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Optimal Geometric Mean Returns of Stocks and Their Options

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  • Guoyi Zhang

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.

Suggested Citation

  • Guoyi Zhang, 2012. "Optimal Geometric Mean Returns of Stocks and Their Options," International Journal of Stochastic Analysis, Hindawi, vol. 2012, pages 1-8, December.
    • Handle: RePEc:hin:jnijsa:498050
    DOI: 10.1155/2012/498050
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