Stationary and multi-self-similar random fields with stochastic volatility

This paper introduces stationary and multi-self-similar random fields which account for stochastic volatility and have type G marginal law. The stationary random fields are constructed using volatility modulated mixed moving average (MA) fields and their probabilistic properties are discussed. Also,...

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Published inStochastics (Abingdon, Eng. : 2005) Vol. 87; no. 5; pp. 848 - 870
Main Author Veraart, Almut E.D.
Format Journal Article
LanguageEnglish
Published Abingdon Taylor & Francis 03.09.2015
Taylor & Francis Ltd
Subjects
AMS Subject Classification: 60G10
Construction
Fields (mathematics)
Fourier analysis
generalized Lamperti transform
infinite divisibility
Lévy basis
mixed moving average fields
multi-self-similarity
Representations
stationarity
Stochastic processes
stochastic volatility
Stochasticity
Transforms
type G distribution
Volatility
Weight function
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Summary:This paper introduces stationary and multi-self-similar random fields which account for stochastic volatility and have type G marginal law. The stationary random fields are constructed using volatility modulated mixed moving average (MA) fields and their probabilistic properties are discussed. Also, two methods for parameterizing the weight functions in the MA representation are presented: one method is based on Fourier techniques and aims at reproducing a given correlation structure, the other method is based on ideas from stochastic partial differential equations. Moreover, using a generalized Lamperti transform we construct volatility modulated multi-self-similar random fields which have type G distribution.
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ISSN:1744-2508
1744-2516
DOI:10.1080/17442508.2015.1012081