Efficient call pricing model discovery by backpropagation through time

Efficient call pricing model discovery by backpropagation through time

In this paper, we propose a novel call pricing model discovery method using the Heston model to find the set of parameter values that minimize the square loss between our model’s predictions and observed call prices given by market makers such as Jean Street or Two Sigma. The goal of this article is to formulate a stochastic optimization method for the Heston model over a certain period of time. The novelty of this paper is that we treat the Heston model as a Recurrent Neural Network and derive the Gradient of the Heston model by Backpropagation Through Time[1][2] to reduce the computation time for obtaining the gradient from O(τ 2 ) to O(τ ). Further, to stabilize the gradient, we extend our method by adding min-batch method. To our best knowledge, this is the first paper to propose a SGD based Heston calibration method by min-batch extension. Our method minimizes the square loss twice more than model a trivial call pricing discovery method using the Black-Scholes-Merton model.