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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.

Suggested Citation

  • Kabir K. Dutta & David F. Babbel, 2005. "Extracting Probabilistic Information from the Prices of Interest Rate Options: Tests of Distributional Assumptions," The Journal of Business, University of Chicago Press, vol. 78(3), pages 841-870, May.
    • Handle: RePEc:ucp:jnlbus:v:78:y:2005:i:3:p:841-870
    DOI: 10.1086/429646
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    14. 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.
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    1. David Mauler & James McDonald, 2015. "Option Pricing and Distribution Characteristics," Computational Economics, Springer;Society for Computational Economics, vol. 45(4), pages 579-595, April.
    2. 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.
    3. 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.
    4. 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.
    5. Ornelas, José Renato Haas & Barbachan, José Santiago 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, FGV EBAPE - Escola Brasileira de Administração Pública e de Empresas (Brazil).
    6. Sanjiv Jaggia & Alison Kelly-Hawke, 2009. "Modelling skewness and elongation in financial returns: the case of exchange-traded funds," Applied Financial Economics, Taylor & Francis Journals, vol. 19(16), pages 1305-1316.
    7. 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.
    8. Marcos Massaki Abe & Eui Jung Chang & Benjamin Miranda Tabak, 2007. "Forecasting Exchange Rate Density Using Parametric Models: the Case of Brazil," Brazilian Review of Finance, Brazilian Society of Finance, vol. 5(1), pages 29-39.
    9. 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.
    10. 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 Limited, vol. 15(4), pages 423-449, November.
    11. José María Sarabia & Vanesa Jordá & Faustino Prieto & Montserrat Guillén, 2020. "Multivariate Classes of GB2 Distributions with Applications," Mathematics, MDPI, vol. 9(1), pages 1-21, December.
    12. José Renato Haas Ornelas & Marcelo Yoshio Takami, 2011. "Recovering Risk-Neutral Densities from Brazilian Interest Rate Options," Brazilian Review of Finance, Brazilian Society of Finance, vol. 9(1), pages 9-26.

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