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Retrieving risk neutral densities from European option prices based on the principle of maximum entropy

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  • Rompolis, Leonidas S.

Abstract

This paper suggests a new method of implementing the principle of maximum entropy to retrieve the risk neutral density of future stock, or any other asset, returns from European call and put prices. The method maximizes the entropy measure subject to risk neutral moment constraints in place of option prices used by previous studies. These moments can be retrieved from market option prices at each point of time, in a first step. Compared to other existing methods of retrieving the risk neutral density based on the principle of maximum entropy, the benefits of the method that the paper suggests is the use of all the available information provided by the market more efficiently. To evaluate the performance of the suggested method, the paper compares it to other risk neutral density estimation techniques by conducting a simulation study and carrying out some crucial empirical exercises.

Suggested Citation

  • Rompolis, Leonidas S., 2010. "Retrieving risk neutral densities from European option prices based on the principle of maximum entropy," Journal of Empirical Finance, Elsevier, vol. 17(5), pages 918-937, December.
    • Handle: RePEc:eee:empfin:v:17:y:2010:i:5:p:918-937
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    2. Leonidas S. Rompolis & Elias Tzavalis, 2017. "Retrieving risk neutral moments and expected quadratic variation from option prices," Review of Quantitative Finance and Accounting, Springer, vol. 48(4), pages 955-1002, May.
    3. Chalamandaris, Georgios & Rompolis, Leonidas S., 2012. "Exploring the role of the realized return distribution in the formation of the implied volatility smile," Journal of Banking & Finance, Elsevier, vol. 36(4), pages 1028-1044.
    4. Xixuan Han & Boyu Wei & Hailiang Yang, 2018. "Index Options And Volatility Derivatives In A Gaussian Random Field Risk-Neutral Density Model," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 21(04), pages 1-41, June.
    5. Parnes, Dror, 2024. "Copper-to-gold ratio as a leading indicator for the 10-Year Treasury yield," The North American Journal of Economics and Finance, Elsevier, vol. 69(PA).
    6. Fabozzi, Frank J. & Leccadito, Arturo & Tunaru, Radu S., 2014. "Extracting market information from equity options with exponential Lévy processes," Journal of Economic Dynamics and Control, Elsevier, vol. 38(C), pages 125-141.
    7. Cortés, Lina M. & Mora-Valencia, Andrés & Perote, Javier, 2020. "Retrieving the implicit risk neutral density of WTI options with a semi-nonparametric approach," The North American Journal of Economics and Finance, Elsevier, vol. 54(C).
    8. J. Arismendi-Zambrano & R. Azevedo, 2020. "Implicit Entropic Market Risk-Premium from Interest Rate Derivatives," Economics Department Working Paper Series n303-20.pdf, Department of Economics, National University of Ireland - Maynooth.
    9. J. C. Arismendi & Marcel Prokopczuk, 2016. "A moment-based analytic approximation of the risk-neutral density of American options," Applied Mathematical Finance, Taylor & Francis Journals, vol. 23(6), pages 409-444, November.
    10. Vladimir Zdorovenin & Jacques Pézier, 2011. "Does Information Content of Option Prices Add Value for Asset Allocation?," ICMA Centre Discussion Papers in Finance icma-dp2011-03, Henley Business School, University of Reading.
    11. Damir Filipović & Sander Willems, 2020. "A term structure model for dividends and interest rates," Mathematical Finance, Wiley Blackwell, vol. 30(4), pages 1461-1496, October.
    12. Lina M. Cortés & Javier Perote & Andrés Mora-Valencia, 2017. "Implicit probability distribution for WTI options: The Black Scholes vs. the semi-nonparametric approach," Documentos de Trabajo de Valor Público 15923, Universidad EAFIT.
    13. Nessim Souissi, 2017. "The Implied Risk Neutral Density Dynamics: Evidence from the S&P TSX 60 Index," Journal of Applied Mathematics, Hindawi, vol. 2017, pages 1-10, June.

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