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Estimating risk-neutral density with parametric models in interest rate markets


  • Frank Fabozzi
  • Radu Tunaru
  • George Albota


The departure in modelling terms from the log-normal distribution for option pricing has been largely driven by empirical observations on skewness. In recent years, the Weibull and generalized beta distributions have been used to fit the risk-neutral density from option prices. In this article, we also propose the use of the generalized gamma distribution for recovering the risk-neutral density. In terms of complexity, this distribution, having three parameters, falls between the Weibull and generalized beta distributions. New option pricing formulas for European call and put options are derived under the generalized gamma distribution. The empirical evidence based on a set of interest rate derivatives data indicates that this distribution is capable of producing the same type of performance as the Weibull, generalized beta, and Burr3 distributions. In addition, we analyze the effect of July 2005 bombings in London on interest rate markets under the best fitting distribution. Our results indicate that there was very little impact on the volatility of these markets.

Suggested Citation

  • Frank Fabozzi & Radu Tunaru & George Albota, 2009. "Estimating risk-neutral density with parametric models in interest rate markets," Quantitative Finance, Taylor & Francis Journals, vol. 9(1), pages 55-70.
  • Handle: RePEc:taf:quantf:v:9:y:2009:i:1:p:55-70 DOI: 10.1080/14697680802272045

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    References listed on IDEAS

    1. Challet, Damien & Stinchcombe, Robin, 2001. "Analyzing and modeling 1+1d markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 300(1), pages 285-299.
    2. Eckhard Platen & Martin Schweizer, 1998. "On Feedback Effects from Hedging Derivatives," Mathematical Finance, Wiley Blackwell, vol. 8(1), pages 67-84.
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    5. Jean-Philippe Bouchaud & Marc Mezard & Marc Potters, 2002. "Statistical properties of stock order books: empirical results and models," Science & Finance (CFM) working paper archive 0203511, Science & Finance, Capital Fund Management.
    6. Xiaoyan Ni, Sophie & Pearson, Neil D. & Poteshman, Allen M., 2005. "Stock price clustering on option expiration dates," Journal of Financial Economics, Elsevier, vol. 78(1), pages 49-87, October.
    7. Jean-Philippe Bouchaud & Marc Mezard & Marc Potters, 2002. "Statistical properties of stock order books: empirical results and models," Quantitative Finance, Taylor & Francis Journals, vol. 2(4), pages 251-256.
    8. Giulia Iori & Carl Chiarella, 2002. "A simple microstructure model of double auction markets," Computing in Economics and Finance 2002 44, Society for Computational Economics.
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    Cited by:

    1. David Mauler & James McDonald, 2015. "Option Pricing and Distribution Characteristics," Computational Economics, Springer;Society for Computational Economics, vol. 45(4), pages 579-595, April.
    2. 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 CIEF 015923, UNIVERSIDAD EAFIT.
    3. 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.
    4. Ming Shann Tsai & Shu Ling Chiang, 2016. "The Valuation Model for a Risky Asset When Its Risky Factors Follow Gamma Distributions," International Review of Finance, International Review of Finance Ltd., vol. 16(3), pages 421-444, September.
    5. Maria Grith & Volker Krätschmer, 2010. "Parametric estimation of risk neutral density functions," SFB 649 Discussion Papers SFB649DP2010-045, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.


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