Valuing credit spread options under stochastic volatility/interest rates
This thesis studies the pricing of credit spread options in a continuous time setting. Our main examples are credit spreads between US government bonds and highly risky emerging market bonds, such as Argentina, Brazil, Mexico, etc. Based on empirical findings we model the credit spread options as a geometric Brownian Motion with stochastic volatility. We implement and compare several one-factor stochastic volatility models, namely the Vasicek, Cox-Ingersoll-Ross and Ahn/Gao. As a stochastic model for the credit risk free interest rate, we use the Vasicek model. As a further new ingredient we introduce dependence between the spread rate and interest rate in our pricing model (stochastic volatility is assumed to be independent of the other factors). The mean reverting property of the short rate models enables us to view the mean reverting stochastic volatility models as moment generating function of a time integral of positive diffusion. The moment generating function of the average variance of the credit spread price process is evaluated. The Numerical Laplace inversion method is used to invert the moment generating function to obtain the density of the average variance. This average variance density is then used in the analytic pricing formulae. We compare the credit spread option prices under the closed form and the numerical formula in the cases of no correlation and some correlation between the credit spreads and the short rate under the Vasicek, Cox/Ross and Ahn/Gao(Alternative) mean reverting stochastic volatility model. We also look at the delta hedge parameters for the credit spread options under the various stochastic volatility models. Further analysis is carried out on the effects of correlation between the credit spread, the short rate and various mean reversion parameters on the pricing and hedging of the credit spread options. We finally compare our credit spread option price/hedging stochastic volatility model with the Longstaff and Schwartz model on mean reverting credit spreads under constant volatility.