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Extracting Probabilistic Information from the Prices of Interest Rate Options: Tests of Distributional Assumptions

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  • Kabir K. Dutta

    (Federal Reserve Bank of Boston)

  • David F. Babbel

    (Wharton School, University of Pennsylvania)

Abstract

Return distributions in general and interest rates in particular have been observed to exhibit skewness and kurtosis that cannot be explained by the (log)normal distribution. Using g-and-h distribution we derived a closed-form option pricing formula for pricing European options. We measured its performance using interest rate cap data and compared it with the option prices based on the lognormal, Burr-3, Weibull, and GB2 distributions. We observed that the g-and-h distribution exhibited a high degree of accuracy in pricing options, much better than those other distributions in extracting probabilistic information from the option market.

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Bibliographic Info

Article provided by University of Chicago Press in its journal Journal of Business.

Volume (Year): 78 (2005)
Issue (Month): 3 (May)
Pages: 841-870

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Handle: RePEc:ucp:jnlbus:v:78:y:2005:i:3:p:841-870

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Web page: http://www.journals.uchicago.edu/JB/

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  1. Badrinath, S G & Chatterjee, Sangit, 1988. "On Measuring Skewness and Elongation in Common Stock Return Distributions: The Case of the Market Index," The Journal of Business, University of Chicago Press, vol. 61(4), pages 451-72, October.
  2. Jondeau, Eric & Rockinger, Michael, 1998. "Reading the Smile: The Message Conveyed by Methods which Infer Risk Neutral Densities," CEPR Discussion Papers 2009, C.E.P.R. Discussion Papers.
  3. Bookstaber, Richard M & McDonald, James B, 1987. "A General Distribution for Describing Security Price Returns," The Journal of Business, University of Chicago Press, vol. 60(3), pages 401-24, July.
  4. Patrick Navatte & Christophe Villa, 2000. "The information content of implied volatility, skewness and kurtosis: empirical evidence from long-term CAC 40 options," European Financial Management, European Financial Management Association, vol. 6(1), pages 41-56.
  5. Black, Fischer, 1976. "The pricing of commodity contracts," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 167-179.
  6. Kabir K. Dutta & David F. Babbel, 2002. "On Measuring Skewness and Kurtosis in Short Rate Distributions: The Case of the US Dollar London Inter Bank Offer Rates," Center for Financial Institutions Working Papers 02-25, Wharton School Center for Financial Institutions, University of Pennsylvania.
  7. McDonald, James B. & Xu, Yexiao J., 1995. "A generalization of the beta distribution with applications," Journal of Econometrics, Elsevier, vol. 66(1-2), pages 133-152.
  8. Jackwerth, Jens Carsten, 1999. "Option Implied Risk-Neutral Distributions and Implied Binomial Trees: A Literature Review," MPRA Paper 11634, University Library of Munich, Germany.
  9. Mark Rubinstein., 1994. "Implied Binomial Trees," Research Program in Finance Working Papers RPF-232, University of California at Berkeley.
  10. Driessen, Joost & Klaassen, Pieter & Melenberg, Bertrand, 2003. "The Performance of Multi-Factor Term Structure Models for Pricing and Hedging Caps and Swaptions," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 38(03), pages 635-672, September.
  11. Badrinath, S G & Chatterjee, Sangit, 1991. "A Data-Analytic Look at Skewness and Elongation in Common-Stock-Return Distributions," Journal of Business & Economic Statistics, American Statistical Association, vol. 9(2), pages 223-33, April.
  12. Wolfgang Bühler & Marliese Uhrig-Homburg & Ulrich Walter & Thomas Weber, 1999. "An Empirical Comparison of Forward-Rate and Spot-Rate Models for Valuing Interest-Rate Options," Journal of Finance, American Finance Association, vol. 54(1), pages 269-305, 02.
  13. Rubinstein, Mark, 1994. " Implied Binomial Trees," Journal of Finance, American Finance Association, vol. 49(3), pages 771-818, July.
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Cited by:
  1. Eeckhoudt, Louis & Schlesinger, Harris, 2008. "Changes in risk and the demand for saving," Journal of Monetary Economics, Elsevier, vol. 55(7), pages 1329-1336, October.
  2. Xu, Yihuan & Iglewicz, Boris & Chervoneva, Inna, 2014. "Robust estimation of the parameters of g-and-h distributions, with applications to outlier detection," Computational Statistics & Data Analysis, Elsevier, vol. 75(C), pages 66-80.
  3. Kabir K. Dutta & David F. Babbel, 2002. "On Measuring Skewness and Kurtosis in Short Rate Distributions: The Case of the US Dollar London Inter Bank Offer Rates," Center for Financial Institutions Working Papers 02-25, Wharton School Center for Financial Institutions, University of Pennsylvania.
  4. Albrecht, Peter & Schwake, Edmund & Winter, Peter, 2007. "Quantifizierung operationeller Risiken: Der Loss Distribution Approach," German Risk and Insurance Review (GRIR), University of Cologne, Department of Risk Management and Insurance, vol. 3(1), pages 1-45.
  5. Fischer, Matthias J., 2006. "Generalized Tukey-type distributions with application to financial and teletraffic data," Discussion Papers 72/2006, Friedrich-Alexander-University Erlangen-Nuremberg, Chair of Statistics and Econometrics.
  6. Andreas A. Jobst, 2007. "It's all in the data – consistent operational risk measurement and regulation," Journal of Financial Regulation and Compliance, Emerald Group Publishing, vol. 15(4), pages 423-449, November.
  7. Ornelas, Jose Renato Haas & Barbachan, José Fajardo & Farias, Aquiles Rocha de, 2012. "Estimating Relative Risk Aversion, Risk-Neutral and Real-World Densities using Brazilian Real Currency Options," EBAPE Working Papers 1, School of Public and Business Administration, Getulio Vargas Foundation (Brazil).

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