The Variance-Gamma Process for Option Pricing
Mathematical Finance
2025-10-17 v1
Abstract
This paper explores the concept of random-time subordination in modelling stock-price dynamics, and We first present results on the Laplace distribution as a Gaussian variance-mixture, in particular a more efficient volatility estimation procedure through the absolute moments. We generalise the Laplace model to characterise the powerful variance gamma model of Madan et al. as a Gamma time-subordinated Brownian motion to price European call options via an Esscher transform method. We find that the Variance Gamma model is able to empirically explain excess kurtosis found in log-returns data, rejecting a Black-Scholes assumption in a hypothesis test.
Cite
@article{arxiv.2510.14093,
title = {The Variance-Gamma Process for Option Pricing},
author = {Rohan Shenoy and Peter Kempthorne},
journal= {arXiv preprint arXiv:2510.14093},
year = {2025}
}