Tractable Hedging: An Implementation of Robust Hedging Strategies
31 Pages Posted: 28 May 2004
Date Written: March 15, 2004
This paper provides a theoretical and numerical analysis of robust hedging strategies in a diffusion-type setup including stochastic volatility models. A hedging strategy is called robust if the hedger achieves an overprotection whenever the realised volatility stays within a given interval. We focus on the effects of restricting the set of admissible strategies to tractable strategies which are defined as the sum over Gaussian strategies. While the cheapest robust hedge of a mixed payoff-profile is given by a numerical solution of a stochastic control problem, firstly analysed in Avellaneda, Levy, and Paras (1995), a tractable hedge still allows for a closed form solution. It turns out that the cheapest tractable hedge can be represented by one long and one short position in convex claims where each claim is hedged separately. Surprisingly, for this optimal choice it may hold that the portfolio out of these claims truly dominates the payoff to be hedged. We show that although a trivial Gaussian hedge may be prohibitively bad compared to the initial capital which is needed by the cheapest overall hedge, this is not the case for the cheapest tractable hedge. Besides, we analyse the additional robustness which is achieved by the higher initial investment of the tractable hedge. Finally, we use a Monte Carlo simulation to illustrate the hedging performance and the distribution of terminal losses in a stochastic volatility model. The results show that after taking the different initial capital into account, the optimal tractable strategies behave quite similar to the cheapest robust hedge.
Keywords: Uncertain volatility, stochastic volatility, robust hedging, tractable hedging, model misspecication, incomplete markets
JEL Classification: G12, G13
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