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Maximum Entropy Distributions Inferred from Option Portfolios on an Asset

Author

Listed:
  • C. Neri

    (Lloyds Banking Group, London, UK)

  • L. Schneider

    (EMLYON Business School, Lyon, France)

Abstract

We obtain the maximum entropy distribution for an asset from call and digital option prices. A rigorous mathematical proof of its existence and exponential form is given, which can also be applied to legitimise a formal derivation by Buchen and Kelly. We give a simple and robust algorithm for our method and compare our results to theirs. We present numerical results which show that our approach implies very realistic volatility surfaces even when calibrating only to at-the-money options. Finally, we apply our approach to options on the S&P 500 index.

Suggested Citation

  • C. Neri & L. Schneider, 2009. "Maximum Entropy Distributions Inferred from Option Portfolios on an Asset," Papers 0903.4542, arXiv.org, revised Feb 2011.
    • Handle: RePEc:arx:papers:0903.4542
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    References listed on IDEAS

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    1. Joshua Coval & Jakub Jurek & Erik Stafford, 2009. "The Economics of Structured Finance," Journal of Economic Perspectives, American Economic Association, vol. 23(1), pages 3-25, Winter.
    2. Buchen, Peter W. & Kelly, Michael, 1996. "The Maximum Entropy Distribution of an Asset Inferred from Option Prices," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 31(1), pages 143-159, March.
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