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

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  • Jaksa Cvitanic
  • Robert Liptser
  • Boris Rozovskii

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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  • Jaksa Cvitanic & Robert Liptser & Boris Rozovskii, 2005. "A filtering approach to tracking volatility from prices observed at random times," Papers math/0509503, arXiv.org.
    • Handle: RePEc:arx:papers:math/0509503
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    1. Maria Elvira Mancino & Paul Malliavin, 2002. "Fourier series method for measurement of multivariate volatilities," Finance and Stochastics, Springer, vol. 6(1), pages 49-61.
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    Cited by:

    1. Jie Xiong & Yong Zeng, 2011. "A branching particle approximation to a filtering micromovement model of asset price," Statistical Inference for Stochastic Processes, Springer, vol. 14(2), pages 111-140, May.
    2. Yong Zeng, 2005. "Bayesian Inference via Filtering for a Class of Counting Processes: Application to the Micromovement of Asset Price," Statistical Inference for Stochastic Processes, Springer, vol. 8(3), pages 331-354, December.

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