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

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• Mathematics

## Abstract

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

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