Neural Networks with Asymptotics Control

Abstract

Artificial Neural Networks (ANNs) have recently been proposed as accurate and fast approximators in various derivatives pricing applications. ANNs typically excel in fitting functions they approximate at the input parameters they are trained on, and often are quite good in interpolating between them. However, for standard ANNs, their extrapolation behavior – an important aspect for financial applications – cannot be controlled due to complex functional forms typically involved. We overcome this significant limitation and develop a new type of neural networks that incorporate large-value asymptotics, when known, allowing explicit control over extrapolation.

This new type of asymptotics-controlled ANNs is based on two novel technical constructs, a multi-dimensional spline interpolator with prescribed asymptotic behavior, and a custom ANN layer that guarantees zero asymptotics in chosen directions. Asymptotics control brings a number of important benefits to ANN applications in finance such as well-controlled behavior under stress scenarios, graceful handling of regime switching, and improved interpretability.

Keywords: Artificial Neural Network, Machine Learning, Asymptotics Control, Multi-Dimensional Splines, Kolmogorov-Arnold Representation Theorem, SABR Model

JEL Classification: C13, C15, C51, C52, C63, D40, G12, G13, G15, G21, G28