Efficient hedging currency options in fractional Brownian motion model with jumps

• Published in: Physica A Vol. 539; p. 122868
• Main Authors: Kim, Kyong-Hui, Kim, Nam-Ung, Ju, Dong-Chol, Ri, Ju-Hyang
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01.02.2020
• Subjects: Efficient hedging; European call option; Exchange option; Fractional Brownian motion; Jump noise; Jump noise; European call option; Exchange option; Efficient hedging; Fractional Brownian motion
• ISSN: 0378-4371; 1873-2119
• DOI: 10.1016/j.physa.2019.122868

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. •The efficient hedging for European currency option are provided under a fBm model with jumps.•The efficient hedging for Exchange option of two underlying assets are also obtained.•Simulation results and empirical studies show that the proposed efficient hedging is reasonable.