An examination of the effectiveness of static hedging in the presence of stochastic volatility

Abstract

AbstractToft and Xuan (1998) use simulation evidence to demonstrate that the static hedging method of Derman et al. (1995) performs inadequately when volatility is stochastic. Particularly, the greater the “volatility of volatility,” the poorer the static hedge. This article presents an alternative static hedging methodology, denoted the generalized static hedge, that appears to perform more reliably. Specifically, the value, delta, and vega of the static hedges closely approximate those values of the barrier option being hedged. Further, simulation evidence indicates that when volatility of volatility is large, the standard deviation of simulated cash flows from the generalized static hedge position is less than the standard deviation of simulated cash flows from previously defined static hedge positions. © 2003 Wiley Periodicals, Inc. Jrl Fut Mark 23:859–890, 2003