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

Jak\v{s}a Cvitani\'c, Robert Liptser and Boris Rozovskii

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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 \[ dS_{t}=m(\theta_{t})S_{t} dt+v(\theta_{t})S_{t} dB_{t}, \] 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

Date: 2006-12
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Citations: View citations in EconPapers (10)

Published in Annals of Applied Probability 2006, Vol. 16, No. 3, 1633-1652

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