Physics-informed neural network for option pricing weather derivatives model

Weather derivatives are financial tools that use a weather index as the underlying asset to provide protection against non-catastrophic weather events. In this article, we propose a physics-informed neural network (PINN) approach for pricing weather derivatives associated with two standard processes: the Ornstein-Uhlenbeck process and the Ornstein-Uhlenbeck process with jump-diffusions. PINNs are a scientific machine learning method specifically designed to address problems related to partial differential equations (PDEs).

To apply the PINN technique for jump-diffusion, we convert the partial integro-differential equation into a PDE using integral discretization. We randomly select training data points within the domain and utilize the transformed PDE along with the initial and boundary conditions to construct the loss function. For the neurons in the hidden layer, we employ the hyperbolic tangent function (tanh) as the activation function. The weights of the network connection are optimized using the L-BFGS algorithm.

We will conduct numerical experiments to evaluate the efficiency of the proposed technique. Additionally, we compare our method with conventional numerical approaches to show that our technique serves as an effective alternative to existing pricing methods for weather derivatives. Finally, we will examine a real-world case study where the model's parameters are determined using precipitation data.