Filtering a nonlinear stochastic volatility model

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...

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Bibliographic Details
Published in:Nonlinear dynamics 2012, Vol.67 (2), p.1295-1313
Main Authors: Elliott, Robert J., Siu, Tak Kuen, Fung, Eric S.
Format: Article
Language:English
Subjects:
Automotive Engineering
Business
Business cycles
Classical Mechanics
Control
Dynamical Systems
Economics
Engineering
Filtering
Impact analysis
Mechanical Engineering
Nonlinear dynamics
Nonlinear filters
Nonlinearity
Original Paper
Stochastic models
Stochasticity
Vibration
Volatility
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Summary: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.
ISSN:0924-090X
1573-269X
DOI:10.1007/s11071-011-0069-4