," and "connected" are to be construed broadly, and may be either fixedly connected, detachably connected, or integrally connected, for example; can be mechanically or electrically connected; can be directly connected or indirectly connected through an intermediate medium. The specific meaning of the above terms in the present invention will be understood in specific cases by those of ordinary skill in the art.

Referring to fig. 1 to 3, fig. 1 is a graph showing a comparison of estimation of a hazard function and fitting of a nonlinear curve according to the present invention; FIG. 2 is a graph comparing 10000 annual bond Loss Rate (Loss Rate) estimates with log-normal distribution in the present invention; FIG. 3 is a flow chart of a credit asset securitization asset pool rating model based on a survival model of the present invention.

The steps illustrated in the flowchart of the figures may be performed in a computer system, such as a set of computer-executable instructions. Also, while a logical order is depicted in the flowchart, in some cases, the steps depicted or described may be performed in a different order than presented herein.

Survival model

In the method, if a study on when a resource breaks down is needed in the survival model, the time from loan to breaking down is firstly set as T, and T is a random variable.

The possessing cumulative probability density function (CDF) is:

F_T(t)＝P(T≤t)：R→[0，1]

The Probability Density Function (PDF) is:

Definition of a survival function (survival function): s (t) =1-F _T (t)

I.e., the probability that the loan will not violate at time t.

A hazard function (hazard function) is defined, which is the probability density of violations occurring in a very small time at time t.

Thus combining the above living functions and hazard functions

From the above formula:

In practical operation, due to the limitation of the observation time, the complete violation distribution f _T (t) cannot be obtained generally, so that the invention obtains S (t) by fitting h (t) to historical data. After obtaining S (t), the present invention uses the method of monte carlo simulation to simulate a break-through of an asset pool over time sequence, S (t) will provide a probabilistic basis for monte carlo sampling.

The fitting method of the history data to h (t) is as follows:

for a survival model to estimate h (t), the likelihood function of the model, i.e., the joint probability distribution of sample survival times in the asset pool, is first obtained. The following data are required for a resource in the life model: observe time and record of violations and record it as:

In the above formula, T _i is the time-to-live, and C _i is the observation time (loan expiration time). If a violation occurs, Δi=1, otherwise Δi=0. For a loan sample i for which no default occurs during the duration, the joint probability is satisfied on the time axis t:

P(C_i＝t_i)P(T_i＞t_i)

And the sample i, in which the default occurs in the duration, satisfies the joint probability on the time axis:

P(C_i＞t_i)P(T_i＝t_i)

Thus, for all assets in the static pool, the likelihood function is:

Where P (T _i＝t_i)＝f(t_i)＝h(t_i)S(t_i) thus gives the following formula:

Where G (t _i) and G (t _i) are CDF and PDF of observation time C _i, which can be reduced to constants when no effect on the maximum likelihood value of h (t _i) is produced, resulting in the following functions:

The log likelihood function is:

assumption of parameters

Let h (t) be assumed and the most probable value of h (t) be obtained by maximum likelihood estimation. The simplest parametric model is an exponential model (exponenial) in which we assume that the probability of occurrence of a violation in a very short time does not change due to the observation time point, i.e., h (t) =λ, and thus S (t) =e ^-λt.

The likelihood function evolves at this point as:

to obtain the maximum possible value of λ, λ is derived and the result is equal to 0:

The equation reduces to:

From the above equation, we can estimate h (t) by dividing the total number of violations by the total exposure time, where the total exposure time is the cumulative number of outstanding monthly times the monthly observation time.

The advantage of the exponential model is that the data is easy to obtain and requires a small amount of computation, but the exponential model is therefore also limited by a number of factors: there is no leverage to regulate risk and loan time. Thus, the present invention may further contemplate the use of the Weibull model, namely: h (t) =λα (λt) α -1, where α, λ > 0.

The Weibull model increases the variable α to regulate the increase/decrease of the risk function over time (monotonically), the model being an exponential model when α=1, and the risk function increasing over time when α > 1. In actual operation, the likelihood function of Weibull distribution is difficult to calculate the maximum likelihood estimation value. The h (t) analog value is obtained by segmentation, and MCMC or other methods are adopted to fit the curve.

From fig. 1 it can be seen that the numerical distribution obtained by Weibull has a higher degree of rationality for the fit of the data for this static pool (the last months due to less sample deviation from the curve).

