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

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