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An Analysis of the Risk in Discretely Rebalanced Option Hedges and Delta-Based Techniques

  • Russell P. Robins

    (Freeman School of Business, Tulane University, New Orleans, Louisiana 70118-5669)

  • Barry Schachter

    (Freeman School of Business, Tulane University, New Orleans, Louisiana and Commodity Futures Trading Commission, 2033 K Street NW, Washington, DC 20581)

The stochastic properties of discretely rebalanced option hedges have been studied extensively beginning with Black and Scholes (1973). In each analysis hedges were "delta-neutral" after rebalancing. We argue that the distributional properties of discretely rebalanced hedges are such that delta-based hedging is not the variance minimizing strategy. This paper obtains analytical expressions for the variance minimizing option hedge ratios. We also evaluate the hedge variance to assess the magnitude of the variance reduction over delta-based hedges. For representative parameter values, we show that systematic departures from delta-based hedges can yield significant reductions in hedge variance even for one day rebalancing intervals.

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File URL: http://dx.doi.org/10.1287/mnsc.40.6.798
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Article provided by INFORMS in its journal Management Science.

Volume (Year): 40 (1994)
Issue (Month): 6 (June)
Pages: 798-808

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Handle: RePEc:inm:ormnsc:v:40:y:1994:i:6:p:798-808
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