OPTION BETAS: RISK MEASURES FOR OPTIONS

Nicole Branger () and Christian Schlag
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Nicole Branger: Finance Center Münster, Westfälische Wilhelms-Universität Münster, Universitätsstr. 14-16, D-48143 Münster, Germany

International Journal of Theoretical and Applied Finance (IJTAF), 2007, vol. 10, issue 07, 1137-1157

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.

Keywords: Option pricing; beta; hedging; Sharpe ratio; Treynor measure (search for similar items in EconPapers)
Date: 2007
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Citations: View citations in EconPapers (2)

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DOI: 10.1142/S0219024907004585

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