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Maximum Likelihood and Gaussian Estimation of Continuous Time Models in Finance

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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.

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File URL: http://cowles.econ.yale.edu/P/cd/d15b/d1597.pdf
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Bibliographic Info

Paper provided by Cowles Foundation for Research in Economics, Yale University in its series Cowles Foundation Discussion Papers with number 1597.

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Length: 34 pages
Date of creation: Jan 2007
Date of revision:
Handle: RePEc:cwl:cwldpp:1597

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Postal: Cowles Foundation, Yale University, Box 208281, New Haven, CT 06520-8281 USA

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Keywords: Maximum likelihood; Transition density; Discrete sampling; Continuous record; Realized volatility; Bias reduction; Jackknife; Indirect inference;

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Cited by:
  1. 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.
  2. Peter Robinson, 2007. "On Discrete Sampling Of Time-Varyingcontinuous-Time Systems," STICERD - Econometrics Paper Series /2007/520, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.

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