Differential Deep Learning And Physics-Informed Neural Networks For Fast Derivative Pricing

This article examines the Heston model with time-dependent parameters, known to be flexible and complex. Valuing derivative products within this model typically involves numerical methods, such as Monte Carlo (MC) simulations and partial differential equations (PDEs). However, these methods are often computationally intensive. Our approach leverages two advanced Deep Learning (DL) techniques in training an Artificial Neural Network (ANN) that approximates option prices in a Heston model with time-dependent parameters while reducing the number of labels needed for training. This methodology can also be extended to other dynamics, such as Bates or rough volatility models. We use payoff realizations as labels for the accelerated offline generation of datasets and employ a combined Differential Deep Learning (DDL) and Physics-Informed Neural Networks (PINNs) regularization strategy to train the ANN. Our approach captures the dynamics of the underlying risk factors and handles a variety of payoffs using fewer and rapidly computed labels. It allows fast and accurate pricing of derivative products and precise sensitivities computation, which improves risk management.