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Estimating the parameters of stochastic differential equations by Monte Carlo methods

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  • Stan Hurn, A.
  • Lindsay, K.A.

Abstract

We propose a method for the simultaneous estimation of the drift and diffusion coefficients of stochastic differential equations (SDE) from panel data. The method involves matching the distribution of the experimental/field data with a panel of simulated data generated by a Monte Carlo experiment. The fit between the two distributions is assessed by means of the chi-square goodness-of-fit statistic leading to a confidence function computed from an incomplete gamma function. A numerical optimisation algorithm then optimises the choice of parameters to maximise this function. Preliminary evidence is presented which suggests that it is possible to estimate the coefficients of the generating SDE very accurately.

Suggested Citation

  • Stan Hurn, A. & Lindsay, K.A., 1997. "Estimating the parameters of stochastic differential equations by Monte Carlo methods," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 43(3), pages 495-501.
    • Handle: RePEc:eee:matcom:v:43:y:1997:i:3:p:495-501
    DOI: 10.1016/S0378-4754(97)00037-2
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    References listed on IDEAS

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    1. 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 637-654, May-June.
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    1. Stan Hurn & J.Jeisman & K.A. Lindsay, 2006. "Teaching an old dog new tricks: Improved estimation of the parameters of SDEs by numerical solution of the Fokker-Planck equation," Stan Hurn Discussion Papers 2006-01, School of Economics and Finance, Queensland University of Technology.
    2. Alcock, Jamie & Burrage, Kevin, 2004. "A genetic estimation algorithm for parameters of stochastic ordinary differential equations," Computational Statistics & Data Analysis, Elsevier, vol. 47(2), pages 255-275, September.
    3. 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, Oxford University Press, vol. 5(3), pages 390-455.
    4. 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. Working paper #2," NCER Working Paper Series 2, National Centre for Econometric Research.

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