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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. Rubinstein, Mark, 1994. " Implied Binomial Trees," Journal of Finance, American Finance Association, vol. 49(3), pages 771-818, July.
  2. McDonald, James B. & Xu, Yexiao J., 1995. "A generalization of the beta distribution with applications," Journal of Econometrics, Elsevier, vol. 69(2), pages 427-428, October.
  3. 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.
  4. Mark Rubinstein., 1994. "Implied Binomial Trees," Research Program in Finance Working Papers RPF-232, University of California at Berkeley.
  5. Driessen, J.J.A.G. & Klaassen, P. & Melenberg, B., 2000. "The Performance of Multi-Factor Term Structure Models for Pricing and Hedging Caps and Swaptions," Discussion Paper 2000-93, Tilburg University, Center for Economic Research.
  6. Jackwerth, Jens Carsten, 1999. "Option Implied Risk-Neutral Distributions and Implied Binomial Trees: A Literature Review," MPRA Paper 11634, University Library of Munich, Germany.
  7. 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.
  8. 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.
  9. Black, Fischer, 1976. "The pricing of commodity contracts," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 167-179.
  10. 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.
  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. 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.
  13. 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.
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Cited by:
  1. repec:zbw:grirej:68733 is not listed on IDEAS
  2. Louis Eeckhoudt & Harris Schlesinger, 2008. "Changes in Risk and the Demand for Saving," CESifo Working Paper Series 2388, CESifo Group Munich.
  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. José Renato Haas Ornelas & José Santiago Fajardo Barbachan & Aquiles Rocha de Farias, 2012. "Estimating Relative Risk Aversion, Risk-Neutral and Real-World Densities using Brazilian Real Currency Options," Working Papers Series 269, Central Bank of Brazil, Research Department.
  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.

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