We propose a fully data-driven approach to calibrate local stochastic volatility (LSV) models, circumventing in particular the ad hoc interpolation of the volatility surface. To achieve this, we parametrize the leverage function by a family of feed-forward neural networks and learn their...

We give a rigorous proof of the representation of implied volatility as a time-average of weighted expectations of local or stochastic volatility. With this proof we fix the problem of a circular definition in the original derivation of Gatheral, who introduced the implied volatility...

We investigate the performance of the Deep Hedging framework under training paths beyond the (finite dimensional) Markovian setup. In particular, we analyse the hedging performance of the original architecture under rough volatility models in view of existing theoretical results for those....

We investigate the performance of the Deep Hedging framework under training paths beyond the (finite dimensional) Markovian setup. In particular we analyse the hedging performance of the original architecture under rough volatility models with view to existing theoretical results for those....

We introduce a novel stochastic volatility model where the squared volatility of the asset return follows a Jacobi process. It contains the Heston model as a limit case. We show that the joint density of any finite sequence of log returns admits a Gram-Charlier A expansion with closed-form...