Review and Applications of NLL Estimation Method for Diffusion Processes

확산모형에 대한 NLL 추정법의 특성과 적용

  • 홍진영 (건국대학교 응용통계학과) ;
  • 이윤동 (서강대학교 경영학부)
  • Received : 20100100
  • Accepted : 20100400
  • Published : 2010.07.31


Many of financial data are explained via diffusion models in modern financial research. Various types of estimation methods of diffusion processes were suggested by many authors. In this paper, we tested the properties of the NLL estimation method, suggested by Shoji and Ozaki (1998), of diffusion processes in the view of the bias and variance of the estimators and applied the method to estimate the model parameters for the U.S. fedral funds rate data and Korean inter-bank exchange rate data. By simulation study we showed that the NLL method provides relatively good estimators, in the meaning that the estimator has less bias than the Euler method, while keeping the variance similar level. We also provide the NLL estimates of U.S fedral funds rate data and Korean inter-bank exchange rate data.

확산모형은 금융현상을 모형화하기 위한 방법으로 자주 사용된다. 다양한 확산모형들을 추론하기 위한 다양한 추론기법들이 제안되어져 왔다. 본 연구에서는 시뮬레이션 방법을 통하여 Shoji와 Ozaki (1998)에 의하여 제안된 NLL 방법의 성질을 검토하여 보고, 실제 자료에 적용하게 된다.



Supported by : 서강대학교


  1. 홍진영 (2009). , 건국대학교 석사학위 논문.
  2. Ahn, D. and Gao, B. (1999). A parametric nonlinear model of term structure dynamics, The Review of Financial Studies, 12, 721-762.
  3. Ait-Sahalia, Y. (1999). Transition densities for interest rate and other nonlinear diffusions, Journal of Finance, 54, 1361-1395.
  4. Ait-Sahalia, Y. (2002). Maximum-likelihood estimation of discretely-sampled diffusions: A closed-form approximation approach, Econometrica, 70, 223-262.
  5. Bachelier, L. (1900). Theorie de la speculation, Annales Scientifiques de L’E.N.S., 17, 21-86.
  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. Conley, T. G., Hansen, L. P., Luttmer, E. G. T. and Scheinkman, J. A. (1997). Short-term interest rates as subordinated diffusions, The Review of Financial Studies, 10, 525-577.
  8. Cox, J. C., Ingersoll, Jr. and Ross, S. A. (1985). A theory of the term structure of interest rates, Econometrica, 53, 385-407.
  9. Duffie, D. and Kan, R. (1996). A yield-factor model of interest rate, Mathematical Finance, 6, 379-406.
  10. Hurn, A., Jeisman, J. and Linsay, K. (2007). Seeing the wood for the trees: A critical evaluation of methods to estimation methods to estimate the parameters of stochastic differential equations, Journal of Financial Econometrics, 5, 390-455.
  11. Kloeden, P. and Platen, E. (1995). Numerical Solution of Stochastic Differential Equations, Springer, New York.
  12. Samuelson, P. A. (1965). Proof that properly anticipated prices fluctuate randomly, Industrial Management Review, 6, 41-50.
  13. Shoji, I. and Ozaki, T. (1998). Estimation for nonlinear stochastic differential equations by a local linearization method, Stochastic Analysis and Applications, 16, 733-752.
  14. Vasicek, O. (1977). An equilibrium characterization of the term structure, Journal of Financial Economics, 5, 177-188.