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Kelly trading and option pricing

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  • Hans‐Peter Bermin
  • Magnus Holm

Abstract

In this paper we show that a Kelly trader is indifferent to trade a derivative if and only if the no‐arbitrage price is uniquely given by the minimal martingale measure price, thus providing a natural selection mechanism for option pricing in incomplete markets. We also show that the unique Kelly indifference price results in market equilibrium in the sense that no Kelly trader can improve the magnitude of his instantaneous Sharpe ratio, by trading the derivative, given the actions of the other market participants.

Suggested Citation

  • Hans‐Peter Bermin & Magnus Holm, 2021. "Kelly trading and option pricing," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 41(7), pages 987-1006, July.
    • Handle: RePEc:wly:jfutmk:v:41:y:2021:i:7:p:987-1006
    DOI: 10.1002/fut.22210
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    References listed on IDEAS

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    1. Mark Davis & Sébastien Lleo, 2013. "Fractional Kelly Strategies in Continuous Time: Recent Developments," World Scientific Book Chapters, in: Leonard C MacLean & William T Ziemba (ed.), HANDBOOK OF THE FUNDAMENTALS OF FINANCIAL DECISION MAKING Part II, chapter 37, pages 753-787, World Scientific Publishing Co. Pte. Ltd..
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    6. Guiso, Luigi & Sapienza, Paola & Zingales, Luigi, 2018. "Time varying risk aversion," Journal of Financial Economics, Elsevier, vol. 128(3), pages 403-421.
    7. Nielsen, Lars Tyge & Vassalou, Maria, 2004. "Sharpe Ratios and Alphas in Continuous Time," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 39(1), pages 103-114, March.
    8. Merton, Robert C, 1973. "An Intertemporal Capital Asset Pricing Model," Econometrica, Econometric Society, vol. 41(5), pages 867-887, September.
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