Optimizations in financial engineering: The Least-Squares Monte Carlo method of Longstaff and Schwartz

In this paper we identify important opportunities for parallelization in the least-squares Monte Carlo (LSM) algorithm, due to Longstaff and Schwartz, for the pricing of American options. The LSM method can be divided into three phases: path-simulation, calibration and valuation. We describe how each of these phases can be parallelized, with more focus on the calibration phase, which is inherently more difficult to parallelize. We implemented these parallelization techniques on Blue Gene using the Quantlib open source financial engineering package. We achieved up to factor of 9 speed-up for the calibration phase and 18 for the complete LSM method on a 32 processor BG/P system using monomial basis functions.

[1]  P. Glasserman,et al.  Classical solutions to reaction-diffusion systems for hedging problems with interacting Ito and point processes , 2004, math/0505208.

[2]  Raymond H. Chan,et al.  Pricing multi-asset American-style options by memory reduction Monte Carlo methods , 2006, Appl. Math. Comput..

[3]  M. Schweizer,et al.  Classical solutions to reaction-diffusion systems for hedging problems with interacting Ito and point processes , 2005, math/0505208.

[4]  Tze Leung Lai,et al.  Valuation of American options via basis functions , 2004, IEEE Transactions on Automatic Control.

[5]  M. Broadie,et al.  Option Pricing: Valuation Models and Applications , 2004 .

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

[7]  G. Karypis,et al.  Incremental Singular Value Decomposition Algorithms for Highly Scalable Recommender Systems , 2002 .

[8]  Nomesh Bolia,et al.  Monte Carlo methods for pricing financial options , 2005 .

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

[10]  Mark Broadie,et al.  ANNIVERSARY ARTICLE: Option Pricing: Valuation Models and Applications , 2004, Manag. Sci..

[11]  Eckhard Platen,et al.  On the Efficiency of Simplified Weak Taylor Schemes for Monte Carlo Simulation in Finance , 2004, International Conference on Computational Science.

[12]  D. Duffie.  Dynamic Asset Pricing Theory , 1992 .

[13]  Christopher Grover Baker.  Block Incremental Algorithm for Computing Dominant Singular Subspaces , 2004 .

[14]  Noelle Foreshaw.  Options… , 2010 .

[15]  J. Hull.  Options, Futures, and Other Derivatives , 1989 .

[16]  Nicola Moreni.  A variance reduction technique for American option pricing , 2004 .

[17]  Lars Stentoft,et al.  Convergence of the Least Squares Monte Carlo Approach to American Option Valuation , 2004, Manag. Sci..