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 [Viens, F., & Zhang, J. (2019). A martingale approach for fractional Brownian motions and related path dependent PDEs. Ann. Appl. Probab.]. 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.

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