A time-stepping deep gradient flow method for option pricing in (rough) diffusion models
This addresses the computational challenge of option pricing in complex financial models for practitioners, but it is incremental as it builds on existing deep learning and PDE reformulation techniques.
The authors tackled the problem of pricing European options in diffusion models, particularly for high-dimensional cases from rough volatility approximations, by developing a deep learning method that reformulates the PDE as an energy minimization problem solved with time-stepping neural networks. The result showed the method respects asymptotic behavior and known bounds, with accuracy and efficiency demonstrated in numerical examples like the lifted Heston model.
We develop a novel deep learning approach for pricing European options in diffusion models, that can efficiently handle high-dimensional problems resulting from Markovian approximations of rough volatility models. The option pricing partial differential equation is reformulated as an energy minimization problem, which is approximated in a time-stepping fashion by deep artificial neural networks. The proposed scheme respects the asymptotic behavior of option prices for large levels of moneyness, and adheres to a priori known bounds for option prices. The accuracy and efficiency of the proposed method is assessed in a series of numerical examples, with particular focus in the lifted Heston model.