Implementation steps

If a portfolio asset (X, W) needs to be evaluated, where X ε Rn is the expiration time and W ε Rn is the weight, a Monte Carlo simulation algorithm may be used to sample:

u～U(0，1)，Amount～LN(μ，σ2)，

where μ, σ2 is the mean and variance of each loan in the static pool. t to U (0, 1), where t is the repayment time divided by the loan expiration time, specifies that the repayment distribution is uniform, and can be replaced with other distributions.

For i=1, 2,..n, if u _i＞S(X_i×t_i), then Δi=1, otherwise Δi=0, then the loss rate is obtained:

The above steps are repeated 10000 times to obtain the empirical distribution of loss rate. It is assumed here that the assets in the asset pool have no relevance. If the assets in the pool of assets are known to have some correlation (let the correlation matrix be Σ), then the first step can be changed to sample u0 to MN (0, Σ), taking u=Φ (u 0), where Φ ()' is a normally distributed CDF. For an exponential distribution of the values of the distribution, For Weibull distribution,/>

For the most simplified example, assume that there are 10 loan data (upper limit of 12 months)

According to the above table, total outstanding amount 4 was measured using the hazard function, total exposure time was

3+5+11+8+12×6=99, So h (t) =4/99

Then the loan lifetime-probability distribution is e- ^(4/99)t and t is time.

The empirical distribution of loss exposure was x= 800,1300,2000,5000 (1/4 each).

The empirical distribution of recovery was r=0 (p=3/4), 3/4 (p=1/4)

FIG. 2 shows the results of the above model using Monte Carlo simulation compared to the results obtained by the log-normal method. Thereby verifying: when the pool of assets is large enough, the log-normal distribution is very consistent with the results of the simulation of the present invention.

The application can grade the asset pool of mass assets, calculate rapidly, generally in 5 minutes, and can grade millions of data.

The embodiments of the invention have been presented for purposes of illustration and description, and are not intended to be exhaustive or limited to the invention in the form disclosed. Many modifications and variations will be apparent to those of ordinary skill in the art. The embodiments were chosen and described in order to best explain the principles of the invention and the practical application, and to enable others of ordinary skill in the art to understand the invention for various embodiments with various modifications as are suited to the particular use contemplated.

Claims (2)

1. A method of ranking a securitized pool of assets based on a survival model, comprising:

step one, building a survival model:

The time from loan to default distance is T;

the cumulative probability density function is:

F_T(t)＝P(T≤t)：R→[0，1]

The probability density function is:

The survival function of the non-default probability calculation from the loan to the time t is as follows:

S(t)＝1-F_T(t)

the risk function for the occurrence of the calculation of the probability density of a violation in a very small time at the instant t is:

from the above functions, it is possible to:

Namely:

step two, performing default simulation:

After the S (t) function is obtained, a Monte Carlo simulation method is used to make a time-series successive violations of the pool of assets

Simulating and obtaining a rating, wherein S (t) provides a probabilistic basis for the monte carlo samples;

Wherein,

Obtaining S (t) by fitting h (t) to the historical data;

obtaining an h (t) function by a fitting method:

observation time and breach record in the survival model, and determine the function:

Where T _i is time-to-live and C _i is time-of-observation (loan expiration time);

if a violation occurs, note Δi=1, otherwise note Δi=0;

for a loan sample i for which no default occurs in the duration, the joint probability is satisfied on the time axis t as follows:

P(C_i＝t_i)P(T_i＞t_i)

for a sample i for which a violation occurs within a lifetime, the joint probability on the time axis is satisfied as:

P(C_i＞t_i)P(T_i＝t_i)

all assets in the static pool, likelihood functions are:

where P (T _i＝t_i)＝f(t_i)＝h(t_i)S(t_i) thus gives the following function:

Where G (t _i) and G (t _i) are CDF and PDF of observation time C _i, G (t _i) and G (t _i) are constants, thus yielding the following functions:

wherein the log likelihood function is:

the estimated value of h (t) is obtained by maximum likelihood estimation, and it is determined that the probability of occurrence of a violation in a very short time does not change depending on the observation time point, i.e., h (t) =λ, i.e., S (t) =e ^-λt.

2. The method of ranking a securitized asset pool based on a survival model of claim 1,

Obtaining S (t) by fitting h (t) to the historical data;

H (t) is estimated by dividing the total number of violations by the total exposure time, combined with the Weibull model to give the following function:

h (t) =λα (λt) α -1, where α, λ >0;

and h (t) analog values are obtained through segmentation, and an MCMC method is adopted to fit the curve.