Delta Hedging of S&P 500 Options

Abstract

We use stochastic simulation methods to study the efficiency of delta hedging strategies for ordinary, look-back,and Asian call options on the S&P 500 index. Execution is assumed to take place in either the cash or the futures market. Our results clearly show the inadequacy of delta hedging for hedging these options. The outcome of the hedging process is shown to depend heavily on the way the theoretical hedging strategy is operationalized and the gamma characteristics of the option position to be hedged. Apart from discrete hedge rebalancing, our results identify volatility misprediction and, for path-dependent options, the use of hedge ratios derived from Black-Scholes assumptions as the main sources of hedging error risk. Despite mispricings and rollover costs, futures market execution is typically to be preferred over cash market execution.