Filtering a nonlinear stochastic volatility model

doi:10.1007/s11071-011-0069-4

Filtering a nonlinear stochastic volatility model

2011-06-03

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DOI：10.1007/s11071-011-0069-4

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Abstract

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We introduce a class of stochastic volatility models whose parameters are modulated by a hidden nonlinear dynamical system. Our aim is to incorporate the impact of economic cycles, or business cycles, into the long-term behavior of volatility dynamics. We develop a discrete-time nonlinear filter for the estimation of the hidden volatility and the nonlinear dynamical system based on return observations. By exploiting the technique of a reference probability measure we derive filters for the hidden volatility and the nonlinear dynamical system.

Keywords:

Stochastic volatility

Nonlinear dynamical system

Economic cycles

Nonlinear filters

Change of measures

Reference probability

Filtering a nonlinear stochastic volatility model

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