Costs and Benefits of Crash Hedging

Abstract

The worst-case scenario portfolio problem which has been introduced by Korn and Wilmott (2002) will be considered in this paper. In the setting of Korn and Wilmott, approximations for the optimal crash hedging strategy will be derived. Furthermore, the costs and benefits of using the optimal crash hedging strategy instead of the classical optimal portfolio strategy of Merton will be calculated using both a utility based approach and an efficiency approach. Additionally, we derive the break even crash size, that is the crash size where the investor is indifferent towards a crash of the break even size by using either the optimal crash hedging strategy or the classical optimal portfolio strategy of Merton. Finally, we will compute the sensitivities with respect to the worst case crash size of both the optimal crash hedging strategy and the corresponding value function.

Keywords: optimal portfolios, crash modelling, worst-case scenario, efficiency, costs and benefits of crash hedging, portfolio insurance, break even crash sizes, logarithmic utility

JEL Classification: G11