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Online Estimation of Time-Varying Volatility Using a Continuous-Discrete LMS Algorithm


The following paper addresses a problem of inference in financial engineering, namely, online time-varying volatility estimation. The proposed method is based on an adaptive predictor for the stock price, built from an implicit integration formula. An estimate for the current volatility value which minimizes the mean square prediction error is calculated recursively using an LMS algorithm. The method is then validated on several synthetic examples as well as on real data. Throughout the illustration, the proposed method is compared with both UKF and offline volatility estimation.

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Correspondence to Elisabeth Lahalle.

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Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License (, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Lahalle, E., Baili, H. & Oksman, J. Online Estimation of Time-Varying Volatility Using a Continuous-Discrete LMS Algorithm. EURASIP J. Adv. Signal Process. 2008, 532760 (2008).

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