The bilateral generalized inverse Gaussian process with applications to financial modeling

TL;DR

This paper introduces bilateral generalized inverse Gaussian (BGIG) distributions and associated Lévy processes, demonstrating their usefulness in financial modeling, especially for calibrating stock market models and option pricing.

Contribution

The paper develops the theory of BGIG distributions and Lévy processes, and applies them to create a flexible, calibratable stock market model suitable for Monte Carlo and Fourier methods.

Findings

BGIG distributions have favorable properties for financial modeling.

The proposed model fits real market data effectively.

It simplifies calibration and improves option pricing accuracy.

Abstract

We introduce and document a class of probability distributions, called bilateral generalized inverse Gaussian (BGIG) distributions, that are obtained by convolution of two generalized inverse Gaussian distributions supported by the positive and negative semi-axis. We prove several results regarding their analyticity, shapes and asymptotics, and we introduce the associated L\'evy processes as well as their main properties. We study the behaviour of these processes under change of measure, their simulations and the structure of their sample paths, and we introduce a stock market model constructed by means of exponential BGIG processes. Based on real market data, we show that this model is easy to calibrate thanks notably to idiosyncratic properties of BGIG distributions, and that it is well suited to Monte Carlo and Fourier option pricing.