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

Authors

  • Jason Fink

    Corresponding author
    1. Department of Finance and Business Law, James Madison University, Harrisonburg, Virginia
    • MSC 0203 Finance and Business Law Program, James Madison University, Harrisonburg, Virginia 22807
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Abstract

Toft 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

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