A filtering approach to tracking volatility from prices observed at random times
成果类型：
Article
署名作者：
Cvitanic, Jaksa; Liptser, Robert; Rozovskii, Boris
署名单位：
California Institute of Technology; Tel Aviv University; University of Southern California
刊物名称：
ANNALS OF APPLIED PROBABILITY
ISSN/ISSBN：
1050-5164
DOI：
10.1214/105051606000000222
发表日期：
2006
页码：
1633-1652
关键词：
摘要：
This paper is concerned with nonlinear filtering of the coefficients in asset price models with stochastic volatility. More specifically, we assume that the asset price process S=(S-t)(t >= 0) is given by dS(t)=m(theta(t))S(t)dt+v(theta(t))S(t)dB(t), where B=(B-t)(t >= 0) is a Brownian motion, v is a positive function and theta=(theta(t))(t >= 0) is a cadlag strong Markov process. The random process theta is unobservable. We assume also that the asset price St is observed only at random times 0 = 1). turns out that the filter is given by a recursive system that involves only deterministic Kolmogorov-type equations, which should make the numerical implementation relatively easy.