Competing Methods for Option Hedging in the Presence of Transaction Costs

Abstract

Most option pricing models are set in continuous time in order for it to be (theoretically) possible to follow an option replication strategy that continuously rebalances a delta-neutral hedge. One big problem in applying such a model to the real world is that perfect replication theoretically entails trading an infinite amount of the underlying asset. With transactions costs, no matter how small, the cost of this strategy is also infinite. A delta hedge can not be rebalanced continuously, so how should one rebalance periodically to achieve the best replication at minimum cost? Some possibilities are to rebalance at fixed time intervals, or whenever the asset price moves by a preset amount, or when the option’s delta differs from the position’s hedge ratio by a given percentage. Other ideas have also been proposed, but it is still not clear which is best. In this article, Martellini and Priaulet examine this issue in an extensive simulation exercise. Among their results, they find that delta-based rebalancing works best under proportional transactions costs. But adding a fixed component to the transactions cost reduces the effectiveness of that strategy.