Bernoulli

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  • Volume 5, Number 5 (1999), 855-872.

Parameter estimation for discretely observed stochastic volatility models

Valentine Genon-Catalot, Thierry Jeantheau, and Catherine Laredo

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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.

Article information

Source
Bernoulli, Volume 5, Number 5 (1999), 855-872.

Dates
First available in Project Euclid: 12 February 2007

Permanent link to this document
https://projecteuclid.org/euclid.bj/1171290402

Mathematical Reviews number (MathSciNet)
MR1715442

Zentralblatt MATH identifier
0942.62096

Keywords
diffusion processes discrete time observations mathematical finance parametric inference stochastic volatility

Citation

Genon-Catalot, Valentine; Jeantheau, Thierry; Laredo, Catherine. Parameter estimation for discretely observed stochastic volatility models. Bernoulli 5 (1999), no. 5, 855--872. https://projecteuclid.org/euclid.bj/1171290402


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