Parallel simulation of high‐dimensional American option pricing based on CPU versus MIC

American option pricing is a high‐dimensional problem, and its computational challenges have attracted significant attention. We examine this problem using a stochastic mesh method enhanced with bias reduction within the classic Black–Scholes framework. We present Many Integrated Core (MIC) parallelization and acceleration techniques, which result in significant numerical acceleration for large‐scale simulations. In particular, we observe speed‐ups of 21‐fold and 28‐fold for CPU and MIC, respectively, over conventional means. Convergence performance is also examined. Copyright © 2014 John Wiley & Sons, Ltd.

[1]  P. Boyle Options: A Monte Carlo approach , 1977 .

[2]  Justin W. L. Wan,et al.  A parallel quasi-Monte Carlo approach to pricing multidimensional American options , 2006, Int. J. High Perform. Comput. Netw..

[3]  Dawn Hunter,et al.  A stochastic mesh method for pricing high-dimensional American options , 2004 .

[4]  P. Glasserman,et al.  A Sotchastic Mesh Method for Pricing High-Dimensional American Options , 2004 .

[5]  P. Glasserman,et al.  Pricing American-style securities using simulation , 1997 .

[6]  Francis A. Longstaff,et al.  Valuing American Options by Simulation: A Simple Least-Squares Approach , 2001 .

[7]  Pierre L'Ecuyer,et al.  Quasi-Monte Carlo methods with applications in finance , 2008, Finance Stochastics.

[8]  Paul Glasserman,et al.  Monte Carlo Methods in Financial Engineering , 2003 .

[9]  Heinrich Matzinger,et al.  Convergence of the Stochastic Mesh Estimator for Pricing Bermudan Options , 2004 .

[10]  Chi Xue-bin,et al.  Large-Scale Parallel Simulation of High-Dimensional American Option Pricing , 2012 .

[11]  Bo Shen,et al.  High-Performance Computing with MIC , 2014 .

[12]  Paul Hyden,et al.  Efficiency improvements for pricing American options with a stochastic mesh , 1999, WSC'99. 1999 Winter Simulation Conference Proceedings. 'Simulation - A Bridge to the Future' (Cat. No.99CH37038).

[13]  J. Hull Options, futures, and other derivative securities , 1989 .

[14]  Michael B. Giles,et al.  Multilevel Monte Carlo for basket options , 2009, Proceedings of the 2009 Winter Simulation Conference (WSC).

[15]  Yong-Hong Hu,et al.  Parallel Randomized Quasi-Monte Carlo Simulation for Asian Basket Option Pricing , 2012 .

[16]  James Reinders,et al.  Intel Xeon Phi Coprocessor High Performance Programming , 2013 .