An efficient implementation of a least squares Monte Carlo method for valuing American-style options

References

• Andersen , L. 2000 . A simple approach to the pricing of Bermudan swaptions in the multi-factor Libor market model . J. Comput. Finance , 3 : 5 – 23 .
   Google Scholar
• Andersen , L. and Broadie , M. 2004 . Primal-dual simulation algorithm for pricing multidimensional American options . Manag. Sci. , 50 : 1222 – 1234 .
   Web of Science ®Google Scholar
• Barraquand , J. and Martineau , D. 1995 . Numerical valuation of high dimensional multivariate American securities . J. Financ. Quant. Anal. , 30 : 383 – 405 .
   Web of Science ®Google Scholar
• Bensoussan , A. 1984 . On the theory of option pricing . Acta Appl. Math. , 2 : 139 – 158 .
   Web of Science ®Google Scholar
• Berridge , S. J. and Schumacher , J. M. 2007 . “ Pricing high-dimensional American options using local consistency conditions ” . In Numerical Methods for Finance , Edited by: Appleby , J. , Edelman , D. and Miller , J. 13 – 52 . London : Chapman and Hall/CRC .
   Google Scholar
• Björck , Å. 1996 . Numerical Methods for Least Squares Problems , Philadelphia : SIAM .
   Google Scholar
• Boyle , P. 1977 . Options: A Monte Carlo approach . J. Financ. Econ. , 4 : 323 – 338 .
   Web of Science ®Google Scholar
• Boyle , P. 1988 . A lattice framework for option pricing with two state variables . J. Financ. Quant. Anal. , 23 : 1 – 12 .
   Web of Science ®Google Scholar
• Boyle , P. , Evninea , J. and Gibss , S. 1989 . Numerical evaluation of multivariate contingent claims . Rev. Financ. Stud. , 2 : 241 – 250 .
   Web of Science ®Google Scholar
• Bratley , P. and Fox , B. L. 1988 . Algorithm 659: Implementing Sobol's quasirandom sequence generator . ACM Transactions on Mathematical Computer Software , 14 : 88 – 100 .
   Web of Science ®Google Scholar
• Broadie , M. and Glasserman , P. 1997 . Pricing American-style securities using simulation . J. Econ. Dyn. Control , 21 : 1323 – 1352 .
   Web of Science ®Google Scholar
• Broadie , M. and Glasserman , P. 2004 . A stochastic mesh method for pricing high-dimensional American options . J. Comput. Finance , 7 : 35 – 72 .
   Google Scholar
• Carrière , J. F. 1996 . Valuation of early-exercise price of options using simulations and nonparametric regression . Insur. Math. Econ. , 19 : 19 – 30 .
   Web of Science ®Google Scholar
• Carrière , J. F. 2001 . Linear regression and standardized quasi-Monte Carlo for approximating Bermudan options , Alberta, , Canada : University of Alberta . Working Paper
   Google Scholar
• Chaudhary , S. 2005 . American options and the LSM algorithm: Quasi-random sequences and Brownian bridges . J. Comput. Finance , 8 : 101 – 115 .
   Google Scholar
• Clement , E. , Protter , P. and Lamberton , D. 2002 . An analysis of a least squares regression method for American option pricing . Finance Stoch. , 6 : 449 – 471 .
   Web of Science ®Google Scholar
• Cox , J. , Ross , S. and Rubinstein , M. 1979 . Option pricing: A simplified approach . J. Financ. Econ. , 7 : 229 – 263 .
   Web of Science ®Google Scholar
• Egloff , D. 2005 . Monte Carlo algorithms for optimal stopping and statistical learning . Ann. Appl. Probab. , 15 : 1396 – 1432 .
   Web of Science ®Google Scholar
• Fasshauer , G. , Khaliq , A. Q.M. and Voss , D. A. 2004 . Using meshfree approximation for multi-asset American option problems . J. Chin. Inst. Eng. , 27 : 563 – 571 .
   Web of Science ®Google Scholar
• Forsyth , P. A. and Vetzal , K. R. 2002 . Quadratic convergence for valuing American options using a penalty method . SIAM J. Sci. Comput. , 23 : 2095 – 2122 .
   Web of Science ®Google Scholar
• Glasserman , P. 2004 . Monte Carlo Methods in Financial Engineering , New York : Springer .
   Google Scholar
• Glasserman , P. and Yu , B. 2004 . Number of paths versus number of basis functions in Amercian option pricing . Ann. Appl. Probab. , 14 : 2090 – 2119 .
   Web of Science ®Google Scholar
• Golub , G. H. and van Loan , C. F. 1996 . Matrix Computations , 3 , Baltimore : John Hopkins University Press .
