Data assimilation for the stochastic one-layer rotating shallow water system driven by transport noise
Oana Lang (Imperial College London, UK)
Paolo Pigato (WIAS Berlin)
I will review some empirical facts on implied volatility and how they recently led to the introduction of rough (fractional) stochastic volatility models in finance. I will recall some results in asymptotic pricing and discuss a recent precise asymptotic expansion, based on the Laplace method on the space of models, which applies in particular to rough volatility models. I will show an implementation in the case of the rough Bergomi model.
(Based on joint work with P. K. Friz and P. Gassiat)