Tractable Hedging - An Implementation of Robust Hedging Strategies

This paper analyzes tractable robust hedging strategies in diffusion-type models including stochastic volatility models. A robust hedging strategy avoids any losses as long as volatility stays within a given interval. It does not depend on the exact specification of the volatility process and therefore mitigates problems caused by model misspecification. A tractable hedging strategy is defined as the sum over Black-Scholes strategies. For a convex (concave) payoff, the cheapest robust hedge is given by a BS-hedge at the upper (lower) volatility bound. Thus, it is tractable. For all other payoffs, one has to solve a Black-Scholes-Barenblatt equation, and the cheapest robust hedge is not tractable. A tractable hedge can then be found by decomposing the payoff into a convex and a concave function, each of which is hedged separately. We first give the decomposition that minimizes the initial capital. Second, we show that it may be even cheaper to hedge a dominating payoff, and we show explicitly how to determine the optimal dominating payoff. We illustrate our results by two examples.