Closed-form pricing formula for foreign equity option with credit risk

Since credit risk in the over-the-counter (OTC) market has undoubtedly become very important issue, credit risk has to be considered when the options in the OTC market are priced. In this paper, we consider the valuation of foreign equity options with credit risk. In order to derive a closed-form pricing formula of this option, we adopt the partial differential equation (PDE) approach and use the Mellin transform method to solve the PDE. Specifically, triple Mellin transforms are used, and the pricing formula is presented as 3-dimensional normal cumulative distribution functions. Finally, we verify that our closed-form formula is accurate by comparing it with the numerical result from the Monte-Carlo simulation.