Empirical comparisons in short-term interest rate models using nonparametric methods

Arapis, Manuel and Gao, Jiti (2004): Empirical comparisons in short-term interest rate models using nonparametric methods. Published in: Journal of Financial Econometrics , Vol. 4, No. 1 (1 March 2006): pp. 310-345.

Abstract

This study applies the nonparametric estimation procedure to the diffusion process modeling the dynamics of short-term interest rates. This approach allows us to operate in continuous time, estimating the continuous-time model, despite the use of discrete data. Three methods are proposed. We apply these methods to two important financial data. After selecting an appropriate bandwidth for each dataset, empirical comparisons indicate that the specification of the drift has a considerable impact on the pricing of derivatives through its effect on the diffusion function. In addition, a novel nonparametric test has been proposed for specification of linearity in the drift. Our simulation directs us to reject the null hypothesis of linearity at the 5% significance level for the two financial datasets.

• Item Type: MPRA Paper
• Language: English
• Keywords: Diffusion process; drift function; kernel density estimation; stochastic volatility
• Subjects: C - Mathematical and Quantitative Methods > C1 - Econometric and Statistical Methods and Methodology: General > C14 - Semiparametric and Nonparametric Methods: General

References

Ahn, D.-H., andB. Gao. (1999). ‘‘AParametricNonlinear Model of TermStructure Dynamics.’’ Reviewof Financial Studies12, 721–762.

Aı ̈t-Sahalia, Y.(1996a). ‘‘NonparametricPricingofInterestRateDerivativeSecurities.’’ Econometrica64, 527–560.

Aı ̈t-Sahalia, Y. (1996b). ‘‘TestingContinuous-TimeModelsof theSpot Interest Rate.’’ Reviewof Financial Studies9, 385–426.

Aı ̈t-Sahalia, Y. (1999). ‘‘TransitionDensities for Interest RateandOther Nonlinear Diffusions.’’ Journal of Finance54, 1361–1395.

Arapis, M., andJ. Gao. (2005). ‘‘Nonparametric Kernel EstimationandTestingin Continuous-Time Financial Econometrics.’’ Working paper. Available at www.maths.uwa.edu.au/~jiti/ag05.pdf.

Bandi, F. (2002). ‘‘Short-Term Interest Rate Dynamics: A Spatial Approach.’’ Journal of Financial Economics 65, 73–110.

Bandi, F., and P. Phillips. (2003). ‘‘Fully Nonparametric Estimation of Scalar Diffusion Models.’’ Econometrica 71, 241–283.

Black, F., and M. Scholes. (1973). ‘‘The Pricing of Options and Corporate Liabilities.’’ Journal of Political Economy 3, 637–654.

Brennan, M., and E. Schwartz. (1980). ‘‘A Continuous-Time Approach to the Pricing of Bonds.’’ Journal of Banking and Finance 3, 133–145.

Chan, K., F. Karolyi, F. Longstaff, and A. Sanders. (1992). ‘‘An Empirical Comparison of Alternative Models of the Short-TermInterest Rate.’’ Journal of Finance 47, 1209–1227.

Chapman, D., and N. Pearson. (2000). ‘‘Is the Short Rate Drift Actually Nonlinear?’’ Journal of Finance 54, 355–388.

Chen, S., and J. Gao. (2005). ‘‘On the Use of the Kernel Method for Specification Tests of Diffusion Models.’’ Working paper. Available at www.maths.uwa.edu.au/ ~jiti/cg05.pdf.

Chen, S., W. Ha ̈ rdle, and M. Li. (2003). ‘‘An Empirical Likelihood Goodness-of-Fit Test for Time Series.’’ Journal of the Royal Statistical Society Series B 65, 663–678.

Cox, J., E. Ingersoll, and S. Ross. (1985). ‘‘An Intertemporal General Equilibrium Model of Asset Prices.’’ Econometrica 53, 363–384.

Durham, G. (2003). ‘‘Likelihood-Based Specification Analysis of Continuous-Time Models of the Short-Term Interest Rate.’’ Journal of Financial Economics 70, 463–487.

