Analysis of counterparty risks and derivative pricing under stochastic volatility

The understanding of correlation between default events is of importance to credit risk analysis, portfolio management and valuation of credit sensitive instruments. In the first part of my thesis, the effect of counterparty risk on credit derivatives and default correlation is studied. Under the reduced-form framework, we present the two-firm model and three-firm model where the default intensity of a firm increases whenever the default event of a counterparty occurs. We perform the valuation of credit default swap with counterparty risk, and explore how the correlated default structures among the counterparties and reference entity affect the swap rate in credit default swaps. This framework is also applicable to the analysis of default correlation. We introduce two types of default correlations and examine the nature of inter-dependent default risk structure. Theoretical properties on default correlation as deduced from our models are seen to agree quite well with those from empirical findings.; In the second part of my dissertation, we develop a hybrid credit risk model to study the term structure of credit spreads on corporate bonds. In our structural model, the firm value process is taken to have stochastic interest rate and stochastic volatility in an affine setting with a dynamic default barrier. With the aid of time change formula and the main theorem of Duffie, Pan, and Singleton (2000), the pricing formula of defaultable bond can be computed via the Fourier inversion. The unique feature of our model is that the structural approach is used for the default risk of the underlying asset while unexpected default risk or market risk can be modeled using the reduced-form model.; Stochastic volatility is the most common source to explain the empirical findings of fat-tailed return and volatility smirk. We present a time-changed Levy model of option pricing. Each time change is driven by a set of common macroeconomic times changes independent of its underlying process and an "idiosyncratic" time change. We decompose a CIR (Cox, Ingersoll, and Ross, 1985) term structure into a time-changed Levy process and a time dependent function. With this decomposition, we develop a set of analytic pricing formulae for two general types of interest rate derivatives. (Abstract shortened by UMI.)...