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arXiv · 2510.14093

The Variance-Gamma Process for Option Pricing

Rohan Shenoy·Peter Kempthorne
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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.

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Rohan Shenoy, Peter Kempthorne. 2025-10-15. The Variance-Gamma Process for Option Pricing. https://arxiv.org/abs/2510.14093

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