PT  - JOURNAL ARTICLE
AU  - Fabien Le Floc’h
TI  - An Arbitrage-Free Interpolation of Class &lt;span class=&quot;inline-formula&quot; id=&quot;inline-formula-1&quot;&gt;&lt;img src=&quot;pending:yes&quot; l:ref-type=&quot;journal&quot; hwp:journal=&quot;iijderiv&quot; hwp:article=&quot;jod.2020.1.119&quot; l:sub-ref=&quot;inline-graphic-1&quot; l:type=&quot;image/*&quot; class=&quot;inline-graphic&quot; alt=&quot;Graphic&quot;/&gt;&lt;/span&gt; for Option Prices
AID  - 10.3905/jod.2020.1.119
DP  - 2020 Nov 13
TA  - The Journal of Derivatives
PG  - jod.2020.1.119
4099  - https://pm-research.com/content/early/2020/11/12/jod.2020.1.119.short
4100  - https://pm-research.com/content/early/2020/11/12/jod.2020.1.119.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.