Volatility Surface Parameterization: the SVI Model

After an introduction on the modelling of the volatility surface implied by option prices, we will focus in this quantitative finance training course on the parametric methods, and particularly on the Stochastic Volatility Inspired (SVI) model, popular on equities, and some of its extensions.

The volatility surface is not flat, it varies across strikes and time to expiry. Asset returns are not (log)normally distributed, contrary to what the Black-Scholes model assumes. Extreme risks and asymmetric return distributions can explain a part of the shapes of the volatility curves. We will measure the impact of the skewness and kurtosis on the volatility smile using the Cornish Fisher expansion.

There are many ways to build a volatility surface. It has been the topic of many research papers over the past decades.

The SVI parametric model allows to fit a large number of possible volatility curves with its five parameters, with specific non-arbitrage conditions.

The SVI Jump-Wings (SVI-JW) parameterization is an interesting alternative method where the different parameters have a concrete interpretation, each of them controlling a specific aspect of the smile, making model calibration easier and more robust.

After introducing the Breeden-Litzenberger formula which links the second order derivative of vanilla option prices with the risk neutral density function we will see how to apply it to value exotic payoffs with a concrete example using the SVI-JW model through a tutorial in Python.

We will finally present the Surface SVI (SSVI) parameterization, which is an extension of the SVI model for the whole volatility surface, free of arbitrage under certain conditions.

The course is composed of many videos, quizzes, applications in Python.

A certificate of achievements will be delivered once the course has been completed with success.