 We then use it to calibrate the HJM parameters starting from (simulated) option market data. Finally we introduce a new loss function that takes into account bid and ask prices and offers a solution to calibration in illiquid markets . A key issue discovered is that the trained neural network might be non-injective, which could potentially lead to poor accuracy in calibrating the forward curve parameters, even when showing a high degree of accuracy in recovering the prices .
<meaning-changed>  We then use it to calibrate the HJM parameters starting from (simulated) option market data. Finally we introduce a new loss function that takes into account bid and ask prices and offers a solution to calibration in illiquid markets . A key issue discovered is that the trained neural network might be non-injective, which could potentially lead to poor accuracy in calibrating the forward curve parameters, even when showing a high degree of accuracy in recovering the prices .
 We then use it 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 . A key issue discovered is that the trained neural network might be non-injective, which could potentially lead to poor accuracy in calibrating the forward curve parameters, even when showing a high degree of accuracy in recovering the prices .