Analytical Valuation of Vulnerable Exchange Options with Stochastic Volatility in a Reduced-Form Model

This paper investigates the valuation of vulnerable exchange options with two underlying assets that follow a two-factor volatility model. We employ a reduced-form model incorporating a Poisson process with stochastic intensity. The proposed reduced-form model depends on a stochastic intensity process that is guaranteed to remain positive and includes both systemic and idiosyncratic risks. Using measure change techniques and characteristic functions, we obtain an explicit pricing formula for vulnerable exchange options within the proposed framework. We also provide numerical examples demonstrating the sensitivity of option prices to significant parameters.