Multivariate subordination using generalised Gamma convolutions with applications to Variance Gamma processes and option pricing

Boris Buchmann, Benjamin Kaehler, Ross Maller and Alexander Szimayer

Stochastic Processes and their Applications, 2017, vol. 127, issue 7, 2208-2242

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.

Keywords: Lévy process; Variance-Gamma; Multivariate subordination; Generalised Gamma convolutions; Thorin measure; Esscher transformation; Esscher invariance; Superposition; Option pricing (search for similar items in EconPapers)
Date: 2017
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Citations: View citations in EconPapers (8)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:127:y:2017:i:7:p:2208-2242

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DOI: 10.1016/j.spa.2016.10.008

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