Efficient Construction of Robust Hedging Strategies Under Jump Models

Abstract

Markets where asset prices follow processes with jumps are incomplete and any portfolio hedging against large movements in the price of the underlying asset must include other instruments. The standard approach in literature is to minimize the price variance of the hedging portfolio under a certain choice for the jump size distribution. This paper generalizes the hedging strategy of Kennedy, Forsyth, and Vetzal (2009) to minimize the weighted variance of hedging portfolio price and Greeks (sensitivities of portfolio values to changes in the state variables or models parameters). The new approach yields improved hedging portfolios over long horizons (i.e. semi-static and static hedging) and for non-stationary model parameters (e.g. stochastic volatility or jump arrival rate). From the computational perspective, this paper develops a new Fourier transform-based numerical method for computing the Greeks of European options with arbitrary payoffs by extending the work of Jackson, Jaimungal, and Surkov (2008). The new computational method allows to rapidly compute the hedging portfolio weights of the generalized hedging approach. We demonstrate the precision and efficiency of the new numerical scheme and perform a comparative analysis of various hedging approaches.