Option Betas

32 Pages Posted: 22 Jun 2002

See all articles by Nicole Branger

Nicole Branger

University of Muenster - Finance Center Muenster

Christian Schlag

Goethe University Frankfurt - Research Center SAFE

Date Written: May 13, 2002

Abstract

This paper deals with the problem of determining the correct beta for options in a Black-Scholes (BS) framework. For the purpose of testing simple asset pricing relationships previous papers used the 'local' BS beta as the measure of systematic option risk even over return intervals of discrete length. In contrast to that, we derive a closed-form solution for option betas over discrete return periods. We show that the discrete beta of calls and puts involves only simple Black-Scholes option prices and is thus computationally easy. However, the theoretical properties of these discrete betas are fundamentally different from local betas. First of all, the expected return on the stock explicitly enters the formula for discrete betas. Furthermore the range of discrete betas for calls is different from the range of local betas. For a given value of the local beta the discrete beta can take on any value between two finite bounds depending on the expected stock return. Numerical examples are provided to illustrate the size of the discrepancies between the two beta measures.

Keywords: asset pricing, option pricing, beta, risk management

JEL Classification: G12, G13

Suggested Citation

Branger, Nicole and Schlag, Christian, Option Betas (May 13, 2002). Available at SSRN: https://ssrn.com/abstract=314839 or http://dx.doi.org/10.2139/ssrn.314839

Nicole Branger (Contact Author)

University of Muenster - Finance Center Muenster ( email )

Universitatsstr. 14-16
Muenster, 48143
Germany
+49 251 83 29779 (Phone)
+49 251 83 22867 (Fax)

HOME PAGE: http://www.wiwi.uni-muenster.de/fcm/fcm/das-finance-center/details.php?weobjectID=162

Christian Schlag

Goethe University Frankfurt - Research Center SAFE ( email )

(http://www.safe-frankfurt.de)
Theodor-W.-Adorno-Platz 3
Frankfurt am Main, 60323
Germany
+49 69 798 33699 (Phone)

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