Credit Risk Measurement Model In Incomplete Market

The structural method has became one of the most important part in credit risk measure-ment theory, since Merton first apply option pricing theory to bond pricing. Merton model assumed company asset value Vt satisfies Geometric Brownian motionThe ability of redeem its debt is all determined by asset value for a company, the equity can be treated as a call option,whose underlying is asset value, strike price is the face value of its debt, and the equity value when debt is maturity is According to the Black-Scholes formula, Dt= Vt-Et Merton model is the foundation of KMV model. KMV is a model that can measure the default frequency of corporation bond. It has been widely used in about 60 countries all around the world, and it has successfully forecasted financial crisis of company Eron and Worldcom in the United States. The innovation for KMV is that it uses the stock market price and volatility to compute company asset value V, and volatility of asset valueσ.The two formulas are: the EDF isKMV model assumes that company asset value satisfy Geometric Brownian Motion, which is a continuous diffusion process, however, It may not reflect the fact well. For ex-ample, in China company asset value is often affected by government policies, it maybe not suitable to describe its movement by continuous diffusion process. For that reason, Zhou apply jump diffusion to price corporation bond.Zhou's model assume that corporation asset value satisfies the following jump diffusion process. for jump diffusion process, the equity value is andUnder the assumption of KMV and zhou's jump diffusion model we can get the EDF andOn the other hand, the default point is a constant in KMV model, but in fact the balance sheet is always changing, Kay Giesecke(2004) pointed out that default point should be a random variable to get a better default frequency, and he put forward a I2 model. the EDF of I2 model is according to We can use monte carlo method to compute the EDF.In I2 model, with jump diffusion process,we can get the formula of EDF, which isAfter we got the parameter estimations of jump diffusion, we test our model with the dates of GE. Comparing to KMV model, the results show that the EDF of Zhou's jump diffusion model is smaller than that of KMV model. In the I2 model, the EDF is higher than in KMV model, which reflect the advantage that it can forecast the financial depress earlier and more rapidly.