Pricing vulnerable European options with dynamic correlation between market risk and credit risk

In this paper, we study the valuation of vulnerable European options incorporating the reduced-form approach, which models the credit default of the counterparty. We provide an analytical pricing model in which the components of the state processes, including the dynamics of the underlying asset value and the intensity process corresponding to the default event, are cross-exciting and they could facilitate the description of complex structure of events dependence. To illustrate how our model works, we present an application when the state variables follow specific affine jump-diffusion processes. Semi-analytical pricing formulae are obtained through a system of matrix Riccati equations. The derived formula can be implemented numerically, and we give numerical analysis to investigate the impact of the dynamic correlation between jump risk of the underlying asset value and default risk of the counterparty.