Bias in estimating multivariate and univariate diffusions
Multivariate continuous time models are now widely used in economics and finance. Empirical applications typically rely on some process of discretization so that the system may be estimated with discrete data. This paper introduces a framework for discretizing linear multivariate continuous time systems that includes the commonly used Euler and trapezoidal approximations as special cases and leads to a general class of estimators for the mean reversion matrix. Asymptotic distributions and bias formulae are obtained for estimates of the mean reversion parameter. Explicit expressions are given for the discretization bias and its relationship to estimation bias in both multivariate and in univariate settings. In the univariate context, we compare the performance of the two approximation methods relative to exact maximum likelihood (ML) in terms of bias and variance for the Vasicek process. The bias and the variance of the Euler method are found to be smaller than the trapezoidal method, which are in turn smaller than those of exact ML. Simulations suggest that when the mean reversion is slow, the approximation methods work better than ML, the bias formulae are accurate, and for scalar models the estimates obtained from the two approximate methods have smaller bias and variance than exact ML. For the square root process, the Euler method outperforms the Nowman method in terms of both bias and variance. Simulation evidence indicates that the Euler method has smaller bias and variance than exact ML, Nowman's method and the Milstein method.
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- Hansen, Lars Peter & Sargent, Thomas J, 1983.
"The Dimensionality of the Aliasing Problem in Models with Rational Spectral Densities,"
Econometric Society, vol. 51(2), pages 377-87, March.
- Lars Peter Hansen & Thomas J. Sargent, 1981. "The dimensionality of the aliasing problem in models with rational spectral densities," Staff Report 72, Federal Reserve Bank of Minneapolis.
- Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-54, May-June.
- Ai[dieresis]t-Sahalia, Yacine & Yu, Jialin, 2006. "Saddlepoint approximations for continuous-time Markov processes," Journal of Econometrics, Elsevier, vol. 134(2), pages 507-551, October.
- Vasicek, Oldrich Alfonso, 1977. "Abstract: An Equilibrium Characterization of the Term Structure," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 12(04), pages 627-627, November.
- Jun Yu, 2009.
"Bias in the Estimation of the Mean Reversion Parameter in Continuous Time Models,"
Microeconomics Working Papers
23045, East Asian Bureau of Economic Research.
- Yu, Jun, 2012. "Bias in the estimation of the mean reversion parameter in continuous time models," Journal of Econometrics, Elsevier, vol. 169(1), pages 114-122.
- Jun Yu, 2009. "Bias in the Estimation of the Mean Reversion Parameter in Continuous Time Models," Working Papers 16-2009, Singapore Management University, School of Economics.
- Jun Yu, 2007. "Bias in the Estimation of the Mean Reversion Parameter in Continuous Time Models," Working Papers CoFie-06-2008, , revised Oct 2008.
- Phillips, P. C. B., 1973. "The problem of identification in finite parameter continuous time models," Journal of Econometrics, Elsevier, vol. 1(4), pages 351-362, December.
- Durham, Garland B & Gallant, A Ronald, 2002. "Numerical Techniques for Maximum Likelihood Estimation of Continuous-Time Diffusion Processes," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(3), pages 297-316, July.
- Peter C. B. Phillips & Jun Yu, 2005. "Comments on “A Selective Overview of Nonparametric Methods in Financial Econometrics” by Jianqing Fan," Working Papers 08-2005, Singapore Management University, School of Economics.
- Lo, Andrew W., 1988.
"Maximum Likelihood Estimation of Generalized Itô Processes with Discretely Sampled Data,"
Cambridge University Press, vol. 4(02), pages 231-247, August.
- Andrew W. Lo, . "Maximum Likelihood Estimation of Generalized Ito Processes with Discretely Sampled Data," Rodney L. White Center for Financial Research Working Papers 15-86, Wharton School Rodney L. White Center for Financial Research.
- Andrew W. Lo, 1986. "Maximum Likelihood Estimation of Generalized Ito Processes with Discretely Sampled Data," NBER Technical Working Papers 0059, National Bureau of Economic Research, Inc.
- Cox, John C & Ingersoll, Jonathan E, Jr & Ross, Stephen A, 1985. "A Theory of the Term Structure of Interest Rates," Econometrica, Econometric Society, vol. 53(2), pages 385-407, March.
- Bergstrom, A.R., 1984. "Continuous time stochastic models and issues of aggregation over time," Handbook of Econometrics, in: Z. Griliches† & M. D. Intriligator (ed.), Handbook of Econometrics, edition 1, volume 2, chapter 20, pages 1145-1212 Elsevier.
- Peter C.B.Phillips & Jun Yu, . "Simulation-based Estimation of Contingent Claims Prices," Working Papers CoFie-05-2008, .
- Tang, Cheng Yong & Chen, Song Xi, 2009. "Parameter estimation and bias correction for diffusion processes," Journal of Econometrics, Elsevier, vol. 149(1), pages 65-81, April.
- Peter C. B. Phillips & Jun Yu, 2009.
"Simulation-Based Estimation of Contingent-Claims Prices,"
Review of Financial Studies,
Society for Financial Studies, vol. 22(9), pages 3669-3705, September.
- Peter C.B. Phillips & Jun Yu, 2007. "Simulation-based Estimation of Contingent-claims Prices," Cowles Foundation Discussion Papers 1596, Cowles Foundation for Research in Economics, Yale University.
- Peter C. B. Phillips & Jun Yu, 2008. "Simulation-based Estimation of Contingent-claims Prices," Finance Working Papers 22473, East Asian Bureau of Economic Research.
- Peter C.B. Phillips & Jun Yu, 2003.
"Jackknifing Bond Option Prices,"
Cowles Foundation Discussion Papers
1392, Cowles Foundation for Research in Economics, Yale University.
- Jun Yu & Peter Phillips, 2004. "Jackknifing Bond Option Prices," Econometric Society 2004 North American Winter Meetings 115, Econometric Society.
- Yu, Jun & Phillips, Peter, 2002. "Jacknifing Bond Option Prices," Working Papers 187, Department of Economics, The University of Auckland.
- Darrell Duffie & Rui Kan, 1996. "A Yield-Factor Model Of Interest Rates," Mathematical Finance, Wiley Blackwell, vol. 6(4), pages 379-406.
- Yong Bao & Aman Ullah, 2009. "On skewness and kurtosis of econometric estimators," Econometrics Journal, Royal Economic Society, vol. 12(2), pages 232-247, 07.
- Vasicek, Oldrich, 1977. "An equilibrium characterization of the term structure," Journal of Financial Economics, Elsevier, vol. 5(2), pages 177-188, November.
- Ai[diaeresis]t-Sahalia, Yacine & Kimmel, Robert, 2007. "Maximum likelihood estimation of stochastic volatility models," Journal of Financial Economics, Elsevier, vol. 83(2), pages 413-452, February.
- Yacine Ait-Sahalia, 2002. "Maximum Likelihood Estimation of Discretely Sampled Diffusions: A Closed-form Approximation Approach," Econometrica, Econometric Society, vol. 70(1), pages 223-262, January.
- Chan, K C, et al, 1992.
" An Empirical Comparison of Alternative Models of the Short-Term Interest Rate,"
Journal of Finance,
American Finance Association, vol. 47(3), pages 1209-27, July.
- Tom Doan, . "RATS programs to replicate CKLS(1992) estimation of interest rate models," Statistical Software Components RTZ00035, Boston College Department of Economics.
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