2015/02/13 by Boris Buchmann, Benjamin D. Kaehler, Buchmann, Boris +5
Economics, Econometrics and Finance · Engineering · #60F05 #60F15 #60F17 #60G51 #60J65 #60J75 #Advanced Measurement and Metrology Techniques #FOS: Economics and business #FOS: Mathematics #Financial Risk and Volatility Modeling #Mathematical Finance (q-fin.MF) #Probability (math.PR)
paper · pdf · doi:10.48550/arxiv.1502.03901
openalex publication_date 2015/02/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We unify and extend a number of approaches related to constructing\nmultivariate Variance-Gamma (V.G.) models for option pricing. An overarching\nmodel is derived by subordinating multivariate Brownian motion to a\nsubordinator from the Thorin (1977) class of generalised Gamma convolution\nsubordinators. A class of models due to Grigelionis (2007), which contains the\nwell-known Madan-Seneta V.G. model, is of this type, but our multivariate\ngeneralization is considerably wider, allowing in particular for processes with\ninfinite variation and a variety of dependencies between the underlying\nprocesses. Multivariate classes developed by P 'erez-Abreu and Stelzer (2012)\nand Semeraro (2008) and Guillaume (2013) are also submodels. The new models are\nshown to be invariant under Esscher transforms, and quite explicit expressions\nfor canonical measures (and transition densities in some cases) are obtained,\nwhich permit applications such as option pricing using PIDEs or tree based\nmethodologies. We illustrate with best-of and worst-of European and American\noptions on two assets.\n