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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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    3. Robert C. Merton, 2005. "Theory of rational option pricing," World Scientific Book Chapters, in: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 8, pages 229-288, World Scientific Publishing Co. Pte. Ltd..
    4. Harrison, J. Michael & Pliska, Stanley R., 1981. "Martingales and stochastic integrals in the theory of continuous trading," Stochastic Processes and their Applications, Elsevier, vol. 11(3), pages 215-260, August.
    5. Hansen, Lars Peter & Jagannathan, Ravi, 1991. "Implications of Security Market Data for Models of Dynamic Economies," Journal of Political Economy, University of Chicago Press, vol. 99(2), pages 225-262, April.
    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.
    9. Edward. O. Thorp, 2011. "Portfolio Choice And The Kelly Criterion," World Scientific Book Chapters, in: Leonard C MacLean & Edward O Thorp & William T Ziemba (ed.), THE KELLY CAPITAL GROWTH INVESTMENT CRITERION THEORY and PRACTICE, chapter 7, pages 81-90, World Scientific Publishing Co. Pte. Ltd..
    10. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
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    Cited by:

    1. Hans-Peter Bermin & Magnus Holm, 2024. "The geometry of risk adjustments," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 47(1), pages 83-120, June.

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