The CV Makes the Difference – Control Variates for Neural Networks

12 Pages Posted: 25 Feb 2020 Last revised: 27 Apr 2020

See all articles by Joerg Kienitz

Joerg Kienitz

University of Wuppertal - Applied Mathematics; University of Cape Town (UCT); Quaternion Risk Management

Sarp Kaya Acar

Quaternion Risk Management

Qian Liang

Quaternion Risk Management

Nikolai Nowaczyk

Quaternion Risk Management

Date Written: January 29, 2020

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

Suggested Citation

Kienitz, Joerg and Acar, Sarp Kaya and Liang, Qian and Nowaczyk, Nikolai, The CV Makes the Difference – Control Variates for Neural Networks (January 29, 2020). Available at SSRN: https://ssrn.com/abstract=3527314 or http://dx.doi.org/10.2139/ssrn.3527314

Joerg Kienitz (Contact Author)

University of Wuppertal - Applied Mathematics ( email )

Gaußstraße 20
42097 Wuppertal
Germany

University of Cape Town (UCT) ( email )

Private Bag X3
Rondebosch, Western Cape 7701
South Africa

Quaternion Risk Management ( email )

54 Fitzwilliam Square North
Dublin, D02X308
Ireland

Sarp Kaya Acar

Quaternion Risk Management ( email )

54 Fitzwilliam Square North
Dublin, D02X308
Ireland

Qian Liang

Quaternion Risk Management ( email )

54 Fitzwilliam Square North
Dublin, D02X308
Ireland

Nikolai Nowaczyk

Quaternion Risk Management ( email )

54 Fitzwilliam Square North
Dublin, D02X308
Ireland

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