bilateral Gamma distributions selfdecomposability unimodality bilateral Gamma processes measure transformations stock models option pricing term structure models Bilateral Gamma Distributions and Processes in Financial Mathematics Uwe Küchler Küchler Uwe Stefan Tappe Tappe Stefan Institut für Mathematik, Humboldt-Universität zu Berlin (ISSN 0863-0976), 26 pages

Bilateral Gamma Distributions and Processes in Financial Mathematics

Uwe Küchler , Stefan Tappe

Preprint series: Institut für Mathematik, Humboldt-Universität zu Berlin (ISSN 0863-0976), 26 pages

MSC 2000

60G51 Processes with independent increments
62P05 Applications to actuarial sciences and financial mathematics
60E07 Infinitely divisible distributions; stable distributions

Abstract
We present a class of Lévy processes for modelling financial market fluctuations: Bilateral Gamma processes. Our starting point is to explore the properties of bilateral Gamma distributions, and then we turn to their associated Lévy processes. We treat exponential Lévy stock models with an underlying bilateral Gamma process as well as term structure models driven by bilateral Gamma processes and apply our results to a set of real financial data (DAX 1996-1998).

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