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

Boris Buchmann*, Benjamin Kaehler, Ross Maller, Alexander Szimayer

*Corresponding author for this work

    Research output: Contribution to journalArticlepeer-review

    17 Citations (Scopus)

    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.

    Original languageEnglish
    Pages (from-to)2208-2242
    Number of pages35
    JournalStochastic Processes and their Applications
    Volume127
    Issue number7
    DOIs
    Publication statusPublished - Jul 2017

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