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On the convergence of the quasi-regression method: polynomial chaos and regularity

Part of: Probabilistic methods, simulation and stochastic differential equations Mathematical finance

Published online by Cambridge University Press:  22 June 2017

Je Guk Kim
Je Guk Kim*
Affiliation:
SungKyunKwan University
*
* Postal address: SKK Business School, SungKyunKwan University, 25-2, Sungkyunkwan-ro, Jongno-gu, Seoul 03063, Republic of Korea. Email address: jkim74@vols.utk.edu
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Abstract

We present an analysis of convergence of a quasi-regression Monte Carlo method proposed by Glasserman and Yu (2004). We show that the method surely converges to the true price of an American option even under multiple underlyings via polynomial chaos expansion and weaker conditions than those used in Glasserman and Yu (2004). Further, we show the number of simulation paths grows exponentially in the number of basis functions to obtain convergence in implementing the method. Finally, we propose a rate of convergence considering regularity of value functions.

Keywords

American optionMonte Carlopolynomial chaosregularityquasi-regression

MSC classification

Primary: 91G60: Numerical methods (including Monte Carlo methods)
Secondary: 65C05: Monte Carlo methods
Type
Research Papers
Information
Journal of Applied Probability , Volume 54 , Issue 2 , June 2017 , pp. 424 - 443
Copyright
Copyright © Applied Probability Trust 2017 

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