A Comparison of Neural Networks and Bayesian MCMC for the Heston Model Estimation (Forget Statistics - Machine Learning is Sufficient!)

The main goal of this paper is to compare the classical MCMC estimation method with a universal Neural Network (NN) approach to estimate unknown parameters of the Heston stochastic volatility model given a series of observable asset returns. The main idea of the NN approach is to generate a large training synthetic dataset with sampled parameter vectors and the return series conditional on the Heston model. The NN can then be trained reverting the input and output, i.e. setting the return series, or rather a set of derived generalized moments as the input features and the parameters as the target. Once the NN has been trained, the estimation of parameters given observed return series becomes very efficient compared to the MCMC algorithm. Our empirical study implements the MCMC estimation algorithm and demonstrates that the trained NN provides more precise and substantially faster estimations of the Heston model parameters. We discuss some other advantages and disadvantages of the two methods, and hypothesize that the universal NN approach can in general give better results compared to the classical statistical estimation methods for a wide class of models.