“Rough volatility, path-dependent PDEs and weak rates of convergence”
Mercoledì 29 Marzo 2023, ore 13:30 - Aula 2BC30 - Ofelia Bonesini (Imperial College London)
Abstract
In the setting of stochastic Volterra equations, and in particular rough volatility models, we show that conditional expectations are the unique classical solutions to path-dependent PDEs. The latter arise from the functional Itō formula developed by [Viens, F., & Zhang, J. (2019). A martingale approach for fractional Brownian motions and related path dependent PDEs. Ann. Appl. Probab.]. We then leverage on these tools to study weak rates of convergence for discretised stochastic integrals of smooth functions of a Riemann-Liouville fractional Brownian motion with Hurst parameter $H \in (0, 1/2)$. These integrals approximate log-stock prices in rough volatility models. We obtain weak error rates of order $1$ if the test function is quadratic and of order $H + 1/2$ for smooth test functions.
This is a joint work with Prof. Antoine Jacquier (Imperial College London) and Dr Alexandre Pannier (Université Paris Cité).
