Talk by Benjamin Jourdain, Professor Ecole nationale des ponts et chaussées
Title: The implied volatility surface also is path-dependent
Abstract: We propose a new model for the forecasting of both the implied volatility surfaces and the underlying
asset price. In the spirit of Guyon and Lekeufack (2023) who are interested in the dependence of volatility
indices (e.g. the VIX) on the paths of the associated equity indices (e.g. the S&P 500), we first study
how vanilla options implied volatility can be predicted using the past trajectory of the underlying asset
price. Our empirical study reveals that a large part of the movements of the at-the-money-forward implied
volatility for up to two years time-to-maturities can be explained using the past returns and their squares.
Building on this stylized fact, we fit to historical data a parsimonious version of the SSVI parameterization
(Gatheral and Jacquier 2014) of the implied volatility surface relying on only four parameters and show
that the two parameters ruling the at-the-money-forward implied volatility as a function of the time-
to-maturity exhibit a path-dependent behavior with respect to the underlying asset price. Finally, we
propose a model for the joint dynamics of the implied volatility surface and the underlying asset price.
The latter is modelled using a variant of the path-dependent volatility model of Guyon and Lekeufack and
the former is obtained by adding a feedback effect of the underlying asset price onto the two parameters
ruling the at-the-money-forward implied volatility in the parsimonious SSVI parameterization and by
specifying Ornstein-Uhlenbeck processes for the residuals of these two parameters and Jacobi processes
for the two other parameters. This is joint work with Alexandre Boumezoued and Hervé Andrès.