Vulnerable options under a Hawkes jump-diffusion model with two-factor stochastic volatility

Abstract

In this article, we address the valuation of a European vulnerable options within a structural framework. Specifically, we model the underlying asset and the asset of the option writer using a joint Hawkes jump-diffusion model with two-factor stochastic volatility. We derive a general analytical integral formula for prices of European options, applicable under any modeling framework as long as the joint characteristic function of asset prices associated with the underlying and option writer is available analytically. Distinguished from the pricing formulae in the literature, especially in a jump-diffusion framework, which is either in the form of the expectation over the jump process or requires evaluating several layers of infinite sums, our formula is significantly simplified and computationally efficient. Moreover, our model dynamics encompasses a wide range of commonly used models as special cases, for which we provide explicit analytical forms of the joint characteristic functions. Finally, we present numerical experiments demonstrating the accuracy and computational efficiency of our formula, along with sensitivity analysis to highlight the impact of various model parameters on the option prices.