Accuracy of deep learning in calibrating HJM forward curves by Silvia Lavagnini (University of Verona)

Event Date: 

Monday, March 14, 2022 - 3:30pm to 4:30pm

Event Location: 

  • Virtual via zoom
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. I will end the talk by presenting some on going work where we study a constant elasticity of variance-type of specification for the volatility operator. 
This is based on a joint work with Nils Detering (UCSB) and Fred Espen Benth (University of Oslo).