tailieunhanh - Báo cáo "Filtering for stochastic volatility from point process observation "

In this note we consider the filtering problem for financial volatility that is an Ornstein-Ulhenbeck process from point process observation. This problem is investigated for a Markov-Feller process of which the Ornstein-Ulhenbeck process is a particular case. | VNU Journal of Science Mathematics - Physics 23 2007 168-177 Filtering for stochastic volatility from point process observation Tidarut Plienpanich1 Tran Hung Thao2 1 School of Mathematics Suranaree University of Technology 111 University Avenue Muang District Nakhon Ratchasima 30000 Thailand 2 Institute of Mathematics 18 Hoang Quoc Viet Cau Giay Hanoi Vietnam Received 15 November 2006 received in revised form 12 September 2007 Abstract. In this note we consider the filtering problem for financial volatility that is an Ornstein-Ulhenbeck process from point process observation. This problem is investigated for a Markov-Feller process of which the Ornstein-Ulhenbeck process is a particular case. Keywords and phrases filtering volatility point process. AMSC 2000 60H10 93E05. Introduction and notations Stochastic volatility is one of main objective to study of financial mathematics. It reflects qualitively random effects on change of financial derivatives interest rate and other financial product prices. Many results have been received recently for volatility estimation by filtering approach. Rudiger Frey and W. J. Runggaldier 1 studied for the case of high frequency data. Frederi G. Viens 2 considered the problem of portfolio optimization under partially observed stochastic volatility. Wolfgang J. Runggaldier 3 used filtering methods to specify coefficients of financial market models. A filtering approach was introduced by J. Cvitanic R. Liptser and B. Rozovskii 4 to tracking volatility from prices observed at random times. A filtering problem for Ornstein-Ulhenbeck signal from discrete noises was investigated by and 5 to applied to the micro-movement of stock prices. Also a practical method of filtering for stochastic volatility models was given by J. R. Stroud N. G. Polson and P. Muller 6 . These authors introduced also a sequential parameter estimation in stochastic volatility models with jumps 7 . And other contributions were given recently by A.