Short Term Interest Rate Model Using Box-Cox Transformation

Title & Authors
Short Term Interest Rate Model Using Box-Cox Transformation
Choi, Young-Soo; Lee, Yoon-Dong;

Abstract
This paper propose a new short-term interest rate model having a different nonlinear drift function and the same diffusion coefficient with Chan et al. (1992) model. The fractional polynomial power of the drift function in our model is linked to the local volatility elasticity of the diffusion coefficient. While the nonlinear drift function estimated by $\small{A\"{\i}t}$-Sahalia (1996a) and others has a feature that higher interest rates tend to revert downward and low rates upward, the drift function estimated by our nonlinear model shows that higher interest rate mean-reverts strongly, but, medium rates has almost zero drift and low rates has a very small drift. This characteristic coincides the empirical result based on the nonparametric methodology by Stanton (1997) and the implication by the scatter plot of the short rate data.
Keywords
Short-term interest rate model;Box-Cox transformation;
Language
English
Cited by
References
1.
Ait-Sahalia, Y. (1996a). Nonparametric pricing of interest rate derivative securities. Econometrica, 64, 527-560

2.
Ait-Sahalia, Y. (1996b). Testing continuous-time models of the spot interest rate. The Review of Financial Studies. 9, 385-426

3.
Box, G. E. P. and Cox, D. R. (1964). An analysis of transformations. Journal of the Royal Statistical Society Ser. B. 26, 211-252

4.
Conley, T. G., Hansen, L. P., Luttmer, E. G. J. and Scheinkman, J. A. (1997). Short-term interest rates as subordinated diffusions. The Review of Financial Studies, 10, 525-577

5.
Cox, J. C., Ingersoll, J. E. and Ross, S. A. (1985). A theory of the term structure of interest rates, Econometrica, 53, 385-407

6.
Chan, K. C., Karolyi, G. A., Longstaff, F. A. and Sanders, A. B. (1992). An empirical comparison of alternative models of the short-term interest rate. Journal of Finance, 47, 1209-1227

7.
Eom Y. H. (1998). An Efficient GMM Estimation of Continuous-Time Asset Dynamics: Implications for the Term Structure of Interest Rates. Technical Report of Yeonsei University

8.
Jones, C. S. (2003). Nonlinear mean reversion in the short-term interest rate. The Review of Financial Studies, 16, 793-843

9.
Stanton, R. (1997). A nonparametric model of term structure dynamics and the market price of interest rate risk. Journal of Finance, 52, 1973-2002

10.
Vasicek, O. (1977). An equilibrium characterization of the term structure. Journal of Financial Economics, 5, 177-188