Pricing high-dimensional American options by kernel ridge regression

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JournalQuantitative Finance
DateAccepted/In press - 5 Jan 2020
DateE-pub ahead of print (current) - 19 Feb 2020
Issue number5
Volume20
Number of pages16
Pages (from-to)1-16
Early online date19/02/20
Original languageEnglish

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.

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