Algorithm 659: Implementing Sobol's quasirandom sequence generator
ACM Transactions on Mathematical Software (TOMS)
Mersenne twister: a 623-dimensionally equidistributed uniform pseudo-random number generator
ACM Transactions on Modeling and Computer Simulation (TOMACS) - Special issue on uniform random number generation
The Art of Computer Programming Volumes 1-3 Boxed Set
The Art of Computer Programming Volumes 1-3 Boxed Set
Quadratic Convergence for Valuing American Options Using a Penalty Method
SIAM Journal on Scientific Computing
Remark on algorithm 659: Implementing Sobol's quasirandom sequence generator
ACM Transactions on Mathematical Software (TOMS)
Pricing American Options: A Duality Approach
Operations Research
Tools for Computational Finance (Universitext)
Tools for Computational Finance (Universitext)
Regression methods for pricing complex American-style options
IEEE Transactions on Neural Networks
Pricing barrier and American options under the SABR model on the graphics processing unit
Concurrency and Computation: Practice & Experience
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Several methods for valuing high-dimensional American-style options were proposed in the last years. Longstaff and Schwartz (LS) have suggested a regression-based Monte Carlo approach, namely the least squares Monte Carlo method. This article is devoted to an efficient implementation of this algorithm. First, we suggest a code for faster runs. Regression-based Monte Carlo methods are sensitive to the choice of basis functions for pricing high-dimensional American-style options and, like all Monte Carlo methods, to the underlying random number generator. For this reason, we secondly propose an optimal selection of basis functions and a random number generator to guarantee stable results. Our basis depends on the payoff of the high-dimensional option and consists of only three functions. We give a guideline for an efficient option price calculation of high-dimensional American-style options with the LS algorithm, and we test it in examples with up to 10 dimensions.