32 Pages Posted: 22 Jun 2002
Date Written: May 13, 2002
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: Suggested Citation