# Bilateral Gamma distributions and processes in financial mathematics

## TL;DR

This paper introduces Bilateral Gamma processes as a new class of Lévy processes for modeling financial market fluctuations, analyzing their properties and applications in stock and term structure models with real data.

## Contribution

It develops the theory of Bilateral Gamma distributions and processes, applying them to financial modeling and empirical data analysis.

## Key findings

- Bilateral Gamma processes effectively model financial data.
- Application to DAX data shows good fit.
- New Lévy process class for finance.

## Abstract

We present a class of L\'evy 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 L\'evy processes. We treat exponential L\'evy 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).