Zero bound, option-implied PDFs, and term structure models
AbstractThis 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.
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Bibliographic InfoPaper provided by Board of Governors of the Federal Reserve System (U.S.) in its series Finance and Economics Discussion Series with number 2008-31.
Date of creation: 2008
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- Black, Fischer, 1976. "The pricing of commodity contracts," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 167-179.
- Yacine Ait-Sahalia, 1995.
"Testing Continuous-Time Models of the Spot Interest Rate,"
NBER Working Papers
5346, National Bureau of Economic Research, Inc.
- 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.
- 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.
- Markus Leippold & Liuren Wu, 2002. "Design and Estimation of Quadratic Term Structure Models," Finance 0207014, EconWPA.
- Longstaff, Francis A., 1992. "Multiple equilibria and term structure models," Journal of Financial Economics, Elsevier, vol. 32(3), pages 333-344, December.
- Barone-Adesi, Giovanni & Whaley, Robert E, 1987. " Efficient Analytic Approximation of American Option Values," Journal of Finance, American Finance Association, vol. 42(2), pages 301-20, June.
- 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.
- Black, Fischer, 1995. " Interest Rates as Options," Journal of Finance, American Finance Association, vol. 50(5), pages 1371-76, December.
- 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 721-62.
- 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 1111-41, December.
- Stephen G. Cecchetti, 1989. "The Case of the Negative Nominal Interest Rates: New Estimates of the Term Structure of Interest Rates During the Great Depression," NBER Working Papers 2472, National Bureau of Economic Research, Inc.
- Cox, John C & Ingersoll, Jonathan E, Jr & Ross, Stephen A, 1985. "A Theory of the Term Structure of Interest Rates," Econometrica, Econometric Society, vol. 53(2), pages 385-407, March.
- Glenn D. Rudebusch, 2010.
"Macro-finance models of interest rates and the economy,"
Working Paper Series
2010-01, Federal Reserve Bank of San Francisco.
- Glenn D. Rudebusch, 2010. "Macro-Finance Models Of Interest Rates And The Economy," Manchester School, University of Manchester, vol. 78(s1), pages 25-52, 09.
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