Guido Gazzani (ENPC)

Title: Pricing and calibration of path-dependent volatility models


We consider the path-dependent volatility (PDV) model of Guyon and Lekeufack (2023), where the instantaneous volatility is a
linear combination of a weighted sum of past returns and the square root of a weighted sum of past squared returns. We discuss the influence
of an additional parameter that unlocks enough volatility on the upside to reproduce the implied volatility smiles of SPX and VIX options within a 4-factor Markovian model (4FPDV).
This class of PDV models, motivated by empirical studies, comes with computational challenges, especially in relation to VIX options pricing and calibration.
To address these challenges, we propose an accurate neural network approximation of the VIX which leverages on the Markovianity of the 4FPDV model.

This approximation is subsequently used to tackle the joint calibration of SPX and VIX options.