A deep implicit-explicit minimizing movement method for option pricing in jump-diffusion models
This addresses the computational challenge of pricing multi-asset options in financial models with jumps, which is important for quantitative finance practitioners, though it appears to be an incremental improvement over existing deep learning methods.
The authors developed a deep learning method for pricing European basket options under jump-diffusion models, formulating it as a partial integro-differential equation and solving it with an implicit-explicit minimizing movement approach using neural networks. Their method demonstrated robust performance in high dimensions and outperformed existing deep learning approaches like the deep Galerkin method and deep BSDE solver with jumps in numerical experiments.
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 appropriate 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 these methods are assessed in a series of numerical experiments involving the Merton jump-diffusion model, while a comparison with the deep Galerkin method and the deep BSDE solver with jumps further supports the merits of the proposed approach.