RT Journal Article
SR Electronic
T1 An Arbitrage-Free Interpolation of Class <em>C</em><sup>2</sup> for Option Prices
JF The Journal of Derivatives
FD Institutional Investor Journals
SP jod.2020.1.119
DO 10.3905/jod.2020.1.119
A1 Fabien Le Floc’h
YR 2020
UL https://pm-research.com/content/early/2020/11/24/jod.2020.1.119.abstract
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.