Copyright © 2012 Guoyi Zhang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The optimal geometric mean return is an important property of an asset. As a derivative of the underlying asset, the option also has this property. In this paper, we show that the optimal geometric mean returns of a stock and its option are the same from Kelly criterion. It is proved by using binomial option pricing model and continuous stochastic models with self-financing assumption. A simulation study reveals the same result for the continuous option pricing model.