Vulnerable Option Pricing Under the 4/2 Stochastic Volatility Model

In this paper, we study the pricing of vulnerable options, which are exposed to the option issuer’s default risk. We develop a pricing framework that integrates a reduced-form model for default risk with the 4/2 stochastic volatility model for the underlying asset. A feature of our model is the correlation between the issuer’s default intensity and the systematic component of the stochastic volatility. Using the characteristic function method and properties of the Grasselli transform, we derive an analytical pricing formula for a European vulnerable call option. Finally, we conduct numerical experiments to illustrate the impact of significant parameters, such as the recovery rate, default intensity, and the specific parameters of the 4/2 model. The results show that the 4/2 model component, which distinguishes it from the standard Heston model, has a significant effect on option prices.