Dynamically Controlled Kernel Estimation

17 Pages Posted: 20 Apr 2021

See all articles by Joerg Kienitz

Joerg Kienitz

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

Nikolai Nowaczyk


Nancy(Qingxin) Geng

Imperial College London - Department of Mathematics; Goldman Sachs - London

Date Written: April 19, 2021


We introduce a data driven and model free approach for computing conditional expectations. The new method is based on classical techniques combined with machine learning methods. In particular, we consider kernel density estimation based on simulated risk factors combined with a control variate. This is used in a Gaussian process regression for finally approximating the conditional expectation. In this way we increase not only the stability of the estimator but we also need a significantly lower amount of simulations due to the variance reduction. Since we apply Gaussian process regression, we do not only get a point estimate, but also the full distribution. It turns out that the optimal coefficient for the control variate is the minimal variance delta. Thus, in this way we obtain model free and purely data driven hedges. Finally, we apply our method to several examples from option pricing including exotic option payoffs and payoffs with multiple underlyings for different models including the rough Bergomi model. A discussion on the challenges to extend the method to a large dimensional settings is provided and is partially solved by using Quasi random number sequences.

Keywords: Gaussian process regression, control variates, kernel density estimation, Monte Carlo, regression, exposure, hedging, machine learning

JEL Classification: G13, C10, C45, C40, C63

Suggested Citation

Kienitz, Joerg and Nowaczyk, Nikolai and Geng, Nancy(Qingxin), Dynamically Controlled Kernel Estimation (April 19, 2021). Available at SSRN: https://ssrn.com/abstract=3829701 or http://dx.doi.org/10.2139/ssrn.3829701

Joerg Kienitz (Contact Author)

University of Wuppertal - Applied Mathematics ( email )

Gaußstraße 20
42097 Wuppertal

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

Nikolai Nowaczyk

AcadiaSoft ( email )

Broadgate Quarter
One Snowden Street
London, EC2A 2DQ
United Kingdom

Nancy(Qingxin) Geng

Imperial College London - Department of Mathematics ( email )

South Kensington Campus
Imperial College
London, SW7 2AZ
United Kingdom

Goldman Sachs - London ( email )

130 Peterborough Court
133 Fleet Street
London, EC4A 2BB
United Kingdom

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