Testing Continuous-Time Interest Rate Model for Chinese Repo Market
ABSTRACT
This paper tests the popular continuous-time interest rate models for Chinese repo market to address what and how the interest rates change with the marketlization in China. Using Bandi [1]’s method, we get the functional nonparametric estimation of drift and diffusion terms and the local time of the process. We find that the interest rates of China during the period from 1993 to 2003 are bimodal distributed and propose a two-regime model which can fit the data better. We also study the probabilities that the process will stay the two regimes respectively and its transition probability that the process transfers from one regime to another regime.
This paper tests the popular continuous-time interest rate models for Chinese repo market to address what and how the interest rates change with the marketlization in China. Using Bandi [1]’s method, we get the functional nonparametric estimation of drift and diffusion terms and the local time of the process. We find that the interest rates of China during the period from 1993 to 2003 are bimodal distributed and propose a two-regime model which can fit the data better. We also study the probabilities that the process will stay the two regimes respectively and its transition probability that the process transfers from one regime to another regime.
Cite this paper
Zhao, H. and Peng, F. (2015) Testing Continuous-Time Interest Rate Model for Chinese Repo Market. Journal of Mathematical Finance, 5, 26-39. doi: 10.4236/jmf.2015.51003.
Zhao, H. and Peng, F. (2015) Testing Continuous-Time Interest Rate Model for Chinese Repo Market. Journal of Mathematical Finance, 5, 26-39. doi: 10.4236/jmf.2015.51003.
References
[1] Bandi, F.M. (2002) Short-Term Interest Rate Dynamics: A Spatial Approach. Journal of Financial Economics, 65, 73-110.
http://dx.doi.org/10.1016/S0304-405X(02)00135-6 [2] Ait-Sahalia, Y. (1996) Testing Continuous-Time Model of the Spot Interest Rate. Review of Financial Studies, 9, 385-426.
http://dx.doi.org/10.1093/rfs/9.2.385 [3] Stanton, R. (1997) A Nonparametric Model of Term Structure Dynamics and the Market Price of Interest Rate Risk. Journal of Finance, 52, 1973-2002.
http://dx.doi.org/10.1111/j.1540-6261.1997.tb02748.x [4] Jiang, G.J. and Knight, J.L. (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.
http://dx.doi.org/10.1017/S0266466600006101 [5] Motta, G., Hafner, C.M. and Sachs von, R. (2011) Locally Stationary Factor Models: Identification and Nonparametric Estimation. Econometric Theory, 27, 1279-1319.
http://dx.doi.org/10.1017/S0266466611000053 [6] Florens, J.P. and Simoni, A. (2012) Nonparametric Estimation of an Instrumental Regression: A Quasi-Bayesian Approach Based on Regularized Posterior. Journal of Econometrics, 170, 458-475.
http://dx.doi.org/10.1016/j.jeconom.2012.05.016 [7] Restrepo-Tobn, D. and Kumbhakar, S.C. (2014) Nonparametric Estimation of Returns to Scale Using Input Distance Functions: An Application to Large US Banks. Empirical Economics, 1-26. [8] Kristensen, D. (2011) Semi-Nonparametric Estimation and Misspecification Testing of Diffusion Models. Journal of Econometrics, 164, 382-403.
http://dx.doi.org/10.1016/j.jeconom.2011.07.001 [9] Bandi, F.M and Phillips, P.C.B. (2002) Fully Nonparametric Estimation of Scalar Diffusion Models. Econometrica, 71, 241-283.
http://dx.doi.org/10.1111/1468-0262.00395 [10] Bandi, F.M. and Nguyenb, T.H. (2003) On the Functional Estimation of Jump-Diffusion Models. Journal of Econometrics, 116, 293-328.
