W-shaped implied volatility curves in a variance-gamma mixture model

TL;DR

This paper demonstrates that W-shaped implied volatility curves observed in liquid option markets can be modeled using a mixture of two variance-gamma models, simplifying previous approaches that required more complex mixtures.

Contribution

The paper introduces a variance-gamma mixture model that can generate W-shaped implied volatility curves, reducing the complexity compared to prior lognormal mixture models.

Findings

W-shaped implied volatility curves can be reproduced with a two-component variance-gamma mixture.

Contrasts with lognormal models requiring three distributions for similar shapes.

Provides a simpler modeling approach for complex implied volatility patterns.

Abstract

In liquid option markets, W-shaped implied volatility curves have occasionally be observed. We show that such shapes can be reproduced in a mixture of two variance-gamma models. This is in contrast to lognormal models, where at least three different distributions have to be mixed in order to produce a W-shape, as recently shown by Glasserman and Pirjol.