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Option Betas: Risk Measures For Options

Author

Listed:
  • NICOLE BRANGER

    (Finance Center Münster, Westfälische Wilhelms-Universität Münster, Universitätsstr. 14-16, D-48143 Münster, Germany)

  • CHRISTIAN SCHLAG

    (Faculty of Economics and Business Administration, Goethe University, Mertonstr. 17/Uni-Pf 77, D-60054 Frankfurt am Main, Germany)

Abstract

This paper deals with the problem of determining the correct risk measure for options in a Black–Scholes (BS) framework when time is discrete. For the purposes of hedging or testing simple asset pricing relationships previous papers used the "local", i.e., the continuous-time, BS beta as the measure of option risk even over discrete time intervals. We derive a closed-form solution for option betas over discrete return periods where we distinguish between "covariance betas" and "asset pricing betas". Both types of betas involve only simple Black–Scholes option prices and are thus easy to compute. However, the theoretical properties of these discrete betas are fundamentally different from those of local betas. We also analyze the impact of the return interval on two performance measures, the Sharpe ratio and the Treynor measure. The dependence of both measures on the return interval is economically significant, especially for OTM options.

Suggested Citation

  • Nicole Branger & Christian Schlag, 2007. "Option Betas: Risk Measures For Options," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 10(07), pages 1137-1157.
    • Handle: RePEc:wsi:ijtafx:v:10:y:2007:i:07:n:s0219024907004585
    DOI: 10.1142/S0219024907004585
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    References listed on IDEAS

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    1. William Goetzmann & Jonathan Ingersoll & Matthew I. Spiegel & Ivo Welch, 2002. "Sharpening Sharpe Ratios," NBER Working Papers 9116, National Bureau of Economic Research, Inc.
    2. Santa-Clara, Pedro & Saretto, Alessio, 2009. "Option strategies: Good deals and margin calls," Journal of Financial Markets, Elsevier, vol. 12(3), pages 391-417, August.
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    Cited by:

    1. Ryan McKeon, 2016. "Option spread trades: Returns on directional and volatility trades," Journal of Asset Management, Palgrave Macmillan, vol. 17(6), pages 422-433, October.
    2. Peter Reichling & Anastasiia Zbandut, 2017. "Costs of capital under credit risk," FEMM Working Papers 170003, Otto-von-Guericke University Magdeburg, Faculty of Economics and Management.

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