Multivariate subordination using generalised Gamma convolutions with applications to Variance Gamma processes and option pricing
Date
2017
Authors
Buchmann, Boris
Kaehler, Benjamin
Maller, Ross
Szimayer, Alexander
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Elsevier
Abstract
We unify and extend a number of approaches related to constructing multivariate Madan–Seneta Variance-Gamma models for option pricing. Complementing Grigelionis’ (2007) class, an overarching model is derived by subordinating multivariate Brownian motion to a subordinator from Thorin’s (1977) [58, 59] class of generalised Gamma convolutions. Multivariate classes developed by Pérez-Abreu and Stelzer (2014), Semeraro (2008) and Guillaume (2013) are submodels. The classes are shown to be invariant under Esscher transforms, and quite explicit expressions for canonical measures are obtained, which permit applications such as option pricing using PIDEs or tree based methodologies. We illustrate with best-of and worst-of European and American options on two assets.
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Keywords
Levy process, Variance-Gamma, Multivariate subordination, Generalised Gamma convolutions, Thorin measure, Esscher transformation, Esscher invariance, Superposition, Option pricing
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Stochastic Processes and their Applications
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Journal article
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Open Access
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CC-BY-NC-ND 4.0 license
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