Neural Networks with Asymptotics Control

48 Pages Posted: 9 Mar 2020 Last revised: 27 Aug 2020

See all articles by Alexandre Antonov

Alexandre Antonov

Abu Dhabi Investment Authority; ADIA

Michael Konikov


Vladimir Piterbarg

NatWest Markets; Imperial College London

Date Written: February 23, 2020


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

Suggested Citation

Antonov, Alexandre and Konikov, Michael and Piterbarg, Vladimir, Neural Networks with Asymptotics Control (February 23, 2020). Available at SSRN: or

Alexandre Antonov (Contact Author)

Abu Dhabi Investment Authority ( email )

211 Corniche Road
Abu Dhabi, Abu Dhabi PO Box3600
United Arab Emirates

ADIA ( email )

211 Corniche
abu Dhabi
United Arab Emirates

Michael Konikov

Numerix ( email )

99 Park Avenue, 5th Floor
New York, NY 10016
United States

Vladimir Piterbarg

NatWest Markets ( email )

250 Bishopsgate
London, EC2M 4AA
United Kingdom

Imperial College London ( email )

South Kensington Campus
Imperial College
United Kingdom

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