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

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  • Martin Keller-Ressel

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.

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  • Martin Keller-Ressel, 2022. "W-shaped implied volatility curves in a variance-gamma mixture model," Papers 2209.14726, arXiv.org.
    • Handle: RePEc:arx:papers:2209.14726
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    1. Dilip B. Madan & Peter P. Carr & Eric C. Chang, 1998. "The Variance Gamma Process and Option Pricing," Review of Finance, European Finance Association, vol. 2(1), pages 79-105.
    2. Roger W. Lee, 2004. "The Moment Formula For Implied Volatility At Extreme Strikes," Mathematical Finance, Wiley Blackwell, vol. 14(3), pages 469-480, July.
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