Rational Bounds and the Robust Risk Management of Derivatives

The risk management of derivative portfolios is vulnerable to model error. This paper explores risk management strategies based on no-arbitrage bounds, which are independent of any model. In particular, we determine the bounds on the price of a general barrier option given the price of a set of European call options and identify the hedging strategy that enforces the bounds. The strategy puts a floor on the maximum loss that can be incurred by the writer of the barrier option. We show how the strategy can be made dynamic and the floor raised over time. The distribution of hedge errors under the strategy is compared with that under alternative strategies.