Séminaire FDD-FiME

Alexandre Pannier (LPSM, Université Paris Cité) Title : Rough volatility, path-dependent PDEs and weak rates of convergence 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 Itô formula developed by . We then leverage 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 ∈ (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. A joint work with Ofelia Bonesini and Antoine Jacquier. Download slides