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

Accuracy of Deep Learning in Calibrating HJM Forward Curves