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A time-stepping deep gradient flow method for option pricing in (rough) diffusion models (2403.00746v2)

Published 1 Mar 2024 in q-fin.CP, cs.LG, math.PR, and q-fin.MF

Abstract: 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.

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