Dynamic Stable Factor Copula Model And Its Application To Credit Derivatives Pricing

Credit derivatives, which can facilitate seperating, transferring and trading credit risk,are one of the most important financial innovations. In 2008, the credit derivatives market was shocked by the outbreak of the subprime crisis largely and its trading volume had fallen sharply and some species were close to stagnant. With the recovery of the global economy in recent years, the credit derivatives are becoming active and CDO is one of the growing fastest species.The Gaussian factor copula model is the standard model in financial industry for CDO pricing and risk management. However, because of the leptokurtosis feature of financial data, this model can not match all market prices of the standard CDO tranches, and there exists implied correlation smile and other phenomena which are not consistent with the model assumptions. On the other hand, it provides arbitrage opportunity when a nonconstant correlation is involved, and it is a static model, which is not applicable to CDO tranches with di?erent maturities.For the first issue, this thesis introduces the stable distribution, which is characterized of leptokurtosis and four free parameters, to describe the financial risk factor, instead of the gaussian distribution. However, there is no explicit density function or cumulative distribution, which brings the model great computational task and complexity. This thesis references the algorithms of J. P. Nolan and uses matlab codes to realize, which improve the computation time and accuracy of stable distribution. This work laid a solid foundation for parameters estimation of the stable distribution and its implementation in the CDO pricing.For the second issue, this thesis applies the dynamic factor Copula method proposed by Jackson and uses the forward default probability and turns the high dimensional integration problem to a recursive one-dimensional integral problem, which makes the dynamic factor copula method based on the stable distribution more applicable and accurate and is appropriate for CDO pricing with di?erent maturities.This thesis also studies the pricing of other credit derivatives such as BDS and forward CDOs based on the dynamic stable factor model and achieves good results.