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Nonparametric Modeling of U.S. Interest Rate Term Structure Dynamics and Implications on the Prices of Derivative Securities

Published online by Cambridge University Press:  06 April 2009

George J. Jiang
George J. Jiang
Affiliation:
Faculty of Business and Economics, University of Groningen, Room 232 – WSN, PO Box 800, 9700 AV Groningen, The Netherlands.
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Abstract

This paper develops a nonparametric model of interest rate term structure dynamics based on a spot rate process that permits only positive interest rates and a market price of interest rate risk that precludes arbitrage opportunities. Both the spot rate process and the market price of interest rate risk are nonparametrically specified so that the model allows for maximal flexibility in fitting into the data. Marginal density of interest rates and historical term structure data are exploited to provide robust estimation of the nonparametric term structure model. The model is implemented using U.S. data, and the estimation results are compared to those in the available literature. Empirical results not only provide strong evidence that most traditional spot rate models and market prices of interest rate risk are misspecified, but also confirm that the nonparametric model generates significantly different term structures and prices of common derivatives.

Type
Research Article
Information
Journal of Financial and Quantitative Analysis , Volume 33 , Issue 4 , December 1998 , pp. 465 - 497
Copyright
Copyright © School of Business Administration, University of Washington 1998

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References

Aït-Sahalia, Y. “Nonparametric Pricing of Interest Rate Derivative Securities”. Econometrica, 64 (1996a), 527–560.CrossRefGoogle Scholar
Aït-Sahalia, Y. “Testing Continuous-Time Models of the Spot Interest Rate”. Review of Financial Studies, 9 (1996b), 385–426.CrossRefGoogle Scholar
Backus, D. K.; Foresi, S.; and Zin, S. E.. “Arbitrage Opportunities in Arbitrage-Free Models of Bond Pricing”. Working Paper, New York Univ. (1995).CrossRefGoogle Scholar
Banon, G. “Nonparametric Identification for Diffusion Processes”. S.I.A.M. Journal of Control and Optimization, 16 (1978), 380–395.CrossRefGoogle Scholar
Banon, G., and Nguyen, H. T.. “Recursive Estimation in Diffusion Models”. S.I.A.M. Journal of Control and Optimization, 19 (1981), 676–685.CrossRefGoogle Scholar
Black, F. “Interest Rates as Options”. Journal of Finance, 50 (1995), 1371–1376.CrossRefGoogle Scholar
Black, F.; Derman, E.; and Toy, W.. “A One Factor Model of Interest Rates and its Application to Treasury Bond Options”. Financial Analysts Journal (01–02 1990), 33–39.CrossRefGoogle Scholar
Black, F., and Karasinski, P.. “Bond and Option Pricing when Short Rates are Lognormal”. Financial Analysts Journal (07/08 1991), 52–59.CrossRefGoogle Scholar
Boyle, P.; Broadie, M.; and Glasserman, P.. “Monte Carlo Methods for Security Pricing”. Journal of Economic Dynamics and Control, 21 (06 1997), 1267–1321.CrossRefGoogle Scholar
Brennan, M. J., and Schwartz, E. S.. “A Continuous Time Approach to the Pricing of Bonds”. Journal of Banking and Finance, 3 (1979), 133–155.CrossRefGoogle Scholar
Brown, B. M., and Hewitt, J. I.. “Asymptotic Likelihood Theory for Diffusion Process”. Journal of Applied Probability, 12 (1985), 228–238.CrossRefGoogle Scholar
