“Rough volatility, path-dependent PDEs and weak rates of convergence”
Mercoledì 29 Marzo 2023, ore 13:30 - Aula 2BC30 - Ofelia Bonesini (Imperial College London)
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).