Pricing options on flow forwards by neural networks in Hilbert space

TL;DR

This paper introduces a novel neural network approach in Hilbert space for efficiently pricing options on flow forwards, leveraging an infinite-dimensional framework and specialized architecture for continuous function approximation.

Contribution

It develops a new neural network architecture based on Hilbert space principles for option pricing in infinite-dimensional settings, improving computational efficiency.

Findings

Achieves high numerical efficiency in pricing options on flow forwards.

Outperforms classical neural networks trained on term structure data.

Demonstrates the effectiveness of Hilbert space-based neural networks in financial modeling.

Abstract

We propose a new methodology for pricing options on flow forwards by applying infinite-dimensional neural networks. We recast the pricing problem as an optimization problem in a Hilbert space of real-valued function on the positive real line, which is the state space for the term structure dynamics. This optimization problem is solved by facilitating a novel feedforward neural network architecture designed for approximating continuous functions on the state space. The proposed neural net is built upon the basis of the Hilbert space. We provide an extensive case study that shows excellent numerical efficiency, with superior performance over that of a classical neural net trained on sampling the term structure curves.