Analytical Pricing Vulnerable Options with Stochastic Volatility in a Two-Factor Stochastic Interest Rate Model

This paper develops an analytical pricing formula for vulnerable options with stochastic volatility under a two-factor stochastic interest rate model. We consider the underlying asset price following the Heston stochastic volatility model, while the interest rate is modeled as the sum of two processes. Using the joint characteristic function approach and measure change techniques, we derive an explicit pricing formula for a vulnerable European option. We also conduct numerical experiments to examine the effects of various model parameters on option values. This study provides a more realistic framework for pricing OTC derivatives by incorporating credit risk, stochastic volatility, and stochastic interest rates simultaneously.