| Abstract: |
| We develop a novel deep learning approach for pricing European options in diffusion and jump-diffusion models, that can efficiently handle high-dimensional problems resulting from Markovian approximations of rough volatility models or from multi-asset options. 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 and the multi-variate Merton model. Time permitting, theoretical results about the generalization error of this method will be discussed. |
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