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Testing the stability of implied probability density functions

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  • Robert R Bliss
  • Nikolaos Panigirtzoglou

Abstract

Implied probability density functions (PDFs) estimated from cross-sections of observed option prices are gaining increasing attention amongst academics and practitioners. To date, however, little attention has been paid to the robustness of these estimates or to the confidence that users can place in the summary statistics (for example the skewness or the 99th percentile) derived from fitted PDFs. This paper begins to address these questions by examining the absolute and relative robustness of two of the most common methods for estimating implied PDFs - the double-lognormal approximating function and the smoothed implied volatility smile methods. The changes resulting from randomly perturbing quoted prices by no more than a half tick provide a lower bound on the confidence intervals of the summary statistics derived from the estimated PDFs. Tests are conducted using options contracts tied to short sterling futures and the FTSE 100 index - both trading on the London International Financial Futures and Options Exchange. The tests show that the smoothed implied volatility smile method dominates the double-lognormal as a technique for estimating implied PDFs when average goodness-of-fits for both methods are comparable.

Suggested Citation

  • Robert R Bliss & Nikolaos Panigirtzoglou, 2000. "Testing the stability of implied probability density functions," Bank of England working papers 114, Bank of England.
  • Handle: RePEc:boe:boeewp:114
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    References listed on IDEAS

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    Cited by:

    1. Guillermo Benavides Perales & Israel Felipe Mora Cuevas, 2008. "Parametric vs. non-parametric methods for estimating option implied risk-neutral densities: the case of the exchange rate Mexican peso – US dollar," Ensayos Revista de Economia, Universidad Autonoma de Nuevo Leon, Facultad de Economia, vol. 0(1), pages 33-52, May.
    2. Morel, Christophe & Teïletche, Jérôme, 2008. "Do interventions in foreign exchange markets modify investors' expectations? The experience of Japan between 1992 and 2004," Journal of Empirical Finance, Elsevier, vol. 15(2), pages 211-231, March.
    3. repec:dau:papers:123456789/12956 is not listed on IDEAS
    4. Alexandre Ziegler, 2002. "Why does Implied Risk Aversion Smile?," FAME Research Paper Series rp47, International Center for Financial Asset Management and Engineering.
    5. Alexandre Ziegler, 2007. "Why Does Implied Risk Aversion Smile?," The Review of Financial Studies, Society for Financial Studies, vol. 20(3), pages 859-904.
    6. Martin Cincibuch, 2002. "Distributions Implied by Exchange Traded Options: A Ghost’s Smile?," CERGE-EI Working Papers wp200, The Center for Economic Research and Graduate Education - Economics Institute, Prague.
    7. Guillermo Benavides, 2011. "Central Bank Exchange Rate Interventions and Market Expectations: The Case of México During the Financial Crisis 2008-2009," Remef - Revista Mexicana de Economía y Finanzas Nueva Época REMEF (The Mexican Journal of Economics and Finance), Instituto Mexicano de Ejecutivos de Finanzas, IMEF, vol. 6(1), pages 5-27, Julio-Dic.
    8. Aron Gereben, 2002. "Extracting market expectations from option prices: an application to over-the-counter New Zealand dollar options," Reserve Bank of New Zealand Discussion Paper Series DP2002/04, Reserve Bank of New Zealand.
    9. Guillermo Benavides Perales, 2012. "Central Bank Exchange Rate Interventions and Market Expectations: The Case of México During the Financial Crisis 2008-2009," Remef - The Mexican Journal of Economics and Finance, Instituto Mexicano de Ejecutivos de Finanzas. Remef, October.
    10. Marie Briere, 2006. "Market Reactions to Central Bank Communication Policies :Reading Interest Rate Options Smiles," Working Papers CEB 38, ULB -- Universite Libre de Bruxelles.

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