Efficient hedging currency options in fractional Brownian motion model with jumps

Abstract

This paper deals with the problem of efficient hedging for European currency option and exchange option in case that exchange rate is driven by a fractional Brownian motion with jumps. In a complete market, as long as a seller receives a price (of the option) equal to the expectation under the risk-neutral probability measure of the discounted payoff, the seller can hedge this payoff perfectly. As the price is often quite expensive, the investors need partial hedges which require less capital and reduce the risk. The efficient hedge is one of partial hedges. The efficient hedging results for options are obtained under fractional Brownian motion model with jumps using the equivalent martingale measure. Simulation results and empirical studies confirm the theoretical findings and show that the fractional Brownian motion model with jumps is reasonable.