Structural Model And Application Research On The Credit Risk Measurement Based On Incomplete Information

The most of the existing theoretical and applied model of credit risk measurement and valuation is based on the fundamental hypothesis that the information is complete, under which the credit risk model is not only unadapted to the Occident that has the developed financial market, but also be unapplied to Chinese financial market which has the incomplete information seriously. Therefore, how to measure, value and hedge credit risk under the incomplete information markets is an important, practical project.The theoretical model of credit risk measurement can be classified two kinds of model:reduced model and structural model. The reduced model dose not reveal the reason of economy under the default, the resulting model conclusion is mostly determined to the artificial set for the default intensity, which maybe lead to the model specification risk. To the contrary, the structural model gives emphasis to the economy reason under the default, which begins with the capital structure of corporate which can make people understand the change of credit spread deeply. However, under the structural model framework, there maybe emerge the credit spread puzzle phenomenon. One of the key reason for the puzzle is the complete information hypothesis supporting to the structural model. In fact, the information between the bargainers is asymmetric in the actual financial market. Duffie and Lando(2001) firstly considers the effect of the incomplete information on the valuation of the credit spread. After 2007, a few scholar begin to do the same things. Given the few study conference, the resource of the incomplete information is assumed to unbiased finance report. The finance report, however, usually has the systematic bias in the actual market. Under the structural model framework, this paper uses the biased distribution to capture the biased phenomenon which comes from the overstatement or concealment of the assets true value, and formulates the conditional distribution of the asset value, default probability and credit spread under the information bias, and then analysis the effect mechanism of the biased degree of information on the three formulations above.In addition, there is a time delay phenomenon in the finance report publication system, which may makes the information incomplete. This paper suggest to use the delay information filter to describe the time delay of the information report in the security market, and gives the method of measuring the feature of time delay in the information disclosure, then formulates the computation of the default probability and the credit spread under the information delay. Finally, this paper use the numerical simulation trial to analysis the mechanism of the effect of different delay information on the default risk or term structure of credit spread.In the theory, the structural model has perfect economy meanings and mathematical model representation. However, in the practice, the structural model encounters an difficulty that is the unobservable of the asset values, which is the main barrier in the application of the structure model. The existing method of resolving the difficulty involves that KMV, data transformation MLE and iteration method. However, such methods must satisfy an fundamental prerequisite that the market information is complete. Duan and Fulop(2009) firstly put forward the econometric method to estimate the assets values under the incomplete information market, in their paper, they introduced the noise information into Merton model with constant volatility, use the particle filter technology and the state variable extension method to gain the simultaneous estimation of the assets values and parameters. But their method may cause the unreliability of the static parameters, which makes the estimation deteriorate. This paper gives up the state variable extension method and falls back on the particle smooth expectation maximum algorithm to require the parameter estimation. The numerical simulation trial shows that PSEM can improve the estimation accuracy of the parameter greatly. Finally, this paper do the empirical analysis and get the better conclusion.In addition, Many empirical study show that the hypothesis of constant volatility can lead to the bigger estimation error of credit risk in the Merton model. This paper introduces the stochastic volatility into the Merton model and gets the HSV-Merton model in the noise information, and then gives a double state variable(assets values and volatility), nonlinear, non-Gaussian state space model. As for the given SSM, this paper designs BV-APF to estimate the state variable and model parameters. The numerical simulation trial shows BV-APF has the good finite sample estimation performance. Finally, this paper use the real data to analysis empirically, and compare the HSV-Merton model to Merton model, and then use the HSV-Merton model to measure the real credit risk and the conclusion is satisfied.Finally, this paper advances the approach of the nonlinear filter technology to estimate more general structural model —Black-Cox model. Specifically, this paper uses the PMCMC and extended Gibbs sampling algorithm to estimate the parameters and assets values simultaneously, and then makes the empirical analysis to find the support.