   Google Scholar
• Haugh , M. B. and Kogan , L. 2004 . Pricing American options: A duality approach . Oper. Res. , 52 : 258 – 270 .
   Web of Science ®Google Scholar
• He , H. 1990 . Convergence from discrete to continuous-time contingent claim prices . Rev. Financ. Stud. , 3 : 523 – 546 .
   Web of Science ®Google Scholar
• Joe , S. and Kuo , F. Y. 2003 . Remark on algorithm 659: Implementing Sobol's quasirandom sequence generator . ACM Trans. Math. Softw. , 29 : 49 – 57 .
   Web of Science ®Google Scholar
• Kloeden , P. E. and Platen , E. 1992 . Numerical Solution of Stochastic Differential Equations , Berlin : Springer .
   Google Scholar
• Knuth , D. E. 1998 . The Art Of Computer Programming , 2 , Vol. 3 , Reading, MA : Addison-Wesley .
   Google Scholar
• Lamberton , D. and Lapeyre , B. 1996 . Introduction to Stochastic Calculus Applied to Finance , London : Chapman and Hall/CRC .
   Google Scholar
• Leentvaar , C. C.W. and Oosterlee , C. W. 2007 . Multi-asset option pricing using a parallel Fourier-based technique , Delft, , Netherlands : Delft University of Technology . Report 07–12
   Google Scholar
• Longstaff , F. A. and Schwartz , E. S. 2001 . Valuing American options by simulation: A simple least-squares approach . Rev. Financ. Stud. , 14 : 113 – 147 .
   Web of Science ®Google Scholar
• Marsaglia , G. and Tsang , W. W. 2000 . The ziggurat method for generating random variables . J. Statist. Softw. , 5 : 1 – 7 .
   Google Scholar
• Matsumoto , M. and Nishimura , T. 1998 . Mersenne twister: A 623-dimensionally equidistributed uniform pseudo-random number generator . ACM Trans. Model. Comput. Simul. , 8 : 3 – 30 .
   Google Scholar
• Moreno , M. and Navas , J. F. 2003 . On the robustness of least-squares Monte Carlo (LSM) for pricing American derivatives . Rev. Deriv. Res. , 6 : 107 – 128 .
   Google Scholar
• Moro , B. 1995 . The full monte . Risk , 8 : 57 – 58 .
   Google Scholar
• Nielsen , B. F. , Skavhaug , O. and Tveito , A. 2000 . Penalty methods for the numerical solution of American multi-asset option problems , Norway : Department of Informatics, University of Oslo . preprint (2000–289)
   Google Scholar
• Pfeiffer , P. E. 1990 . Probability for Applications , New York : Springer .
   Google Scholar
• Press , W. H. , Teukolsky , S. A. , Vetterling , W. T. and Flannery , B. P. 2007 . Numerical Recipes , 3 , Cambridge : Cambridge University Press .
   Google Scholar
• Rasmussen , N. S. 2005 . Control variates for Monte Carlo valuation of American options . J. Comput. Finance , 9 : 84 – 102 .
   Google Scholar
• Raymar , S. and Zwecher , M. A Monte Carlo valuation of American call options on the maximum of several stocks . J. Deriv. 5 , 7 – 23 .
   Google Scholar
• Rogers , C. 2002 . Monte Carlo valuation of American options . Math. Finance , 12 : 271 – 286 .
   Web of Science ®Google Scholar
• Royden , H. L. 1988 . Real Analysis , 3 , New Jersey : Prentice Hall .
   Google Scholar
• Seydel , R. 2006 . Tools for Computational Finance , 3 , Berlin : Springer .
   Google Scholar
• Stentoft , L. 2004 . Assessing the least squares Monte-Carlo approach to American option valuation . Rev. Deriv. , 7 : 129 – 168 .
   Google Scholar
• Stentoft , L. 2004 . Convergence of the least squares Monte Carlo approach to American option valuation . Manag. Sci. , 50 : 1193 – 1203 .
   Web of Science ®Google Scholar
• Tilley , J. 1993 . Valuing American options in a path simulation model . Trans. Soc. Actuaries , 45 : 83 – 104 .
   Google Scholar
• Tsitsiklis , J. and van Roy , B. 1999 . Optimal stopping of Markov processes: Hilbert space theory, approximation algorithms, and an application to pricing high-dimensional financial derivatives . IEEE Trans. Automat. Contr. , 44 : 1840 – 1851 .
   Web of Science ®Google Scholar
• Tsitsiklis , J. and van Roy , B. 2001 . Regression methods for pricing complex American-style options . IEEE Trans. Neural Netw. , 12 : 694 – 703 .
   PubMed Web of Science ®Google Scholar