Mathematics Colloquium
Antoine Jacquier
Imperial College London
Title: Recent advances in rough volatility
Date: Friday, March 12, 2021
Place and Time: Zoom, 3:05-3:55 pm
Abstract.
Rough volatility models are one the new "hot topics" in Quantitative Finance (its creators, Jim Gatheral and Mathieu Rosenbaum having just been named Risk Quant of the Year!!). They rely on the delicate observation that the instantaneous volatility of asset prices (Equity stocks, indices, commodities,...) is driven by a process featuring characteristics similar to those of a fractional Brownian motion with short memory. This surprising discovery gave rise to a plethora of papers (an exhaustive review of which is available at https://sites.google.com/site/roughvol/home).
Nothing comes for free though and this new modelling paradigm initially suffered from the complexity of introducing non-Markovian dynamics, whereby classical tools (among which Feynman-Kac PDE formulation of Markovian systems, Monte Carlo schemes) need a fresh facelift.
In this context, we introduce a wide variety of new tools and see how they all come together to the rescue, in particular:
1) Large and moderate deviations for non-Markovian systems;
2) Deep learning techniques for path-dependent PDEs.
We shall endeavour to strike a fair balance between technical tools, immediate applications and modelling intuitions.