Valuing American options by least-squares randomized quasi-Monte Carlo methods

Xin-Yu Wu (), Hai-Lin Zhou and Shou-Yang Wang
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Xin-Yu Wu: School of Finance, Anhui University of Finance and Economics, Bengbu 233030, P. R. China
Hai-Lin Zhou: School of Finance, Anhui University of Finance and Economics, Bengbu 233030, P. R. China
Shou-Yang Wang: Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, P. R. China

Journal of Financial Engineering (JFE), 2014, vol. 01, issue 02, 1-16

Abstract: Valuation of American options is a difficult and challenging problem encountered in financial engineering. Longstaff and Schwartz [Longstaff, FA and ES Schwartz (2001). Valuing American Options by Simulation: A Simple Least-squares Approach, Review of Financial Studies, 14(1), 113–147.] Proposed the least-squares Monte Carlo (LSM) method for valuing American options. As this approach is intuitive and easy to apply, it has received much attention in the finance literature. However, a drawback of the LSM method is the low efficiency. In order to overcome this problem, we propose the least-squares randomized quasi-Monte Carlo (LSRQM) methods which can be viewed as a use low-discrepancy sequences as a variance reduction technique in the LSM method for valuing American options in this paper. Numerical results demonstrate that our proposed LSRQM methods are more efficient than the LSM method in terms of the valuation accuracy, the computation time and the convergence rate.

Keywords: American options; least-squares Monte Carlo; randomized quasi-Monte Carlo; least-squares randomized quasi-Monte Carlo (search for similar items in EconPapers)
Date: 2014
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DOI: 10.1142/S2345768614500160

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