Pricing high-dimensional American options by kernel ridge regression

Abstract

In this paper, we propose using kernel ridge regression (KRR) to avoid the step of selecting basis functions for regression-based approaches in pricing high-dimensional American options by simulation. Our contribution is threefold. Firstly, we systematically introduce the main idea and theory of KRR and apply it to American option pricing for the first time. Secondly, we show how to use KRR with the Gaussian kernel in the regression-later method and give the computationally efficient formulas for estimating the continuation values and the Greeks. Thirdly, we propose to accelerate and improve the accuracy of KRR by performing local regression based on the bundling technique. The numerical test results show that our method is robust and has both higher accuracy and efficiency than the Least Squares Monte Carlo method in pricing high-dimensional American options.

Keywords:

• High-dimensional American option
• Monte Carlo
• Regression-based method
• Kernel ridge regression
• Machine learning

JEL Classification:

• C63
• G13

Disclosure statement

No potential conflict of interest was reported by the authors.

ORCID

Wenbin Hu  http://orcid.org/0000-0002-3494-366X

Notes

1 https://www.rocq.inria.fr/mathfi/Premia/index.html

Additional information

Funding

This work was supported by the National Social Science Foundation of China [grant no. 17BJY233] and the Humanity and Social Science Youth foundation of the Ministry of Education of China under grant number 16YJCZH031.