Pricing European vanilla options under a jump-to-default threshold diffusion model

In this paper, we study option prices under a feasible threshold diffusion model subject to jump-to-default risk where the default intensity takes a negative power of the underlying stock price. The model incorporates the regime switches endogenously by assuming the volatility to shift from one regime to another when the stock price crosses the pre-specified threshold level. This threshold can be understood as the psychological price barrier. Using the probabilistic approach, we obtain the Laplace-transform-based analytical solutions to the pricing problem of European vanilla options. Numerical analysis in the end examines the option-related quantities using the derived results and shows the impact of jump-to-default risk and threshold effect.