A Gradient Descent Algorithm for the Heston model

The Heston model is a well-known two-dimensional financial model. Since the Heston model contains implicit parameters that cannot be determined directly from real market data, calibrating the parameters to real market data is challenging. Moreover, some of the parameters within the model are nonlinear, which makes it difficult to find the global minimum of the optimization problem. In our paper, we present a gradient descent algorithm for parameter calibration of the Heston model. Numerical results show that our calibration of the Heston partial differential equation (PDE) works well for the various challenges in the calibration process. Since the model and algorithm are well known, this work is formulated as a proof of concept. This proof of concept will be incorporated into the space mapping approach in the future