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Estimating the Risk Neutral Probability Density Functions Natural Spline versus Hypergeometric Approach Using European Style Options

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  • Ruijun Bu

    ()
    (Management School, University of Liverpool, UK)

  • Kaddour Hadri

    (Management School, University of Liverpool, UK)

Abstract

This paper examines the ability of two recent approaches to estimate implied risk neutral probability density functions (RNDs) - the smoothed implied volatility smile method (SML) and the density functionals based on the confluent hypergeometric functions (DFCH) from the prices of European-style options. A Monte Carlo experiment is conducted to compare the capability of the two techniques to recover simulated distributions based on Heston's (1993) stochastic volatility model. The paper investigates the accuracy and stability of the two methods via two categories of estimated summary statistics. We find that while the SML method outperforms the DFCH method for the summary statistics which are sensitive to the tails of the distribution, the DFCH method dominates the SML method for the summary statistics that are less sensitive to outliers. Due to the lack of observations in the tails when estimating RNDs, we feel that the most appropriate measures for comparing the two methods are the ones less sensitive to extreme values. In this sense, the DFCH method seems to be more appealing. We also apply the two methods via an empirical application.

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Bibliographic Info

Paper provided by University of Liverpool Management School in its series Research Papers with number 200510.

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Length: 42 pages
Date of creation: 2005
Date of revision:
Handle: RePEc:liv:livedp:200510

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Postal: Management School University of Liverpool, Chatham Street, Liverpool, L69 7ZH, Great Britain
Phone: +44(0)151 795 3108
Fax: +44(0)151 795 3004
Web page: http://www.liv.ac.uk/management/
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Related research

Keywords: Risk-neutral density; Smoothed implied volatility smile; Point Conversion; Natural spline; Hypergeometric functions;

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References

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