Accuracy of Deep Learning in Calibrating HJM Forward Curves

TL;DR

This paper introduces a neural network-based calibration method for a new class of HJM models in commodity markets, demonstrating high accuracy in price recovery even in illiquid market conditions.

Contribution

It develops a novel state-dependent volatility operator for HJM models and proposes a neural network approach for efficient calibration using observed option prices.

Findings

Neural network calibration accurately recovers option prices.

Method performs well even with large bid-ask spreads.

Benchmarking shows high precision in price approximation.

Abstract

We price European-style options written on forward contracts in a commodity market, which we model with an infinite-dimensional Heath-Jarrow-Morton (HJM) approach. For this purpose we introduce a new class of state-dependent volatility operators that map the square integrable noise into the Filipovi\'{c} space of forward curves. For calibration, we specify a fully parametrized version of our model and train a neural network to approximate the true option price as a function of the model parameters. This neural network can then be used to calibrate the HJM parameters based on observed option prices. We conduct a numerical case study based on artificially generated option prices in a deterministic volatility setting. In this setting we derive closed pricing formulas, allowing us to benchmark the neural network based calibration approach. We also study calibration in illiquid markets with a large bid-ask spread. The experiments reveal a high degree of accuracy in recovering the prices after calibration, even if the original meaning of the model parameters is partly lost in the approximation step.