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Growth Optimal Investment and Pricing of Derivatives

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  • Erik Aurell
  • Roberto Baviera
  • Ola Hammarlid
  • Maurizio Serva
  • Angelo Vulpiani

Abstract

We introduce a criterion how to price derivatives in incomplete markets, based on the theory of growth optimal strategy in repeated multiplicative games. We present reasons why these growth-optimal strategies should be particularly relevant to the problem of pricing derivatives. We compare our result with other alternative pricing procedures in the literature, and discuss the limits of validity of the lognormal approximation. We also generalize the pricing method to a market with correlated stocks. The expected estimation error of the optimal investment fraction is derived in a closed form, and its validity is checked with a small-scale empirical test.

Suggested Citation

  • Erik Aurell & Roberto Baviera & Ola Hammarlid & Maurizio Serva & Angelo Vulpiani, 1999. "Growth Optimal Investment and Pricing of Derivatives," Papers cond-mat/9910212, arXiv.org.
    • Handle: RePEc:arx:papers:cond-mat/9910212
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    References listed on IDEAS

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    1. Ola Hammarlid, 1998. "On Minimizing Risk in Incomplete Markets Option Pricing Models," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 1(02), pages 227-233.
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