Brown, S. J., and Dybvig, P. H.. “The Empirical Implications of the Cox, Ingersoll, and Ross Theory of the Term Structure of Interest Rates”. Journal of Finance, 41 (1986), 617–632.CrossRefGoogle Scholar
Broze, L.; Scaillet, O.; and Zakoïn, J.. “Testing for Continuous-Time Models of Short-Term Interest Rate”. Journal of Empirical Finance, 2 (1995), 199–223.Google Scholar
Chan, K. C.; Karolyi, G. A.; Longstaff, F. A.; and Sanders, A. B.. “An Empirical Comparison of Alternative Models of the Short-Term Interest Rate”. Journal of Finance, 47 (1992), 1209–1227.Google Scholar
Conley, T. G.; Hansen, L. P.; Luttmer, E. G. J.; and Scheinkman, J. A.. “Short-Term Interest Rates as Subordinated Diffusions”. Review of Financial Studies, 10 (1997), 525–577.CrossRefGoogle Scholar
Constantinides, G. M. “A Theory of the Nominal Term Structure of Interest Rates”. Review of Financial Studies, 5 (1992), 531–552.CrossRefGoogle Scholar
Courtadon, G. “The Pricing of Options on Default Free Bonds”. Journal of Financial and Quantitative Analysis, 17 (1982), 75–100.CrossRefGoogle Scholar
Cox, J. C. “Notes on Option Pricing I: Constant Elasticity of Variance Diffusion”. Working Paper, Stanford Univ. (1975).Google Scholar
Cox, J. C.; Ingersoll, J. E.; and Ross, S. A.. “An Analysis of Variable Rate Loan Contracts”. Journal of Finance, 35 (1980), 389–403.CrossRefGoogle Scholar
Cox, J. C.; Ingersoll, J. E.; and Ross, S. A.. “A Theory of the Term Structure of Interest Rates”. Econometrica, 53 (1985), 385–407.CrossRefGoogle Scholar
Dacunha-Castelle, D., and Florens-Zmirou, D.. “Estimation of the Coefficient of a Diffusion from Discrete Observations”. Stochastics, 19 (1986), 263–284.CrossRefGoogle Scholar
Dohnal, G. “On Estimating the Diffusion Coefficient”. Journal of Applied Probability, 24 (1987), 105–114.CrossRefGoogle Scholar
Dorogovcev, A. J. “The Consistency of an Estimate of a Parameter of a Stochastic Differential Equation”. Theoretical Probability and Mathematical Statistics, 10 (1976), 73–82.Google Scholar
Dothan, L. U. “On the Term Structure of Interest Rates”. Journal of Financial Economics, 6 (1978), 59–69.CrossRefGoogle Scholar
Duffie, D.Security Markets: Stochastic Models. Boston, MA: Academic Press (1988).Google Scholar
Duffie, D.Dynamic Asset Pricing Theory. Princeton, NJ: Princeton Univ. (1992).Google Scholar
Duffie, D., and Kan, R.. “A Yield Curve Model of Interest Rates”. Working Paper, Stanford Univ. (1993).Google Scholar
Duffie, D., and Singleton, K. J.. “Simulated Moments Estimation of Markov Models for Asset Prices”. Econometrica, 61 (1993), 929–952.CrossRefGoogle Scholar
Fama, E. F. “Term Premiums in Bond Returns”. Journal of Financial Economics, 13 (1984), 529–546.CrossRefGoogle Scholar
Fama, E. F., and Bliss, R. R.. “The Information in Long-Maturity Forward Rates”. American Economic Review, 77 (1987), 680–692.Google Scholar
Friedman, A.Partial Differential Equations of Parabolic Type. Englewood Cliffs, NJ: Prentice-Hall (1964).Google Scholar
Florens-Zmirou, D. “On Estimating the Diffusion Coefficient from Discrete Observations”. Journal of Applied Probability, 30 (1993), 790–804.CrossRefGoogle Scholar
Gallant, A. R., and Tauchen, G.. “Which Moments to Match”. Econometric Theory, 12 (1996), 657–681.CrossRefGoogle Scholar
Geman, S. A. “On a Common Sense Estimator for the Drift of a Diffusion”. Pattern Analysis #79, Division of Applied Mathematics, Brown Univ., Providence, RI (1979).Google Scholar
