Arbitrage-free SVI volatility surfaces

TL;DR

This paper presents a method to calibrate the SVI implied volatility surface ensuring no static arbitrage, with a simple closed-form representation and demonstrated effectiveness on SPX options data.

Contribution

It introduces a calibration technique for SVI surfaces that guarantees arbitrage-free conditions with a straightforward closed-form solution.

Findings

High-quality SVI fits achieved on SPX options data

The method guarantees absence of static arbitrage in the calibrated surface

A large class of arbitrage-free SVI surfaces with simple representation

Abstract

In this article, we show how to calibrate the widely-used SVI parameterization of the implied volatility surface in such a way as to guarantee the absence of static arbitrage. In particular, we exhibit a large class of arbitrage-free SVI volatility surfaces with a simple closed-form representation. We demonstrate the high quality of typical SVI fits with a numerical example using recent SPX options data.