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Testing the stability of implied probability density functions

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Author Info
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.

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Paper provided by Bank of England in its series Bank of England working papers with number 114.

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Handle: RePEc:boe:boeewp:114

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References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  1. Rubinstein, Mark, 1994. " Implied Binomial Trees," Journal of Finance, American Finance Association, vol. 49(3), pages 771-818, July. [Downloadable!] (restricted)
  2. Malz, Allan M., 1996. "Using option prices to estimate realignment probabilities in the European Monetary System: the case of sterling-mark," Journal of International Money and Finance, Elsevier, vol. 15(5), pages 717-748, October. [Downloadable!] (restricted)
  3. Allan M. Malz, 1997. "Option-implied probability distributions and currency excess returns," Staff Reports 32, Federal Reserve Bank of New York. [Downloadable!]
  4. Soderlind, Paul & Svensson, Lars, 1997. "New techniques to extract market expectations from financial instruments," Journal of Monetary Economics, Elsevier, vol. 40(2), pages 383-429, October. [Downloadable!] (restricted)
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  5. Mc Manus, Des, 1999. "The Information Content of Interest Rate Futures Options," Working Papers 99-15, Bank of Canada. [Downloadable!]
  6. Jose M. Campa & P.H. Kevin Chang & Robert L. Reider, 1997. "Implied Exchange Rate Distributions: Evidence from OTC Option Markets," NBER Working Papers 6179, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
    Other versions:
  7. Shiratsuka, Shigenori, 2001. "Information Content of Implied Probability Distributions: Empirical Studies of Japanese Stock Price Index Options," Monetary and Economic Studies, Institute for Monetary and Economic Studies, Bank of Japan, vol. 19(3), pages 143-70, November. [Downloadable!]
  8. Yacine Ait-Sahalia & Andrew W. Lo, 1995. "Nonparametric Estimation of State-Price Densities Implicit in Financial Asset Prices," NBER Working Papers 5351, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
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  9. Peter A. Abken & Dilip B. Madan & Sailesh Ramamurtie, 1996. "Estimation of risk-neutral and statistical densities by Hermite polynomial approximation: with an application to Eurodollar futures options," Working Paper 96-5, Federal Reserve Bank of Atlanta. [Downloadable!]
  10. Breeden, Douglas T & Litzenberger, Robert H, 1978. "Prices of State-contingent Claims Implicit in Option Prices," Journal of Business, University of Chicago Press, vol. 51(4), pages 621-51, October. [Downloadable!] (restricted)
  11. Buchen, Peter W. & Kelly, Michael, 1996. "The Maximum Entropy Distribution of an Asset Inferred from Option Prices," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 31(01), pages 143-159, March. [Downloadable!]
  12. Cox, John C. & Ross, Stephen A., 1976. "The valuation of options for alternative stochastic processes," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 145-166. [Downloadable!] (restricted)
  13. Dilip B. Madan & Frank Milne, 1992. "Contingent Claims Valued and Hedged by Pricing and Investing in a Basis," Working Papers 868, Queen's University, Department of Economics.
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  14. Mark Rubinstein., 1994. "Implied Binomial Trees," Research Program in Finance Working Papers RPF-232, University of California at Berkeley. [Downloadable!]
  15. Michael P. Leahy & Charles P. Thomas, 1996. "The sovereignty option: the Quebec referendum and market views on the Canadian dollar," International Finance Discussion Papers 555, Board of Governors of the Federal Reserve System (U.S.). [Downloadable!]
  16. Daniel F. Waggoner, 1997. "Spline methods for extracting interest rate curves from coupon bond prices," Working Paper 97-10, Federal Reserve Bank of Atlanta. [Downloadable!]
  17. María C. Manzano & Isabel Sánchez, 1998. "Indicators of Short-Term Interest Rate Expectations. The Information Contained in the Options Market," Banco de España Working Papers 9816, Banco de España.
  18. Jackwerth, Jens Carsten & Rubinstein, Mark, 1996. " Recovering Probability Distributions from Option Prices," Journal of Finance, American Finance Association, vol. 51(5), pages 1611-32, December. [Downloadable!] (restricted)
  19. María C. Manzano & Isabel Sánchez, 1998. "Indicators of Short-Term Interest Rate Expectations. The Information Contained in the Options Market," Banco de España Working Papers 9816, Banco de España.
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(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. 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 - Economic Institute, Prague. [Downloadable!]
  2. 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. [Downloadable!]
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