Genon-Catalot, V. “Maximum Contrast Estimation for Diffusion Processes from Discrete Observations”. Statistics, 21 (1990), 99–116.CrossRefGoogle Scholar
Genon-Catalot, V., and Jacod, J.. “On the Estimation of the Diffusion Coefficient for Multidimensional Diffusion Processes”. Univ. of Marne-La-Vallée, France (1993).Google Scholar
Genon-Catalot, V.; Laredo, C.; and Picard, D.. “Nonparametric Estimation of the Diffusion Coefficient by Wavelets Methods”. Scandinavian Journal of Statistics, 19 (1992), 317–335.Google Scholar
Gibbons, M. R., and Ramaswamy, K.. “A Test of the Cox, Ingersoll and Ross Model of the Term Structure”. Review of Financial Studies, 6 (1993), 619–658.CrossRefGoogle Scholar
Gouriéroux, C.; Monfort, A.; and Renault, E.. “Indirect Inference”. Journal of Applied Econometrics, 8 (1993), S85–S118.Google Scholar
Hansen, L. P. “Large Sample Properties of Generalized Method of Moments Estimators”. Econometrica, 50 (1982), 1029–1054.CrossRefGoogle Scholar
Hansen, L. P., and Scheinkman, J. A.. “Back to the Future: Generating Moment Implications for Continuous-Time Markov Processes”. Econometrica, 63 (1995), 767–804.CrossRefGoogle Scholar
Härdle, W., and Vieu, P.. “Nonparametric Prediction by the Kernel Method”. Mimeo, Rheinishe-Friedrich-Wilhelms Univ. (1987).Google Scholar
Harvey, A. C.Time Series Models, 2nd ed.Cambridge, MA: The MIT Press (1993).Google Scholar
Heath, D. C.; Jarrow, R. A.; and Morton, A.. “Bond Pricing and the Term Structure of Interest Rates: A New Methodology for Contingent Claims Valuation”. Econometrica, 60 (1992), 77–105.CrossRefGoogle Scholar
Ho, T. S. Y., and Lee, S. B.. “Term Structure Movements and Pricing Interest Rate Contingent Claims”. Journal of Finance, 41 (1986), 1011–1029.CrossRefGoogle Scholar
Hull, J., and White, A.. “Pricing Interest-Rate-Derivative Securities”. Review of Financial Studies, 3 (1990), 573–92.CrossRefGoogle Scholar
Hull, J., and White, A.. “One Factor Interest Rate Models and the Valuation of Interest Rate Derivative Securities”. Journal of Financial and Quantitative Analysis, 28 (1993), 235–254.CrossRefGoogle Scholar
Ingersoll, J. E. Jr. Theory of Financial Decision Making. Baltimore, MD: Rowman and Littlefield (1987).Google Scholar
Jacod, J. “Random Sampling in Estimation Problems for Continuous Gaussian Processes with Independent Increments”. Stochastic Processes and Their Applications, 44 (1993), 181–204.CrossRefGoogle Scholar
Jamshidian, F. “The Preference-Free Determination of Bond and Option Prices from the Spot Interest Rate”. Advances in Futures and Options Research, 4 (1990), 51–67.Google Scholar
Jamshidian, F. “Bond and Option Valuation in the Gaussian Interest Model”. Research in Finance, 9 (1991), 131–170.Google Scholar
Jiang, G. J. “Nonparametric Estimation of Diffusion Processes and Applications in Pricing Derivative Securities”. Ph.D. Diss., Univ. of Western Ontario, Canada (1996).Google Scholar
Jiang, G. J., and Knight, J. L.. “A Nonparametric Approach to the Estimation of Diffusion Processes”. Econometric Theory (1995).Google Scholar
Jiang, G. J., and Knight, J. L.. “Parametric versus Nonparametric Estimation of Diffusion Processes—A Monte Carlo Comparison”. MimeoUniv. of Western Ontario (1996).Google Scholar
Karlin, S., and Taylor, H. M.. A Second Course in Stochastic Processes. New York, NY: Academic Press (1981).Google Scholar
Kasonga, R. A. “The Consistency of a Non-Linear Least Squares Estimator from Diffusion Processes”. Stochastic Processes and Their Applications, 30 (1988), 263–275.CrossRefGoogle Scholar
