Valuing Vulnerable Basket Options with Stochastic Liquidity Risk in Reduced-form Models

In this paper, we investigate the pricing problem of vulnerable basket options with stochastic liquidity risk in reduced-form models. We use a liquidity-adjusted model to describe all the underlying asset prices and adopt an intensity-based model to capture default risk. Additionally, we incorporate the correlation between the underlying assets and default risk through the liquidity risk channel. In the proposed framework, we obtain an explicit approximation of vulnerable basket option prices. Finally, we illustrate the effects of liquidity risk and default risk on (vulnerable) basket option prices after checking the accuracy of the approximations.