An arbitrage-free interpolation of class C2 for option prices

Fabien Le Floch*

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review


This article presents simple formulae for the local variance gamma model of Carr and Nadtochiy (2017), extended with a piecewise-linear local variance function. The new formulae allow us to calibrate the model efficiently to market option quotes. On a small set of quotes, exact calibration is achieved under one millisecond. This effectively results in an arbitrage-free interpolation of class C2. The article proposes a good regularization when the quotes are noisy. Finally, it puts in evidence an issue of the model at-the-money, which is also present in the related one-step finite difference technique of Andreasen and Huge (2011), and gives two solutions for it.

Original languageEnglish
Pages (from-to)64-86
Number of pages23
JournalJournal of Derivatives
Issue number4
Publication statusPublished - 2021


  • Options
  • Statistical methods


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