Applications of multivariate quasi-random sampling with neural networks

TL;DR

This paper explores the use of generative moment matching networks (GMMNs) for modeling dependence in stochastic processes, demonstrating their advantages in financial applications and variance reduction techniques.

Contribution

It introduces the application of GMMNs to model dependence in stochastic processes like Brownian motions and GARCH models, highlighting their benefits over parametric models.

Findings

GMMNs effectively model dependence in stochastic processes.

Using GMMNs improves variance reduction in simulations.

Applications include pricing American basket options and simulating predictive distributions.

Abstract

Generative moment matching networks (GMMNs) are suggested for modeling the cross-sectional dependence between stochastic processes. The stochastic processes considered are geometric Brownian motions and ARMA-GARCH models. Geometric Brownian motions lead to an application of pricing American basket call options under dependence and ARMA-GARCH models lead to an application of simulating predictive distributions. In both types of applications the benefit of using GMMNs in comparison to parametric dependence models is highlighted and the fact that GMMNs can produce dependent quasi-random samples with no additional effort is exploited to obtain variance reduction.