Fan, J., and I. Gijbels. (1996). Local Polynomial Modelling and Its Applications. London: Chapman & Hall.

Fan, J., and C. Zhang. (2003). ‘‘A Re-examination of Stanton’s Diffusion Estimators with Applications to Financial Model Validation.’’ Journal of the American Statistical Association 461, 118–134.

Gao, J., and M. King. (2004). ‘‘Adaptive Testing in Continuous-Time Diffusion Models.’’ Econometric Theory 20, 844–882.

Gao, J., and M. King. (2005). ‘‘Adaptive Model Specification Testing in Nonlinear Time Series Econometrics.’’ Working paper. Available at www.maths.uwa.edu.au/ ~jiti/san04.pdf.

Ha ̈rdle, W., and E. Mammen. (1993). ‘‘Comparing Nonparametric versus Parametric Regression Fits.’’ Annals of Statistics 21, 1926–1947.

Hjellvik, V., and D. Tjøstheim. (1995). ‘‘Nonparametric Tests of Linearity for Time Series.’’ Biometrika 82, 351–368.

Hjellvik, V., Q. Yao, and D. Tjøstheim. (1998). ‘‘Linearity Testing Using Local Polynomial Approximation.’’ Journal of Statistical Planning and Inference 68, 295–321.

Hong, Y., and H. Li. (2005). ‘‘Nonparametric Specification Testing for ContinuousTime Models with Applications to Term Structure of Interest Rates.’’ Review of Financial Studies 18, 37–84.

Horowitz, J., and V. Spokoiny. (2001). ‘‘An Adaptive, Rate-Optimal Test of a Parametric Mean-Regression Model Against a Nonparametric Alternative.’’ Econometrica 69, 599–632.

Jiang, G. (1998). ‘‘Nonparametric Modelling of US Interest Rate Term Structure Dynamics and Implication on the Prices of Derivative Securities.’’ Journal of Financial and Quantitative Analysis 33, 465–497.

Jiang, G., and J. Knight. (1997). ‘‘A Nonparametric Approach to the Estimation of Diffusion Processes with an Application to a Short-Term Interest Rate Model.’’ Econometric Theory 13, 615–645.

Jones, C. (2003). ‘‘Nonlinear Mean Reversion in the Short-Term Interest Rate.’’ Review of Financial Studies 16, 793–843.

Li, M., N. Pearson, and A. Poteshman. (2004). ‘‘Facing Up to Conditioned Diffusions.’’ Journal of Financial Economics 74, 31–66.

Li, Q. (1999). ‘‘Consistent Model Specification Tests for Time Series Econometric Models.’’ Journal of Econometrics 92, 101–147.

Li, Q., and S. Wang. (1998). ‘‘A Simple Consistent Bootstrap Tests for a Parametric Regression Functional Form.’’ Journal of Econometrics 87, 145–165.

Merton, R. (1973). ‘‘The Theory of Rational Option Pricing.’’ Bell Journal of Economics 4, 141–183.

Nicolau, J. (2003). ‘‘Bias Reduction in Nonparametric Diffusion Coefficient Estimation.’’ Econometric Theory 19, 754–777.

Pritsker, M. (1998). ‘‘Nonparametric Density Estimation and Tests of Continuous Time Interest Rate Models.’’ Review of Financial Studies 11, 449–487.

Stanton, R. (1997). ‘‘A Nonparametric Model of Term Structure Dynamics and the Market Price of Interest Rate Risk.’’ Journal of Finance 52, 1973–2002.

Sundaresan, S. (2001). ‘‘Continuous-Time Methods in Finance: A Review and an Assessment.’’ Journal of Finance 55, 1569–1622.

Vasicek, O. (1977). ‘‘An Equilibrium Characterization of the Term Structure.’’ Journal of Financial Economics 5, 177–188.

Zheng, J. (1996). ‘‘A Consistent Test of Functional Form via Nonparametric Estimation Techniques.’’ Journal of Econometrics 75, 263–289.