A Portfolio Approach to Risk Reduction in Discretely Rebalanced Option Hedges

This paper analyses the accumulated hedging errors generated by discretely rebalanced option hedges. We show that simple generalizations of the prior research can underestimate the variance of the accumulated hedging errors and that even with daily rebalancing, these accumulated hedging errors can introduce substantial risk in arbitrage strategies suggested by the Black-Scholes option pricing model. We also show that the correlation between the accumulated hedging errors for different options can be quite high, so that the risk of arbitrage due to hedging errors can be substantially reduced by optimally combining options into portfolios. The results also suggest that tests of market pricing of traded options which are based on employing a portfolio approach are likely to be much better specified than the standard tests that focus on individual options.