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Zero bound, option-implied PDFs, and term structure models

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  • Don H. Kim

Abstract

This paper points out that several known ways of modeling non-negative nominal interest rates lead to different implications for the risk-neutral distribution of the short rate that can be checked with options data. In particular, Black's boundary models ("interest rates as options") imply a probability density function (pdf) that contains a Dirac delta function and a cumulative distribution function (cdf) that is nonzero at the zero boundary, while models like the CIR and positive-definite quadratic-Gaussian (QG) models have a zero cdf at the boundary. Eurodollar futures options data are found to favor Black's boundary models: the CIR/QG models, even multifactor versions, have difficulty capturing option prices accurately not only in low interest rate environments but also in higher interest rate environments, and data in early 2008 provide an almost tangible signature of the Dirac delta function in Black's boundary pdf models. Options data also contradict the prediction of well-known models whose cdf is zero at the zero boundary, namely that the risk-neutral pdf is always positively skewed.

Suggested Citation

  • Don H. Kim, 2008. "Zero bound, option-implied PDFs, and term structure models," Finance and Economics Discussion Series 2008-31, Board of Governors of the Federal Reserve System (U.S.).
  • Handle: RePEc:fip:fedgfe:2008-31
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    References listed on IDEAS

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    1. Ait-Sahalia, Yacine, 1996. "Testing Continuous-Time Models of the Spot Interest Rate," Review of Financial Studies, Society for Financial Studies, vol. 9(2), pages 385-426.
    2. Black, Fischer, 1995. " Interest Rates as Options," Journal of Finance, American Finance Association, vol. 50(5), pages 1371-1376, December.
    3. John C. Cox & Jonathan E. Ingersoll Jr. & Stephen A. Ross, 2005. "A Theory Of The Term Structure Of Interest Rates," World Scientific Book Chapters,in: Theory Of Valuation, chapter 5, pages 129-164 World Scientific Publishing Co. Pte. Ltd..
    4. Dong-Hyun Ahn & Robert F. Dittmar, 2002. "Quadratic Term Structure Models: Theory and Evidence," Review of Financial Studies, Society for Financial Studies, vol. 15(1), pages 243-288, March.
    5. Duffie, Darrell & Singleton, Kenneth J, 1997. " An Econometric Model of the Term Structure of Interest-Rate Swap Yields," Journal of Finance, American Finance Association, vol. 52(4), pages 1287-1321, September.
    6. Cecchetti, Stephen G, 1988. "The Case of the Negative Nominal Interest Rates: New Estimates of the Term Structure of Interest Rates during the Great Depression," Journal of Political Economy, University of Chicago Press, vol. 96(6), pages 1111-1141, December.
    7. Breeden, Douglas T & Litzenberger, Robert H, 1978. "Prices of State-contingent Claims Implicit in Option Prices," The Journal of Business, University of Chicago Press, vol. 51(4), pages 621-651, October.
    8. Markus Leippold & Liuren Wu, 2002. "Design and Estimation of Quadratic Term Structure Models," Finance 0207014, EconWPA.
    9. Barone-Adesi, Giovanni & Whaley, Robert E, 1987. " Efficient Analytic Approximation of American Option Values," Journal of Finance, American Finance Association, vol. 42(2), pages 301-320, June.
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    12. Ahn, Dong-Hyun & Gao, Bin, 1999. "A Parametric Nonlinear Model of Term Structure Dynamics," Review of Financial Studies, Society for Financial Studies, vol. 12(4), pages 721-762.
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    Cited by:

    1. Glenn D. Rudebusch, 2010. "Macro-Finance Models Of Interest Rates And The Economy," Manchester School, University of Manchester, vol. 78(s1), pages 25-52, September.
    2. Lemke, Wolfgang & Vladu, Andreea, 2015. "A Shadow-Rate Term Structure Model for the Euro Area," Annual Conference 2015 (Muenster): Economic Development - Theory and Policy 113159, Verein für Socialpolitik / German Economic Association.
    3. repec:bfr:rueban:2017:52 is not listed on IDEAS
    4. Monfort, Alain & Pegoraro, Fulvio & Renne, Jean-Paul & Roussellet, Guillaume, 2017. "Staying at zero with affine processes: An application to term structure modelling," Journal of Econometrics, Elsevier, vol. 201(2), pages 348-366.

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    Keywords

    Interest rates ; Econometric models;

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