Asymptotic properties of Monte Carlo estimators of diffusion processes

This paper studies the limit distributions of Monte Carlo estimators of diffusion processes. We examine two types of estimators based on the Euler scheme, one applied to the original processes, the other to a Doss transformation of the processes. We show that the transformation increases the speed o...

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Bibliographic Details
Published in:Journal of econometrics 2006-09, Vol.134 (1), p.1-68
Main Authors: Detemple, Jérôme, Garcia, René, Rindisbacher, Marcel
Format: Article
Language:English
Subjects:
Applications
Approximation
Diffusion
Diffusion processes
Distribution theory
Doss transformation
Estimation
Eulers equations
Exact sciences and technology
Insurance, economics, finance
Mathematics
Monte Carlo estimators
Monte Carlo simulation
Numerical analysis
Numerical analysis. Scientific computation
Numerical methods in probability and statistics
Probability and statistics
Sciences and techniques of general use
Simulation-based estimation
Statistics
Studies
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Summary:This paper studies the limit distributions of Monte Carlo estimators of diffusion processes. We examine two types of estimators based on the Euler scheme, one applied to the original processes, the other to a Doss transformation of the processes. We show that the transformation increases the speed of convergence of the Euler scheme. We also study estimators of conditional expectations of diffusions. After characterizing expected approximation errors, we construct second-order bias-corrected estimators. We also derive new convergence results for the Mihlstein scheme. Illustrations of the results are provided in the context of simulation-based estimation of diffusion processes.
ISSN:0304-4076
1872-6895
DOI:10.1016/j.jeconom.2005.06.028