Abstract
This work proposes a tractable multivariate Lévy process able to approximate margins of VG type. Jump arrivals are modelled as multivariate subordinators with common and idiosyncratic components which generate linear and nonlinear dependence. Jumps of any sign and size show an own degree of common jump arrivals which is explicitly modelled and offers high flexibility in calibrating nonlinear dependence. The approximation of margins, the joint characteristic exponent and measures of dependence are studied via simple closed formulas and a multivariate simulation procedure is available. An empirical analysis supports the choice of VG margins and documents an accurate fit of linear and nonlinear dependence.
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Acknowledgements
The Author is grateful to Hansjoerg Albrecher, Michael Rockinger, Olivier Scaillet and especially Elisa Luciano for their useful comments and suggestions.
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© 2012 Springer-Verlag Italia
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Marfè, R. (2012). Multivariate jump arrivals: The variance gamma case. In: Perna, C., Sibillo, M. (eds) Mathematical and Statistical Methods for Actuarial Sciences and Finance. Springer, Milano. https://doi.org/10.1007/978-88-470-2342-0_32
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DOI: https://doi.org/10.1007/978-88-470-2342-0_32
Publisher Name: Springer, Milano
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