%0 Journal Article
%A Floc’h, Fabien Le
%T An Arbitrage-Free Interpolation of Class *C*^{2} for Option Prices
%D 2021
%R 10.3905/jod.2020.1.119
%J The Journal of Derivatives
%P 64-86
%V 28
%N 4
%X 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.
%U https://jod.pm-research.com/content/iijderiv/28/4/64.full.pdf