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sept 1998 Limit theorems for discretely observed stochastic volatility models
Valentine Genon-Catalot, Thierry Jeantheau, Catherine Larédo
Bernoulli 4(3): 283-303 (sept 1998).

Abstract

A general set-up is proposed to study stochastic volatility models. We consider here a two-dimensional diffusion process (Yt,Vt) and assume that only (Yt) is observed at n discrete times with regular sampling interval Δ. The unobserved coordinate (Vt) is an ergodic diffusion which rules the diffusion coefficient (or volatility) of (Yt). The following asymptotic framework is used: the sampling interval tends to 0, while the number of observations and the length of the observation time tend to infinity. We study the empirical distribution associated with the observed increments of (Yt). We prove that it converges in probability to a variance mixture of Gaussian laws and obtain a central limit theorem. Examples of models widely used in finance, and included in this framework, are given.

Citation

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Valentine Genon-Catalot. Thierry Jeantheau. Catherine Larédo. "Limit theorems for discretely observed stochastic volatility models." Bernoulli 4 (3) 283 - 303, sept 1998.

Information

Published: sept 1998
First available in Project Euclid: 19 March 2007

zbMATH: 0916.60075
MathSciNet: MR1653264

Keywords: Diffusion processes , discrete time observations , empirical istributios , limit theorems , mathematical finance , stochastic volatility

Rights: Copyright © 1998 Bernoulli Society for Mathematical Statistics and Probability

Vol.4 • No. 3 • sept 1998
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