Pricing currency options in a fractional Brownian motion with jumps

Abstract

A new framework for pricing the European currency option is developed in the case where the spot exchange rate fellows a fractional Brownian motion with jumps. An analytic formula for pricing European foreign currency options is proposed using the equivalent martingale measure and the estimation method of parameters in the pricing model is given, enabling option prices to be computed efficiently and accurately. For the purpose of understanding the pricing model, some properties of this pricing model are discussed in the latter part of this paper. Finally, the numerical simulations illustrate that our model is flexible and easy to implement.