A deep implicit-explicit minimizing movement method for option pricing in jump-diffusion models (2401.06740v1)

Abstract: We develop a novel deep learning approach for pricing European basket options written on assets that follow jump-diffusion dynamics. The option pricing problem is formulated as a partial integro-differential equation, which is approximated via a new implicit-explicit minimizing movement time-stepping approach, involving approximation by deep, residual-type Artificial Neural Networks (ANNs) for each time step. The integral operator is discretized via two different approaches: a) a sparse-grid Gauss--Hermite approximation following localised coordinate axes arising from singular value decompositions, and b) an ANN-based high-dimensional special-purpose quadrature rule. Crucially, the proposed ANN is constructed to ensure the asymptotic behavior of the solution for large values of the underlyings and also leads to consistent outputs with respect to a priori known qualitative properties of the solution. The performance and robustness with respect to the dimension of the methods are assessed in a series of numerical experiments involving the Merton jump-diffusion model.