Hedging European options under a jump-diffusion model with transaction costs

Abstract

This thesis investigates the performance of hedging strategies when the underlying asset is governed by Merton (1976)’s jump-diffusion model. We hedge a written European call option and analyse the performance through simulation of stock prices. We find that delta hedging is costly and poorly performing regardless of rebalancing frequency and that the performance is improved when an option is used instead of the underlying asset. The Gauss-Hermite quadratures strategy is an improvement to the delta hedging strategies. It is found to require a wide range of strike prices but that its performance is only moderately affected by restrictions on the strikes available. The Least squares hedge is the best performing strategy for all number of options included and the range of strikes required is relatively narrow. We find that this strategy performs equally well with five options as the Gauss-Hermite quadratures hedge does with 15 options. Both of the latter strategies are treated as static and found to be relatively cheap due to the limited number of transactions.