The CV Makes the Difference – Control Variates for Neural Networks

Abstract

We consider the application of a control variate technique for Deep Learning. In analogy to applications for Monte Carlo simulation or Fourier integration methods, this technique improves the quality of deep learning applied to option pricing problems. Many well known approximation methods are limited for practical applications but can be used as a control variate. For instance approximation formulas for SABR or the Black-Scholes price when pricing options in the Heston model. The neural network is only applied to calculate the difference to an accurate numerical method. In this way we increase the accuracy of applying neural nets since a large portion of the price is already mimicked by the control variate. This may result in a higher acceptance of such numerical techniques for financial applications.

Keywords: machine learning, neural networks, control variates, Bermudan swaption, SABR, free SABR, Heston

JEL Classification: C10, C40, C63