Exploding hedging errors for digital options

Christoph Gallus
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Christoph Gallus: Deutsche Bank AG, Equities, Global Equity Derivatives, D-60325 Frankfurt am Main, Germany Manuscript

Finance and Stochastics, 1999, vol. 3, issue 2, 187-201

Abstract: In the complete market model of geometric Brownian motion, all kinds of exotic options can be priced and hedged perfectly using a delta hedging strategy which duplicates the option's payoff. If trading takes place in a frictionless market, this delta hedging strategy is said to eliminate the option writer's risk completely. It will be shown that for certain contingent claims, for example digital options, the hedge can fail completely if the underlying risky asset does not follow the assumed geometric Brownian motion. Indeed, the hedging error may diverge and delta hedging can actually increase the risk of the option writer.

Keywords: Option pricing; digital option hedging; hedging error (search for similar items in EconPapers)
Date: 1999-01-29
Note: received: October 1996; final version received: February 1998
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