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Determination of the Probability Distribution Measures from Market Option Prices Using the Method of Maximum Entropy in the Mean


  • Henryk Gzyl
  • Silvia Mayoral


We consider the problem of recovering the risk-neutral probability distribution of the price of an asset, when the information available consists of the market price of derivatives of European type having the asset as underlying. The information available may or may not include the spot value of the asset as data. When we only know the true empirical law of the underlying, our method will provide a measure that is absolutely continuous with respect to the empirical law, thus making our procedure model independent. If we assume that the prices of the derivatives include risk premia and/or transaction prices, using this method it is possible to estimate those values, as well as the no-arbitrage prices. This is of interest not only when the market is not complete, but also if for some reason we do not have information about the model for the price of the underlying.

Suggested Citation

  • Henryk Gzyl & Silvia Mayoral, 2012. "Determination of the Probability Distribution Measures from Market Option Prices Using the Method of Maximum Entropy in the Mean," Applied Mathematical Finance, Taylor & Francis Journals, vol. 19(4), pages 299-312, August.
  • Handle: RePEc:taf:apmtfi:v:19:y:2012:i:4:p:299-312 DOI: 10.1080/1350486X.2011.621354

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    References listed on IDEAS

    1. Markus Haas, 2004. "A New Approach to Markov-Switching GARCH Models," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 2(4), pages 493-530.
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    6. Ram Bhar & Carl Chiarella, 1995. "The Estimation of the Heath-Jarrow-Morton Model by Use of Kalman Filtering Techniques," Working Paper Series 54, Finance Discipline Group, UTS Business School, University of Technology, Sydney.
    7. Carl Chiarella & Sara Pasquali & Wolfgang Runggaldier, 2001. "On Filtering in Markovian Term Structure Models (An Approximation Approach)," Research Paper Series 65, Quantitative Finance Research Centre, University of Technology, Sydney.
    8. Elliott, R. J. & Malcolm, W. P. & Tsoi, Allanus H., 2003. "Robust parameter estimation for asset price models with Markov modulated volatilities," Journal of Economic Dynamics and Control, Elsevier, vol. 27(8), pages 1391-1409, June.
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