Cross-Currency Bond Option Pricing

Abstract

This paper concerns the pricing of European options on foreign discount bonds, or cross-currency bond options. Using techniques similar to those in Merton (1973) and Grabbe (1983), we solve a general partial differential equation (PDE) subject to proper boundary conditions for different categories of cross-currency bond options to get closed-form pricing formulas. Lognormal distribution is assumed for both the discount bond prices (domestic and foreign) and the exchange rate. The pricing models can be parameterized with specific interest rate processes. Yield-curve models such as the extended Vasicek model in Hull and White (1990) and the dampening volatility model in Heath, Jarrow and Morton (1992) can also be accommodated. Finally, we show that the PDE approach and the risk-neutral approach yield the same pricing results.

JEL Classification: G13