A new Input Convex Neural Network with application to options pricing

TL;DR

This paper presents a novel convex neural network architecture tailored for accurately approximating convex option prices, supported by theoretical convergence guarantees and enhanced training techniques, with demonstrated effectiveness on various options.

Contribution

The paper introduces a new input convex neural network architecture with theoretical convergence bounds and a scrambling training phase, specifically designed for convex option pricing.

Findings

Effective approximation of convex option prices demonstrated on Basket, Bermudan, and Swing options.

Theoretical convergence bounds validate the network's approximation capabilities.

Scrambling phase improves training efficiency and accuracy.

Abstract

We introduce a new class of neural networks designed to be convex functions of their inputs, leveraging the principle that any convex function can be represented as the supremum of the affine functions it dominates. These neural networks, inherently convex with respect to their inputs, are particularly well-suited for approximating the prices of options with convex payoffs. We detail the architecture of this, and establish theoretical convergence bounds that validate its approximation capabilities. We also introduce a \emph{scrambling} phase to improve the training of these networks. Finally, we demonstrate numerically the effectiveness of these networks in estimating prices for three types of options with convex payoffs: Basket, Bermudan, and Swing options.