Pricing American options on foreign currency with stochastic volatility, jumps, and stochastic interest rates

By applying the Heath-Jarrow-Morton (HJM) framework, an analytical approximation for pricing American options on foreign currency under stochastic volatility and double jump is derived. This approximation is also applied to other existing models for the purpose of comparison. There is evidence that such types of jumps can have a critical impact on early-exercise premiums that will be significant for deep out-of-the-money options with short maturities. Moreover, the importance of the term structure of interest rates to early-exercise premiums is demonstrated as is the sensitivity of these premiums to correlation-related parameters.