A filtering approach to tracking volatility from prices observed at random times

By Jakša Cvitanić, Robert Sh. Liptser, Boris L. Rozovskii. 2005

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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\geq0} $ is given by \[ dS_{t}=r(\theta_{t})S_{t}dt+v(\theta_{t})S_{t}dB_{t}, \] where $B=(B_{t})_{t\geq0}$ is a Brownian motion, $v$ is a positive function, and $\theta=(\theta_{t})_{t\geq0}$ is a c\'{a}dl\'{a}g strong Markov process. The random process $\theta$ is unobservable. We assume also that the asset price $S_{t}$ is observed only at random times $0

Subfields: Economics and Econometrics, Finance

View Paper: https://www.semanticscholar.org/paper/7c3eff32cd667ff7ae90c34488cd1f7bf8c567b9