Research On Intensity Pricing Model For Housing Mortgage

Mortgages are important assets of commercial banks. The pricing of mortgages has direct impact on bank asset management and the feasibility of securitization. Mortgage intensity pricing model integrates reduced-form model and structure model effectively. Although there are some results on intensity model study, most of them were published before the sub-prime crisis, thus they are unable to meet the new situation. Furthermore, it is unreasonable to apply existing results of intensity model based on other markets directly to China's housing mortgage loan market. Default intensity and prepayment intensity of Chinese housing mortgage have the characteristic of higher peak and fat tail. Now Domestic and foreign scholars use jump-diffusion process and Copula function to describe this characteristic. Subject to the large amount of computation, we can not simultaneously use jump-diffusion process and Copula function to measure default intensity and prepayment intensity. Therefore this paper respectively uses those two methods and builds a jump diffusion process-based intensity housing mortgage pricing model and a Clayton Copula-based intensity housing mortgage pricing model; also I propose two new methods to estimate parameters such as discount rate, default intensity and prepayment intensity. The main results are listed as follows:(1) The jump diffusion process-based intensity housing mortgage pricing model built in this paper considers default, prepayment, building property and interest rate risk factors. The model improves four key factors of KKS model: discounting method, calculation approach of recovery value and interest rate stochastic model. Payment per month is discounted by different rate. Fixed recovery value in KKS model is replaced by minimum of mortgaged house price and remained mortgage principle. In addition, two-factor CIR interest model is substituted by Vasicek model with jumps. The default intensity and prepayment intensity are measured by the CIR model which belongs to jump-diffusion process. The discount rate is measured by Vasicek model with jumps which belong to jump-diffusion process. Stability analysis of the model shows that the jump diffusion process-based intensity housing mortgage pricing model can meet commercial bank's requirement. Finally, this paper examines the impact of housing price trend, the proportion of initial payment to principal, loan interest, scale and term to mortgage value.(2) This paper uses Vasicek model with jumps as the one-factor interest rate model to estimate the 3-month Shibor. I propose an adaptive estimation algorithm based on combination of particle filter and simultaneous perturbation stochastic approximation method to estimate parameters of this model.Statistical tests indicate that three-month Shibor has the characteristics of mean reversion and fat tails. Therefore I use Vasicek model with jumps or exponential Vasicek model with jumps as alternatives since these two are nonlinear and non-Gaussian models. Common methods such as least squares, maximum likelihood estimation and Kalman filtering can not estimate parameters of these two models very well. The particle filter algorithm is suitable for nonlinear and non-Gaussian model. Therefore, this paper proposes adaptive estimation algorithm based on combination of particle filter and simultaneous perturbation stochastic approximation method. At last, we compare goodness-of-fit and forecast effectiveness between the two models, and the result shows that Vasicek model with jumps does better than exponential Vasicek model with jumps in fitting Shibor.(3) To estimate parameters of default intensity and prepayment intensity of jump diffusion process-based intensity housing mortgage pricing model with small-size samples, this paper proposes a two-stage MCMC (Markov chain Monte Carlo) approach.I use "Jianyuan 2005-1", the first MBS (Mortgage Backed Securities) in China to construct my sample. However, the sample size is limited so that it is difficult to estimate parameters of default intensity and prepayment intensity properly. Existing literature suggests that MCMC can effectively estimate parameters of the jump-diffusion process, but only for large samples. Therefore, this paper proposes a two-stage MCMC (Markov chain Monte Carlo) approach. In the first stage, I adopt non-parametric estimation method developed by Lee and Mykland to estimate the parameters of jumps. In the second stage, I use MCMC to estimate parameters of diffusion and drift. Then we compare the estimation error of the two-stage MCMC approach and MCMC approach, and analyze their stability. All of the above show that the former is less than the latter in error.(4) This paper establishes a Clayton Copula-based intensity housing mortgage pricing model which considers the default, prepayment, building property, interest rate and correlation.To analyse mortgage default, we use Copula models to measure the influence of default correlation and prepayment correlation on the mortgage value, i.e. establishing an intensity housing mortgage pricing model based on Clayton Copula. The analysis about the influence of default correlation and prepayment correlation on the mortgage value shows that Clayton Copula model describes fat-tailedness better. The sensitivity analysis results of main parameters indicate that this model is necessary and effective. Stress test results show that if house prices fall sharply in recent years, the bank that issued many housing mortgages with low proportion of initial payment to principal is exposed to huge losses. Clayton Copula-based intensity housing mortgage pricing model is more sensitive to the risk of housing price falling quickly than jump diffusion process-based intensity housing mortgage pricing model. If the bank uses this model to measure the value of housing mortgages, the risk will be warned earlier.In summary, this paper builds two housing mortgage pricing models and adapts the two models to China's housing mortgage market. These two models improve existing mortgage pricing models in measuring dafault risk, prepayment risk, building property risk and interest risk. For overcoming the difficulties of data limitation, this paper does simulation analysis and empirical analysis to the two pricing model by use of various methods of parameters estimation and numerical analysis. Research on housing mortgage pricing model is promoted in the theoretical and practical aspects. Thus it is in favor of improving the asset management efficiency and operational safety of Chinese banks.