✦ LIBER ✦

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

✍ Scribed by Jason Fink

Publisher: John Wiley and Sons
Year: 2003
Tongue: English
Weight: 305 KB
Volume: 23
Category: Article
ISSN: 0270-7314
DOI: 10.1002/fut.10089

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✦ Synopsis

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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