The Calibration of the Heston Model Using Neural Network Pricing Approximations

Abstract

The calibration of certain stochastic volatility models is an important daily routine for financiers, and balancing accuracy with speed has been an area of recent research in quantitative finance. In the environment of the Heston model, one of the most popular stochastic volatility models, traditional calibration methods are often reasonably accurate but lacking in speed. Building on the growing literature surrounding the implementation of neural network methods in the calibration process, this thesis improves upon previous models and examines the effectiveness of approximating the semi-closed Heston pricing function using neural networks. We show that in line with previous results, the neural network implementation is able to dramatically speed up calibration of the Heston model compared to more traditional global optimization routines, with very small losses in accuracy. We also show that the effectiveness of the neural network approach relies heavily on the characteristics of the training set and the beliefs of the parameter bounds. Finally, as a case study we examine the application of our neural network approach to calibration to the S&P 500 index (SPX) over a recent period of time.