Three essays in credit derivative pricing models

The credit derivatives market has grown rapidly during last decade with the introduction of different forms of credit derivative contracts. These contracts allow investors to totally or partially reduce their credit risks by giving a certain payoff if some event, such as a default or downgrade, occurs. This dissertation proposes three credit risk pricing models with focus on credit spread index derivatives and Collateral Debt Obligations (CDO).; I present a bushy tree model for pricing derivatives on credit spreads in Chapter l. The model is based on the Heath-Jarrow-Morton (HJM) model for default-free interest rates, where the arbitrage-free forward credit spread term structure is constructed. The forward credit spread term structures is calibrated with nearly proportional volatility functions that avoid the negative credit spreads. Examples are provided to illustrate pricing the European call options and put options on credit spread indexes.; With the rapid growth of credit derivative market, in particular, CDO market, financial institutes have more ways to hedging credit risk on their portfolio or freeing up their capital reserve. Chapter 2 presents a survey of CDO pricing models with focus on stochastic default correlation models. In order to match correlation smile observed in the CDO market, a number of copula functions have been introduced to CDO pricing models. It illustrates that a simplified stochastic model based on Li and Liang (2005) model significantly improves fitting to CDX market quotes compared to basic Gaussian model. Chapter 3 proposes a stochastic recovery rate extension of the stochastic correlation copula where both the time-to-default and recovery rate in each state are determined by the market factor. As a result, the expected recovery rate is negatively correlated with the expected default rate and this relationship is consistent with the linear regression results in Moody's reports. It illustrates that a stochastic default and recovery rate correlation model outperforms a stochastic default correlation model by reducing Sum of Squared Errors (SSE) more than 50%.