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Extraction of market expectations from risk-neutral density

Author

Listed:
  • Josip Arneric

    (Faculty of Economics and Business, University of Zagreb,Zagreb,Croatia)

  • Zdravka Aljinovic

    (Faculty of Economics,University of Split, Split, Croatia)

  • Tea Poklepovic

    (Faculty of Economics,University of Split, Split, Croatia)

Abstract

The purpose of this paper is to investigate which of the proposed parametric models for extracting risk-neutral density; among Black-Scholes Merton, mixture of two log-normals and generalized beta; give the best fit. The model that fits sample data better is used to describe different characteristics (moments) of the ex ante probability distribution. The empirical findings indicate that no matter which parametric model is used, the best fit is always obtained for short maturity horizon, but when comparing models in short-run, the mixture of two log-normals gives statistically significant smaller MSE. According to the pair-wise comparison results, the basic conclusion is that the mixture of two log-normals is superior to the other parametric models and has proven to be very flexible in capturing commonly observed characteristics of the underlying financial assets, such as asymmetries and “fat-tails” in implied probability distribution.

Suggested Citation

  • Josip Arneric & Zdravka Aljinovic & Tea Poklepovic, 2015. "Extraction of market expectations from risk-neutral density," Zbornik radova Ekonomskog fakulteta u Rijeci/Proceedings of Rijeka Faculty of Economics, University of Rijeka, Faculty of Economics and Business, vol. 33(2), pages 235-256.
    • Handle: RePEc:rfe:zbefri:v:33:y:2015:i:2:p:235-256
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    References listed on IDEAS

    as
    1. Bødskov Andersen, Allan & Wagener, Tom, 2002. "Extracting risk neutral probability densities by fitting implied volatility smiles: some methodological points and an application to the 3M Euribor futures option prices," Working Paper Series 198, European Central Bank.
    2. Bookstaber, Richard M & McDonald, James B, 1987. "A General Distribution for Describing Security Price Returns," The Journal of Business, University of Chicago Press, vol. 60(3), pages 401-424, July.
    3. Bhupinder Bahra, 1997. "Implied risk-neutral probability density functions from option prices: theory and application," Bank of England working papers 66, Bank of England.
    4. 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.
    5. Banz, Rolf W & Miller, Merton H, 1978. "Prices for State-contingent Claims: Some Estimates and Applications," The Journal of Business, University of Chicago Press, vol. 51(4), pages 653-672, October.
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    Cited by:

    1. Fabien Le Floc’h & Cornelis W. Oosterlee, 2019. "Model-Free Stochastic Collocation for an Arbitrage-Free Implied Volatility, Part II," Risks, MDPI, vol. 7(1), pages 1-21, March.

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    More about this item

    Keywords

    market expectation; risk-neutral density; mixture of log-normals; Black-Scholes Merton; generalized beta; maturity horizon; DAX index options;
    All these keywords.

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C58 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Financial Econometrics
    • G1 - Financial Economics - - General Financial Markets

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