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.