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October 1999 Parameter estimation for discretely observed stochastic volatility models
Valentine Genon-Catalot, Thierry Jeantheau, Catherine Laredo
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Bernoulli 5(5): 855-872 (October 1999).

Abstract

This paper deals with parameter estimation for stochastic volatility models. We consider a two-dimensional diffusion process (Yt,Vt). Only (Yt) is observed at n discrete times with a regular sampling interval. The unobserved coordinate (Vt) rules the diffusion coefficient (volatility) of (Yt) and is an ergodic diffusion depending on unknown parameters. We build estimators of the parameters present in the stationary distribution of (Vt), based on appropriate functions of the observations. Consistency is proved under the asymptotic framework that the sampling interval tends to 0, while the number of observations and the length of the observation time tend to infinity. Asymptotic normality is obtained under an additional condition on the rate of convergence of the sampling interval. Examples of models from finance are treated, and numerical simulation results are given.

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Valentine Genon-Catalot. Thierry Jeantheau. Catherine Laredo. "Parameter estimation for discretely observed stochastic volatility models." Bernoulli 5 (5) 855 - 872, October 1999.

Information

Published: October 1999
First available in Project Euclid: 12 February 2007

zbMATH: 0942.62096
MathSciNet: MR1715442

Keywords: Diffusion processes , discrete time observations , mathematical finance , Parametric inference , stochastic volatility

Rights: Copyright © 1999 Bernoulli Society for Mathematical Statistics and Probability

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Vol.5 • No. 5 • October 1999
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