An arbitrage-free interpolation of class C2 for option prices

Journal article (2021)

Authors

F.L.Y. Le Floch Numerical Analysis - EEMCS , Calypso Technology
Research Group
Numerical Analysis (EEMCS) (TU Delft)
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Published Date

2021

Language

English

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Faculty

Electrical Engineering, Mathematics and Computer Science

Department

Delft Institute of Applied Mathematics

Research Group

Numerical Analysis

Abstract

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.