PT  - JOURNAL ARTICLE
AU  - Fabien Le Floc’h
TI  - An Arbitrage-Free Interpolation of Class <em>C</em><sup>2</sup> for Option Prices
AID  - 10.3905/jod.2020.1.119
DP  - 2021 May 31
TA  - The Journal of Derivatives
PG  - 64--86
VI  - 28
IP  - 4
4099  - https://pm-research.com/content/28/4/64.short
4100  - https://pm-research.com/content/28/4/64.full
AB  - 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 . 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.TOPICS: Options, statistical methodsKey Findings▪ The local variance gamma model, extended with piecewise-linear local variance function, leads to simple formulae for vanilla option prices.▪ This model leads to a fast, exact arbitrage-free interpolation of market quotes.▪ A specific regularization is required to overcome an artificial spike in the implied probability density, when fitting the model to noisy quotes.