This thesis presents a uni ed framework for studying the impact of the correlation between interest rate volatility and counterparty default... Show moreThis thesis presents a uni ed framework for studying the impact of the correlation between interest rate volatility and counterparty default probability on the credit risk of collateralized interest-rate derivative contracts. A defaultable term structure model is proposed in which the default risk is correlated with interest rate volatility. In particular, an existence and uniqueness theorem of this model is proved. The pricing formula of credit derivatives under the proposed model is derived and the stochastic interest rate model and credit model are calibrated together . Finally, given all the parameters calibrated by the unscented Kalman lter, a sensitivity analysis of the impact of the correlation between interest rate volatility and a counterparty's default probability on the credit risk of collateralized interest-rate derivative contracts is presented. Ph.D. in Applied Mathematics, July 2012 Show less
