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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).


A general set-up is proposed to study stochastic volatility models. We consider here a two-dimensional diffusion process ( Y t,V t) and assume that only ( Y t) is observed at n discrete times with regular sampling interval Δ . The unobserved coordinate ( V t) is an ergodic diffusion which rules the diffusion coefficient (or volatility) of ( Y t) . 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 ( Y t) . 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.


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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.


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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