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

2005/09/22 by Cvitanic, Jaksa, R. Liptser, Liptser, Robert +2 · 1 citation
Economics, Econometrics and Finance · #Complex Systems and Time Series Analysis #FOS: Economics and business #FOS: Mathematics #Financial Markets and Investment Strategies #Probability (math.PR) #Statistical Finance (q-fin.ST) #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.math/0509503

openalex publication_date 2005/09/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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≥0 is given by dS_t=r(θ_t)S_tdt+v(θ_t)S_tdB_t, where B=(B_t)_t≥0 is a Brownian motion, v is a positive function, and θ=(θ_t)_t≥0 is a cádlág strong Markov process. The random process θ is unobservable. We assume also that the asset price S_t is observed only at random times 0

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