Parameter estimation and bias correction for diffusion processes

This paper considers parameter estimation for continuous-time diffusion processes which are commonly used to model dynamics of financial securities including interest rates. To understand why the drift parameters are more difficult to estimate than the diffusion parameter, as observed in previous st...

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Bibliographic Details
Published in:Journal of econometrics 2009-04, Vol.149 (1), p.65-81
Main Authors: Tang, Cheng Yong, Chen, Song Xi
Format: Article
Language:English
Subjects:
Applications
Bias
Bias correction
Bias correction Bootstrap Continuous-time models Diffusion processes Jackknife Parameter estimation
Bootstrap
Bootstrap mechanism
Continuous-time models
Diffusion processes
Econometrics
Estimation
Estimation bias
Exact sciences and technology
Financial analysis
Insurance, economics, finance
Interest rates
Jackknife
Linear inference, regression
Markov processes
Mathematics
Maximum likelihood method
Option pricing
Parameter estimation
Parametric inference
Probability and statistics
Probability theory and stochastic processes
Sciences and techniques of general use
Securities prices
Statistics
Studies
Variance
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Summary:This paper considers parameter estimation for continuous-time diffusion processes which are commonly used to model dynamics of financial securities including interest rates. To understand why the drift parameters are more difficult to estimate than the diffusion parameter, as observed in previous studies, we first develop expansions for the bias and variance of parameter estimators for two of the most employed interest rate processes, Vasicek and CIR processes. Then, we study the first order approximate maximum likelihood estimator for linear drift processes. A parametric bootstrap procedure is proposed to correct bias for general diffusion processes with a theoretical justification. Simulation studies confirm the theoretical findings and show that the bootstrap proposal can effectively reduce both the bias and the mean square error of parameter estimates, for both univariate and multivariate processes. The advantages of using more accurate parameter estimators when calculating various option prices in finance are demonstrated by an empirical study.
ISSN:0304-4076
1872-6895
DOI:10.1016/j.jeconom.2008.11.001