http://dx.doi.org/10.1016/S0304-4076(03)00110-6 [11] Johannes, M. (2004) The Statistical and Economic Role of Jumps in Continuous-Time Interest Rate Models. The Journal of Finance, 59, 227-260. [12] Hong, Y.M. and Lin, H. (2006) Performance of Discrete-Time Spot Rate Models in China: An Empirical Test on Chinese Repo Rates. China Economic Quarterly, 5, 511-532. [13] Duffee, G.R. and Stanton, R.H. (2012) Estimation of Dynamic Term Structure Models. The Quarterly Journal of Finance, 2, Article ID: 125008.
http://dx.doi.org/10.1142/S2010139212500085 [14] Siegel, A.F. (2014) Price-Admissibility Conditions for Arbitrage-Free Linear Price Function Models for the Term Structure of Interest Rates. Mathematical Finance, Early View.
http://dx.doi.org/10.1111/mafi.12075 [15] He, D. and Wang, H.L. (2012) Dual-Track Interest Rates and the Conduct of Monetary Policy in China. China Economic Review, 23, 928-947. [16] Harvey, A.C. (1993) Time Series Models. 2nd Edition, MIT Press, Cambridge. [17] Cox, J.C., Ingersoll, J.E. and Ross, S.A. (1985) A Theory of the Term Structure of Interest Rates. Econometrica, 53, 363-384.
http://dx.doi.org/10.2307/1911241 [18] Vasicek, O. (1977) An Equilibrium Characterization of the Term Structure. Journal of Financial Economics, 5, 177-188.
http://dx.doi.org/10.1016/0304-405X(77)90016-2 [19] Hull, J. and White, A. (1990) Pricing Interest Rate Derivative Securities. The Review of Financial Studies, 3, 573-592.
http://dx.doi.org/10.1093/rfs/3.4.573 [20] Jiang, G.J. (1998) Nonparametric Approach to the Estimation of US Interest Rate Term Structure Dynamics and Implications on the Prices of Derivative Securities. Journal of Financial and Quantitative Analysis, 33, 465-497.
http://dx.doi.org/10.2307/2331128 [21] Scott, D.W. (1992) Multivariate Density Estimation: Theory, Practice and Visualization. John Wiley & Sons, Inc., New York.
http://dx.doi.org/10.1002/9780470316849 [22] Chung, K.L. and Williams, R.J. (1990) Introduction to Stochastic Integration. Birkhäuser, Boston. [23] Karatzas, I. and Shreve, S.E. (1991) Brownian Motion and Stochastic Calculus. Springer, New York. [24] Revuz, D. and Yor, M. (1994) Continuous Martingales and Brownian Motion. 2nd Edition, Springer, New York. [25] Hamilton, J.D. (1994) Time Series Analysis. Princeton University Press, Princeton. [26] Hamilton, J.D. (1990) Analysis of Time Series Subject to Changes in Regime. Journal of Econometrics, 45, 39-70.
http://dx.doi.org/10.1016/0304-4076(90)90093-9
[1] Bandi, F.M. (2002) Short-Term Interest Rate Dynamics: A Spatial Approach. Journal of Financial Economics, 65, 73-110.
http://dx.doi.org/10.1016/S0304-405X(02)00135-6 [2] Ait-Sahalia, Y. (1996) Testing Continuous-Time Model of the Spot Interest Rate. Review of Financial Studies, 9, 385-426.
http://dx.doi.org/10.1093/rfs/9.2.385 [3] Stanton, R. (1997) A Nonparametric Model of Term Structure Dynamics and the Market Price of Interest Rate Risk. Journal of Finance, 52, 1973-2002.
http://dx.doi.org/10.1111/j.1540-6261.1997.tb02748.x [4] Jiang, G.J. and Knight, J.L. (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.
http://dx.doi.org/10.1017/S0266466600006101 [5] Motta, G., Hafner, C.M. and Sachs von, R. (2011) Locally Stationary Factor Models: Identification and Nonparametric Estimation. Econometric Theory, 27, 1279-1319.
http://dx.doi.org/10.1017/S0266466611000053 [6] Florens, J.P. and Simoni, A. (2012) Nonparametric Estimation of an Instrumental Regression: A Quasi-Bayesian Approach Based on Regularized Posterior. Journal of Econometrics, 170, 458-475.
