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Article Dans Une Revue Statistical Inference for Stochastic Processes Année : 2012

Estimation of the instantaneous volatility

Alexander Alvarez
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Résumé

This paper is concerned with the estimation of the volatility process in a stochastic volatility model of the following form: $dX_t=a_tdt+\sigma_tdW_t$, where $X$ denotes the log-price and $\sigma$ is a cádlág semi-martingale. In the spirit of a series of recent works on the estimation of the cumulated volatility, we here focus on the instantaneous volatility for which we study estimators built as finite differences of the \textit{power variations} of the log-price. We provide central limit theorems with an optimal rate depending on the local behavior of $\sigma$. In particular, these theorems yield some confidence intervals for $\sigma_t$.

Dates et versions

hal-00761710 , version 1 (06-12-2012)

Identifiants

Citer

Alexander Alvarez, Fabien Panloup, Monique Pontier, Nicolas Savy. Estimation of the instantaneous volatility. Statistical Inference for Stochastic Processes, 2012, 15 (1), pp.27-59. ⟨10.1007/s11203-011-9062-2⟩. ⟨hal-00761710⟩
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