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Efficient estimation of drift parameters in stochastic volatility models

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Abstract

We study the parametric problem of estimating the drift coefficient in a stochastic volatility model \(Y_{t}=\int_{0}^{t}\sqrt{V_{s}}\,\mathrm {d}W_{s}\) , where Y is a log price process and V the volatility process. Assuming that one can recover the volatility, precisely enough, from the observation of the price process, we construct an efficient estimator for the drift parameter of the diffusion V. As an application we present the efficient estimation based on the discrete sampling \((Y_{i\delta_{n}})_{i=0,\dots,n}\) with δ n →0 and n δ n →∞. We show that our setup is general enough to cover the case of ‘microstructure noise’ for the price process as well.

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  1. Laboratoire d’Analyse et de Mathématiques Appliquées, Université Paris-Est, UMR 8050, 5 boulevard Descartes, 77454, Marne-la-Vallée cedex 2, France

    Arnaud Gloter

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  1. Arnaud Gloter
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Gloter, A. Efficient estimation of drift parameters in stochastic volatility models. Finance Stoch 11, 495–519 (2007). https://doi.org/10.1007/s00780-007-0048-2

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