Kim, T. Y., and Cox, D. D.. “Bandwidth Selection in Kernel Smoothing of Time Series”. Journal of Time Series Analysis, 17 (1996), 49–63.CrossRefGoogle Scholar
Künsch, H. R. “The Jackknife and the Bootstrap for General Stationary Observations”. Annals of Statistics, 17 (1989), 1217–1241.CrossRefGoogle Scholar
Kutoyants, Y.Parameter Estimation for Stochastic Processes. Heldermann (1984).Google Scholar
Lanska, V. “Minimum Contrast Estimation in Diffusion Processes”. Journal of Applied Probability, 16 (1979), 65–75.CrossRefGoogle Scholar
Laredo, C. “A Sufficient Condition for Asymptotic Sufficiency of Incomplete Observations of a Diffusion Process”. Annals of Statistics, 18 (1990), 1158–1171.CrossRefGoogle Scholar
Lo, A. W. “Maximum Likelihood Estimation of Generalized Itô Processes with Discretely Sampled Data”. Econometric Theory, 4 (1988), 231–247.CrossRefGoogle Scholar
Lo, A. W., and Wang, J.. “Implementing Option Pricing Models when Asset Returns are Predictable”. Journal of Finance, 50 (1995), 87–129.CrossRefGoogle Scholar
Marsh, T. A., and Rosenfeld, E. R.. “Stochastic Processes for Interest Rates and Equilibrium Bond Prices”. Journal of Finance, 38 (1983), 635–646.CrossRefGoogle Scholar
Merton, R. C. “Theory of Rational Option Pricing”. Bell Journal of Economics and Management Science, 4 (1973), 141–183.Google Scholar
Merton, R. C. “On Estimating the Expected Return on the Market: An Exploratory Investigation”. Journal of Financial Economics, 8 (1980), 323–361.CrossRefGoogle Scholar
Monfort, A. “A Reappraisal of Misspecified Econometric Models”. Econometric Theory, 12 (1996), 597–619.CrossRefGoogle Scholar
Pedersen, A. R. “Consistency and Asymptotic Normality of an Approximate Maximum Likelihood Estimator for Discretely Observed Diffusion Processes”. Bernoulli, 1 (1995), 257–279.CrossRefGoogle Scholar
Pham Dinh, T. D. “Nonparametric Estimator of the Drift Coefficient in the Diffusion Equation”. Math. Operations Statist. Ser Statist., 12 (1981), 61–73.Google Scholar
Prohorov, Y. V. and Rozanov, Y. A.. Probability Theory. Translated by Krickeberg, K. and Urmitzer, H.. New York, NY: Springer-Verlag (1969).CrossRefGoogle Scholar
Rice, J. A., and Silverman, B. W.. “Estimating the Mean and Covariance Structure Nonparametrically when the Data are Curves”. Journal of the Royal Statistical Society B, 53 (1991), 233–244.Google Scholar
Ronn, E., and Wadhwa, P.. “On the Relationship between Expected Returns and Implied Volatility of Interest Rate-dependent Securities”. Working Paper, Univ. of Texas at Austin (1995).Google Scholar
Scott, D. W.Multivariate Density Estimation: Theory, Practice and Visualization. New York, NY: John Wiley (1992).CrossRefGoogle Scholar
Stanton, R. “A Nonparametric Model of Term Structure Dynamics and the Market Price of Interest Rate Risk”. Journal of Finance, 52 (1997), 1973–2002.CrossRefGoogle Scholar
Talay, D. “Probabilistic Numerical Methods for PDEs”. In Probabilistic Methods for Nonlinear Partial Differential Equations, Talay, D. and Tubaro, L. eds. Berlin, Germany: Springer (1996).Google Scholar
Vasicek, O. “An Equilibrium Characterization of the Term Structure”. Journal of Financial Economics, 5 (1977), 177–188.CrossRefGoogle Scholar
Wehrly, T. E., and Hart, J. D.. “Bandwidth Selection for Kernel Estimation of Growth Curves with Correlated Errors (abstract)”. Institute of Mathematical Statistics Bulletin, 17 (1988), 236.Google Scholar