http://dx.doi.org/10.1016/j.jeconom.2012.05.016 [7] Restrepo-Tobn, D. and Kumbhakar, S.C. (2014) Nonparametric Estimation of Returns to Scale Using Input Distance Functions: An Application to Large US Banks. Empirical Economics, 1-26. [8] Kristensen, D. (2011) Semi-Nonparametric Estimation and Misspecification Testing of Diffusion Models. Journal of Econometrics, 164, 382-403.
http://dx.doi.org/10.1016/j.jeconom.2011.07.001 [9] Bandi, F.M and Phillips, P.C.B. (2002) Fully Nonparametric Estimation of Scalar Diffusion Models. Econometrica, 71, 241-283.
http://dx.doi.org/10.1111/1468-0262.00395 [10] Bandi, F.M. and Nguyenb, T.H. (2003) On the Functional Estimation of Jump-Diffusion Models. Journal of Econometrics, 116, 293-328.
http://dx.doi.org/10.1016/S0304-4076(03)00110-6 [11] Johannes, M. (2004) The Statistical and Economic Role of Jumps in Continuous-Time Interest Rate Models. The Journal of Finance, 59, 227-260. [12] Hong, Y.M. and Lin, H. (2006) Performance of Discrete-Time Spot Rate Models in China: An Empirical Test on Chinese Repo Rates. China Economic Quarterly, 5, 511-532. [13] Duffee, G.R. and Stanton, R.H. (2012) Estimation of Dynamic Term Structure Models. The Quarterly Journal of Finance, 2, Article ID: 125008.
http://dx.doi.org/10.1142/S2010139212500085 [14] Siegel, A.F. (2014) Price-Admissibility Conditions for Arbitrage-Free Linear Price Function Models for the Term Structure of Interest Rates. Mathematical Finance, Early View.
http://dx.doi.org/10.1111/mafi.12075 [15] He, D. and Wang, H.L. (2012) Dual-Track Interest Rates and the Conduct of Monetary Policy in China. China Economic Review, 23, 928-947. [16] Harvey, A.C. (1993) Time Series Models. 2nd Edition, MIT Press, Cambridge. [17] Cox, J.C., Ingersoll, J.E. and Ross, S.A. (1985) A Theory of the Term Structure of Interest Rates. Econometrica, 53, 363-384.
http://dx.doi.org/10.2307/1911241 [18] Vasicek, O. (1977) An Equilibrium Characterization of the Term Structure. Journal of Financial Economics, 5, 177-188.
http://dx.doi.org/10.1016/0304-405X(77)90016-2 [19] Hull, J. and White, A. (1990) Pricing Interest Rate Derivative Securities. The Review of Financial Studies, 3, 573-592.
http://dx.doi.org/10.1093/rfs/3.4.573 [20] Jiang, G.J. (1998) Nonparametric Approach to the Estimation of US Interest Rate Term Structure Dynamics and Implications on the Prices of Derivative Securities. Journal of Financial and Quantitative Analysis, 33, 465-497.
http://dx.doi.org/10.2307/2331128 [21] Scott, D.W. (1992) Multivariate Density Estimation: Theory, Practice and Visualization. John Wiley & Sons, Inc., New York.
http://dx.doi.org/10.1002/9780470316849 [22] Chung, K.L. and Williams, R.J. (1990) Introduction to Stochastic Integration. Birkhäuser, Boston. [23] Karatzas, I. and Shreve, S.E. (1991) Brownian Motion and Stochastic Calculus. Springer, New York. [24] Revuz, D. and Yor, M. (1994) Continuous Martingales and Brownian Motion. 2nd Edition, Springer, New York. [25] Hamilton, J.D. (1994) Time Series Analysis. Princeton University Press, Princeton. [26] Hamilton, J.D. (1990) Analysis of Time Series Subject to Changes in Regime. Journal of Econometrics, 45, 39-70.
http://dx.doi.org/10.1016/0304-4076(90)90093-9