Optimal Geometric Mean Returns of Stocks and Their Options

Abstract EN

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.