- Volume 4, Number 3 (1998), 283-303.
Limit theorems for discretely observed stochastic volatility models
A general set-up is proposed to study stochastic volatility models. We consider here a two-dimensional diffusion process and assume that only is observed at discrete times with regular sampling interval . The unobserved coordinate is an ergodic diffusion which rules the diffusion coefficient (or volatility) of . The following asymptotic framework is used: the sampling interval tends to , 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 . 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.
Bernoulli, Volume 4, Number 3 (1998), 283-303.
First available in Project Euclid: 19 March 2007
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Genon-Catalot, Valentine; Jeantheau, Thierry; Larédo, Catherine. Limit theorems for discretely observed stochastic volatility models. Bernoulli 4 (1998), no. 3, 283--303. https://projecteuclid.org/euclid.bj/1174324982