Publikation: Working paper › Forskning

**The multivariate supOU stochastic volatility model.** / Barndorff-Nielsen, Ole; Stelzer, Robert.

Publikation: Working paper › Forskning

Barndorff-Nielsen, O & Stelzer, R 2009 'The multivariate supOU stochastic volatility model' Institut for Økonomi, Aarhus Universitet, Aarhus.

Barndorff-Nielsen, O., & Stelzer, R. (2009). *The multivariate supOU stochastic volatility model*. Institut for Økonomi, Aarhus Universitet.

Barndorff-Nielsen O, Stelzer R. 2009. The multivariate supOU stochastic volatility model. Aarhus: Institut for Økonomi, Aarhus Universitet.

Barndorff-Nielsen, Ole og Robert Stelzer *The multivariate supOU stochastic volatility model*. Aarhus: Institut for Økonomi, Aarhus Universitet. 2009., 21 s.

Barndorff-Nielsen O, Stelzer R. The multivariate supOU stochastic volatility model. Aarhus: Institut for Økonomi, Aarhus Universitet. 2009.

Barndorff-Nielsen, Ole ; Stelzer, Robert. / **The multivariate supOU stochastic volatility model**. Aarhus : Institut for Økonomi, Aarhus Universitet, 2009.

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title = "The multivariate supOU stochastic volatility model",

abstract = "Using positive semidefinite supOU (superposition of Ornstein-Uhlenbeck type) processesto describe the volatility, we introduce a multivariate stochastic volatility modelfor 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 examplesin which long memory effects occur and study how the model as well as thesimple Ornstein-Uhlenbeck type stochastic volatility model behave under linear transformations.In particular, the models are shown to be preserved under invertible lineartransformations. Finally, we discuss how (sup)OU stochastic volatility models can becombined with a factor modelling approach.",

keywords = "factor modelling, L{\'e}vy bases, linear transformations, long memory, Ornstein-Uhlenbeck type process, second order moment structure, stochastic volatility",

author = "Ole Barndorff-Nielsen and Robert Stelzer",

year = "2009",

language = "English",

publisher = "Institut for {\O}konomi, Aarhus Universitet",

type = "WorkingPaper",

institution = "Institut for {\O}konomi, Aarhus Universitet",

}

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T1 - The multivariate supOU stochastic volatility model

AU - Barndorff-Nielsen, Ole

AU - Stelzer, Robert

PY - 2009

Y1 - 2009

N2 - Using positive semidefinite supOU (superposition of Ornstein-Uhlenbeck type) processesto describe the volatility, we introduce a multivariate stochastic volatility modelfor 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 examplesin which long memory effects occur and study how the model as well as thesimple Ornstein-Uhlenbeck type stochastic volatility model behave under linear transformations.In particular, the models are shown to be preserved under invertible lineartransformations. Finally, we discuss how (sup)OU stochastic volatility models can becombined with a factor modelling approach.

AB - Using positive semidefinite supOU (superposition of Ornstein-Uhlenbeck type) processesto describe the volatility, we introduce a multivariate stochastic volatility modelfor 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 examplesin which long memory effects occur and study how the model as well as thesimple Ornstein-Uhlenbeck type stochastic volatility model behave under linear transformations.In particular, the models are shown to be preserved under invertible lineartransformations. Finally, we discuss how (sup)OU stochastic volatility models can becombined with a factor modelling approach.

KW - factor modelling, Lévy bases, linear transformations, long memory, Ornstein-Uhlenbeck type process, second order moment structure, stochastic volatility

M3 - Working paper

BT - The multivariate supOU stochastic volatility model

PB - Institut for Økonomi, Aarhus Universitet

CY - Aarhus

ER -