Optimal Derivative Strategies with Discrete Rebalancing

Abstract

Continuous-time derivatives models are based on the assumption that a hedged portfolio can be constructed and adjusted continuously over time. But practically speaking, of course, continuous rebalancing is impossible. This means that a hedged option position will still be exposed to risk. It also means that the delta hedge from the model, which an investor would choose if continuous rebalancing were possible, may not be optimal when the hedge is only adjusted at discrete intervals. In this article, Branger, Breuer, and Schlag simulate hedging strategies in a world with periodic rebalancing and stochastic volatility. They consider hedging an option with the underlying alone, with the underlying and another option, and with the underlying and a contract based on realized variance. Interestingly, the optimal hedge changes sharply in some cases when rebalancing is only at discrete intervals, but a large fraction of the theoretically possible utility increase from continuous hedging can be achieved by trading continuous-time derivatives models are based on the assumption that a hedged portfolio can be constructed and adjusted continuously over time. But practically speaking, of course, continuous rebalancing is impossible. This means that a hedged option position will still be exposed to risk. It also means that the delta hedge from the model, which an investor would choose if continuous rebalancing were possible, may not be optimal when the hedge is only adjusted at discrete intervals. In this article, Branger, Breuer, and Schlag simulate hedging strategies in a world with periodic rebalancing and stochastic volatility. They consider hedging an option with the underlying alone, with the underlying and another option, and with the underlying and a contract bas at much longer intervals.