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A Portfolio Approach to Risk Reduction in Discretely Rebalanced Option Hedges

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  • Antonio S. Mello

    (School of Business, University of Wisconsin-Madison, 975 University Avenue, Madison, Wisconsin 53706-1323)

  • Henrik J. Neuhaus

    (The Nikko Securities Company, 55 Victoria Street, London SW11I 0EU, United Kingdom)

Abstract

This paper analyses the accumulated hedging errors generated by discretely rebalanced option hedges. We show that simple generalizations of the prior research can underestimate the variance of the accumulated hedging errors and that even with daily rebalancing, these accumulated hedging errors can introduce substantial risk in arbitrage strategies suggested by the Black-Scholes option pricing model. We also show that the correlation between the accumulated hedging errors for different options can be quite high, so that the risk of arbitrage due to hedging errors can be substantially reduced by optimally combining options into portfolios. The results also suggest that tests of market pricing of traded options which are based on employing a portfolio approach are likely to be much better specified than the standard tests that focus on individual options.

Suggested Citation

  • Antonio S. Mello & Henrik J. Neuhaus, 1998. "A Portfolio Approach to Risk Reduction in Discretely Rebalanced Option Hedges," Management Science, INFORMS, vol. 44(7), pages 921-934, July.
  • Handle: RePEc:inm:ormnsc:v:44:y:1998:i:7:p:921-934
    DOI: 10.1287/mnsc.44.7.921
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    References listed on IDEAS

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    1. Leland, Hayne E, 1985. "Option Pricing and Replication with Transactions Costs," Journal of Finance, American Finance Association, vol. 40(5), pages 1283-1301, December.
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    Cited by:

    1. Luca Di Persio & Luca Prezioso & Kai Wallbaum, 2019. "Closed-End Formula for options linked to Target Volatility Strategies," Papers 1902.08821, arXiv.org.
    2. Bas Peeters & Cees L. Dert & André Lucas, 2003. "Black Scholes for Portfolios of Options in Discrete Time: the Price is Right, the Hedge is wrong," Tinbergen Institute Discussion Papers 03-090/2, Tinbergen Institute.
    3. Cheng Cai & Tiziano De Angelis & Jan Palczewski, 2020. "Optimal hedging of a perpetual American put with a single trade," Papers 2003.06249, arXiv.org, revised Sep 2020.
    4. Miklavž Mastinšek, 2006. "Discrete–time delta hedging and the Black–Scholes model with transaction costs," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 64(2), pages 227-236, October.
    5. Borochin, Paul & Wu, Zekun & Zhao, Yanhui, 2021. "The effect of option-implied skewness on delta- and vega-hedged option returns," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 74(C).

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