Teaching an Old Dog New Tricks: Improved Estimation of the Parameters of Stochastic Differential Equations by Numerical Solution of the Fokker-Planck Equation
Many stochastic differential equations (SDEs) do not have readily available closed-form expressions for their transitional probability density functions (PDFs). As a result, a large number of competing estimation approaches have been proposed in order to obtain maximum-likelihood estimates of their parameters. Arguably the most straightforward of these is one in which the required estimates of the transitional PDF are obtained by numerical solution of the Fokker-Planck(or forward-Kolmogorov) partial differential equation. Despite the fact that this method produces accurate estimates and is completely generic, it has not proved popular in the applied literature. Perhaps this is attributable to the fact that this approach requires repeated solution of a parabolic partial differential equation to obtain the transitional PDF and is therefore computationally quite expensive. In this paper, three avenues for improving the reliability and speed of this estimation method are introduced and explored in the context of estimating the parameters of the popular Cox-Ingersoll-Ross and Ornstein-Uhlenbeck models. The recommended algorithm that emerges from this investigation is seen to offer substantial gains in reliability and computational time.
|Date of creation:||27 Feb 2007|
|Date of revision:|
|Contact details of provider:|| Phone: 07 3138 5066|
Fax: 07 3138 1500
Web page: http://www.ncer.edu.au
More information through EDIRC
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Stan Hurn & J.Jeisman & K.A. Lindsay, 2006.
"Seeing the wood for the trees: A critical evaluation of methods to estimate the parameters of stochastic differential equations,"
Stan Hurn Discussion Papers
2006, School of Economics and Finance, Queensland University of Technology.
- A. S. Hurn & J. I. Jeisman & K. A. Lindsay, 0. "Seeing the Wood for the Trees: A Critical Evaluation of Methods to Estimate the Parameters of Stochastic Differential Equations," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 5(3), pages 390-455.
- Suresh M. Sundaresan, 2000. "Continuous-Time Methods in Finance: A Review and an Assessment," Journal of Finance, American Finance Association, vol. 55(4), pages 1569-1622, 08.
- 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.
- Chacko, George & Viceira, Luis M., 2003. "Spectral GMM estimation of continuous-time processes," Journal of Econometrics, Elsevier, vol. 116(1-2), pages 259-292.
- 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.
- Yacine Ait-Sahalia, 1995.
"Testing Continuous-Time Models of the Spot Interest Rate,"
NBER Working Papers
5346, National Bureau of Economic Research, Inc.
- Ait-Sahalia, Yacine, 1996. "Testing Continuous-Time Models of the Spot Interest Rate," Review of Financial Studies, Society for Financial Studies, vol. 9(2), pages 385-426.
- Vasicek, Oldrich, 1977. "An equilibrium characterization of the term structure," Journal of Financial Economics, Elsevier, vol. 5(2), pages 177-188, November.
- 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.
- Brandt, Michael W. & Santa-Clara, Pedro, 2002. "Simulated likelihood estimation of diffusions with an application to exchange rate dynamics in incomplete markets," Journal of Financial Economics, Elsevier, vol. 63(2), pages 161-210, February.
- Hansen, Lars Peter & Scheinkman, Jose Alexandre, 1995.
"Back to the Future: Generating Moment Implications for Continuous-Time Markov Processes,"
Econometric Society, vol. 63(4), pages 767-804, July.
- Lars Peter Hansen & Jose Alexandre Scheinkman, 1993. "Back to the Future: Generating Moment Implications for Continuous-Time Markov Processes," NBER Technical Working Papers 0141, National Bureau of Economic Research, Inc.
- Michael Sørensen, 2000. "Prediction-based estimating functions," Econometrics Journal, Royal Economic Society, vol. 3(2), pages 123-147.
- Sundaresan, S.M., 2000. "Continuous-Time Methods in Finance: A Review and an Assessment," Papers 00-03, Columbia - Graduate School of Business.
- Elerain, Ola & Chib, Siddhartha & Shephard, Neil, 2001.
"Likelihood Inference for Discretely Observed Nonlinear Diffusions,"
Econometric Society, vol. 69(4), pages 959-93, July.
- Elerian, O. & Chib, S. & Shephard, N., 1998. "Likelihood INference for Discretely Observed Non-linear Diffusions," Economics Papers 146, Economics Group, Nuffield College, University of Oxford.
- Neil Shephard & Ola Elerian & Siddhartha Chib, 1998. "Likelihood inference for discretely observed non-linear diffusions," Economics Series Working Papers 1998-W10, University of Oxford, Department of Economics.
- Ola Elerian & Siddhartha Chib & Neil Shephard, 2000. "Likelihood inference for discretely observed non-linear diffusions," OFRC Working Papers Series 2000mf02, Oxford Financial Research Centre.
- Eraker, Bjorn, 2001. "MCMC Analysis of Diffusion Models with Application to Finance," Journal of Business & Economic Statistics, American Statistical Association, vol. 19(2), pages 177-91, April.
- 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.
- Hurn, A.S. & Lindsay, K.A., 1999. "Estimating the parameters of stochastic differential equations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 48(4), pages 373-384.
- A. S. Hurn & K. A. Lindsay & V. L. Martin, 2003. "On the efficacy of simulated maximum likelihood for estimating the parameters of stochastic differential Equations," Journal of Time Series Analysis, Wiley Blackwell, vol. 24(1), pages 45-63, 01.
- Singleton, Kenneth J., 2001. "Estimation of affine asset pricing models using the empirical characteristic function," Journal of Econometrics, Elsevier, vol. 102(1), pages 111-141, May.
- Jiang, George J & Knight, John L, 2002. "Estimation of Continuous-Time Processes via the Empirical Characteristic Function," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(2), pages 198-212, April.
When requesting a correction, please mention this item's handle: RePEc:qut:auncer:2007-3. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (School of Economics and Finance)The email address of this maintainer does not seem to be valid anymore. Please ask School of Economics and Finance to update the entry or send us the correct address
If references are entirely missing, you can add them using this form.