Ole Eiler Barndorff-Nielsen () (Thiele Centre, Department of Mathematical Sciences & CREATES, Aarhus University) Robert Stelzer () (TUM Institute for Advanced Study & Zentrum Mathematik, Technische Universität München)
Abstract
Using positive semidefinite supOU (superposition of Ornstein-Uhlenbeck type) processes to describe the volatility, we introduce a multivariate stochastic volatility model for financial data which is capable of modelling long range dependence effects. The finiteness of moments and the second order structure of the volatility, the log returns, as well as their “squares” are discussed in detail. Moreover, we give several examples in which long memory effects occur and study how the model as well as the simple Ornstein-Uhlenbeck type stochastic volatility model behave under linear transformations. In particular, the models are shown to be preserved under invertible linear transformations. Finally, we discuss how (sup)OU stochastic volatility models can be combined with a factor modelling approach.
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Publisher Info
Paper provided by School of Economics and Management, University of Aarhus in its series CREATES Research Papers with number
2009-42.