# Pricing options on flow forwards by neural networks in Hilbert space

arXiv: https://arxiv.org/abs/2202.11606 · HTML: https://mlsanity.com/paper/2202.11606/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 43 references that are in the map.
- First posted on arXiv 17 Feb 2022.

## Builds on (most cited first, 7 of 7)

- [Solving high-dimensional partial differential equations using deep learning](https://mlsanity.com/paper/1707.02568/) (2017)
- [Deep Hedging](https://mlsanity.com/paper/1802.03042/) (2018)
- [An overview on deep learning-based approximation methods for partial differential equations](https://mlsanity.com/paper/2012.12348/) (2020)
- [Solving the Kolmogorov PDE by means of deep learning](https://mlsanity.com/paper/1806.00421/) (2018)
- [Neural networks for option pricing and hedging: a literature review](https://mlsanity.com/paper/1911.05620/) (2019)
- [Deep neural networks, generic universal interpolation, and controlled ODEs](https://mlsanity.com/paper/1908.07838/) (2019)
- [Deep calibration of rough stochastic volatility models](https://mlsanity.com/paper/1810.03399/) (2018)

## Built on by (most cited first, 5 of 5)

- [Designing Universal Causal Deep Learning Models: The Case of Infinite-Dimensional Dynamical Systems from Stochastic Analysis](https://mlsanity.com/paper/2210.13300/) (2022)
- [Solving Optimal Execution Problems via In-Context Operator Networks](https://mlsanity.com/paper/2501.15106/) (2025)
- [Neural networks in non-metric spaces](https://mlsanity.com/paper/2406.09310/) (2024)
- [Parametric Numerical Integration with (Differential) Machine Learning](https://mlsanity.com/paper/2512.11530/) (2025)
- [NeuralChaos: Optimal Adapted Approximation of Square Integrable Predictable Processes](https://mlsanity.com/paper/2607.14361/) (2026)

## Abstract (arXiv)

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.