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

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  • Frank Fabozzi
  • Radu Tunaru
  • George Albota

Abstract

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.

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Bibliographic Info

Article provided by Taylor & Francis Journals in its journal Quantitative Finance.

Volume (Year): 9 (2009)
Issue (Month): 1 ()
Pages: 55-70

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Handle: RePEc:taf:quantf:v:9:y:2009:i:1:p:55-70

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Related research

Keywords: Risk-neutral density; Real-world density; Power utility function; Generalized beta distribution; Generalized gamma distribution; Burr3 distribution; Caps and floors;

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Cited by:
  1. 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.
  2. 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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