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

Abstract

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.

Valuation of Commodity-Linked Bond with Stochastic Convenience Yield, Stochastic Volatility, and Credit Risk in an Intensity-Based Model

“…Yoon and Kim [16] were the first to apply Mellin transforms to calculate vulnerable European option prices. Several recent studies have demonstrated that the Mellin transforms can be used to solve the PDE for many types of financial derivatives with credit risk (path-dependent option [17], exchange option [18], and foreign equity option [19]).…”

A Simplified Approach to the Pricing of Vulnerable Options with Two Underlying Assets in an Intensity-Based Model

“…More recently, Wang [11], He et al [12], Kim et al [13] and Jeon et al [14] investigated the pricing of vulnerable options in the presence of stochastic volatility affecting asset price processes. In addition, there have been numerous research on vulnerable options with multi-assets [15][16][17][18][19].…”