• Bernoulli
  • Volume 4, Number 3 (1998), 283-303.

Limit theorems for discretely observed stochastic volatility models

Valentine Genon-Catalot, Thierry Jeantheau, and Catherine Larédo

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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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Bernoulli, Volume 4, Number 3 (1998), 283-303.

First available in Project Euclid: 19 March 2007

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diffusion processes discrete time observations empirical istributios limit theorems mathematical finance stochastic volatility


Genon-Catalot, Valentine; Jeantheau, Thierry; Larédo, Catherine. Limit theorems for discretely observed stochastic volatility models. Bernoulli 4 (1998), no. 3, 283--303.

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