Accuracy of deep learning in calibrating HJM forward curves

Fred Espen Benth (), Nils Detering () and Silvia Lavagnini ()
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Fred Espen Benth: University of Oslo
Nils Detering: University of California
Silvia Lavagnini: University of Oslo

Digital Finance, 2021, vol. 3, issue 3, No 2, 209-248

Abstract: 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 Filipović 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.

Keywords: Heath–Jarrow–Morton approach; Infinite dimension; Energy markets; Option pricing; Neural networks; Model calibration (search for similar items in EconPapers)
JEL-codes: C45 C63 G13 (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (5)

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DOI: 10.1007/s42521-021-00030-w

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