No arbitrage global parametrization for the eSSVI volatility surface

TL;DR

This paper introduces a global, arbitrage-free parametrization of the eSSVI volatility surface that improves calibration speed and guarantees arbitrage-free market data fitting, enhancing existing methods.

Contribution

It proposes a novel, faster calibration approach for the eSSVI surface that ensures arbitrage-free fits, providing a comprehensive global view unlike previous sequential methods.

Findings

Faster calibration method for eSSVI surfaces.

Guarantees arbitrage-free fit of market data.

Provides a global parametrization of the volatility surface.

Abstract

The article describes a global and arbitrage-free parametrization of the eSSVI surfaces introduced by Hendriks and Martini in 2019. A robust calibration of such surfaces has already been proposed by the quantitative research team at Zeliade in 2019, but it is sequential in expiries and lacks of a global view on the surface. The alternative calibration suggested in this article is faster and always guarantees an arbitrage-free fit of market data.