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Maximum Likelihood and Gaussian Estimation of Continuous Time Models in Finance

Author

Listed:
  • Peter C. B. Phillips

    (SMU)

  • Jun Yu
Abstract
This paper overviews maximum likelihood and Gaussian methods of estimating continuous time models used in finance. Since the exact likelihood can be constructed only in special cases, much attention has been devoted to the development of methods designed to approximate the likelihood. These approaches range from crude Euler-type approximations and higher order stochastic Taylor series expansions to more complex polynomial-based expansions and infill approximations to the likelihood based on a continuous time data record. The methods are discussed, their properties are outlined and their relative finite sample performance compared in a simulation experiment with the nonlinear CIR diffusion model, which is popular in empirical finance. Bias correction methods are also considered and particular attention is given to jackknife and indirect inference estimators. The latter retains the good asymptotic properties of ML estimation while removing finite sample bias. This method demonstrates superior performance in finite samples.

Suggested Citation

  • Peter C. B. Phillips & Jun Yu, 2006. "Maximum Likelihood and Gaussian Estimation of Continuous Time Models in Finance," Development Economics Working Papers 22471, East Asian Bureau of Economic Research.
    • Handle: RePEc:eab:develo:22471
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    References listed on IDEAS

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    Cited by:

    1. Peter C. B. Phillips & Jun Yu, 2009. "Simulation-Based Estimation of Contingent-Claims Prices," The Review of Financial Studies, Society for Financial Studies, vol. 22(9), pages 3669-3705, September.
    2. Robinson, Peter, 2007. "On discrete sampling of time-varying continuous-time systems," LSE Research Online Documents on Economics 6795, London School of Economics and Political Science, LSE Library.
    3. Peter Robinson, 2007. "On Discrete Sampling Of Time-Varyingcontinuous-Time Systems," STICERD - Econometrics Paper Series 520, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
    4. Choi Seungmoon, 2009. "Regime-Switching Univariate Diffusion Models of the Short-Term Interest Rate," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 13(1), pages 1-41, March.

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    More about this item

    Keywords

    Maximum likelihood; Transition density; Discrete sampling; Continuous record; realized volatility; Bias Reduction; Jackknife; Indirect Inference;
    All these keywords.

    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models

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