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

Author

Listed:
  • 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)

Abstract

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.

Suggested Citation

  • Russell P. Robins & Barry Schachter, 1994. "An Analysis of the Risk in Discretely Rebalanced Option Hedges and Delta-Based Techniques," Management Science, INFORMS, vol. 40(6), pages 798-808, June.
    • Handle: RePEc:inm:ormnsc:v:40:y:1994:i:6:p:798-808
    DOI: 10.1287/mnsc.40.6.798
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    Citations

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    Cited by:

    1. Joshua V. Rosenberg & Robert F. Engle, 1997. "Option Hedging Using Empirical Pricing Kernels," NBER Working Papers 6222, National Bureau of Economic Research, Inc.
    2. N. Chidambaran, 2007. "Density estimation through quasi-analytic Monte-Carlo simulation: Options arbitrage with transactions costs," Review of Quantitative Finance and Accounting, Springer, vol. 28(1), pages 101-122, January.
    3. Lim, Terence & Lo, Andrew W. & Merton, Robert C. & Scholes, Myron S., 2006. "The Derivatives Sourcebook," Foundations and Trends(R) in Finance, now publishers, vol. 1(5–6), pages 365-572, April.
    4. Robert F. Engle & Joshua V. Rosenberg, 1995. "GARCH Gamma," NBER Working Papers 5128, National Bureau of Economic Research, Inc.
    5. Balder, Sven & Brandl, Michael & Mahayni, Antje, 2009. "Effectiveness of CPPI strategies under discrete-time trading," Journal of Economic Dynamics and Control, Elsevier, vol. 33(1), pages 204-220, January.

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