Testing hedge effectiveness for option positions

Jeroen Kerkhof, Bertrand Melenberg and J. M. Schumacher*

Journal of Risk

Abstract: ABSTRACT In this paper we test several models for the computation of risk measures. Our framework applies not only to value-at-risk but also to expected shortfall and other risk measures that depend on information from the tail distribution. We concentrate on market risk as represented by single-period hedge errors of delta-hedged option positions. For cases in which we only have price data for options with fixed time of maturity, we propose a transformation procedure to compensate for the change in risk characteristics of the option position over time. Our results indicate that it is crucial to take changes of volatility into account; this may be done by using historical simulation or by a simple vector autoregressive model.

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