tailieunhanh - Báo cáo hóa học: "Research Article Online Estimation of Time-Varying Volatility Using a Continuous-Discrete LMS Algorithm"

Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: Research Article Online Estimation of Time-Varying Volatility Using a Continuous-Discrete LMS Algorithm | Hindawi Publishing Corporation EURASIP Journal on Advances in Signal Processing Volume 2008 Article ID 532760 8 pages doi 2008 532760 Research Article Online Estimation of Time-Varying Volatility Using a Continuous-Discrete LMS Algorithm Elisabeth Lahalle Hana Baili and Jacques Oksman Department of Signal Processing and Electronic Systems Supelec 3 rue Joliot-Curie Plateau de Moulon 91192 Gifsur Yvette France Correspondence should be addressed to Elisabeth Lahalle Received 27 March 2007 Revised 21 December 2007 Accepted 9 July 2008 Recommended by Ioannis Psaromiligkos 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. Copyright 2008 Elisabeth Lahalle et al. This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited. 1. INTRODUCTION In 1973 Black Scholes and Merton 1 2 reasoned that under certain idealized market assumptions the prices of stocks and the derivatives on these stocks are coupled. One of the crucial assumptions is that the traded asset price s follows dSt pStdt ơStdBt 1 where Bt is a Brownian motion. and Ơ are called respectively drift and volatility of the stock both are deterministic constants. Nevertheless it turns out that the assumption of constant volatility does not hold in practice. Traders in the market are supposed to assess returns .