On improving the least squares Monte Carlo option valuation method

  • Nelson ArealEmail author
  • Artur Rodrigues
  • Manuel R. Armada


This paper studies various possible approaches to improving the least squares Monte Carlo option valuation method. We test different regression algorithms and suggest a variation to estimating the option continuation value, which can reduce the execution time of the algorithm by one third. We test the choice of varying polynomial families with different number of basis functions. We compare several variance reduction techniques, and find that using low discrepancy sequences can improve the accuracy up to four times. We also extend our analysis to compound and mutually exclusive options. For the latter, we propose an improved algorithm which is faster and more accurate.


American options Real options Simulation Quasi Monte Carlo methods 

JEL Classifications

D81 G13 G31 


  1. Black F., Scholes M. (1973) The pricing of options and corporate liabilities. Journal of Political Economy 81(3): 637–654CrossRefGoogle Scholar
  2. Bolia N., Juneja S., Glasserman P. (2004) Function-approximation-based importance sampling for pricing American options. In: Ingalls R. G., Rossetti M. D., Smith J. S., Peters B. A. (eds) Proceedings of the 2004 Winter Simulation Conference. IEEE Press, Piscataway NJ, pp 604–611Google Scholar
  3. Box G., Muller M. (1958) A note on the generation of random normal deviates. Annals of Mathematical Statistics 29(2): 610–611CrossRefGoogle Scholar
  4. Boyle P.P. (1977) Options: A Monte Carlo approach. Journal of Financial Economics 4: 323–338CrossRefGoogle Scholar
  5. Boyle P.P., Broadie M., Glasserman P. (1997) Monte Carlo methods for security pricing. Journal of Economic Dynamics and Control 21(8): 1267–1321CrossRefGoogle Scholar
  6. Bratley P., Fox B.L. (1988) Algorithm 659: Implementing sobol’s quasirandom sequence generator. ACM Transaction on Mathematical Software 14(1): 88–100CrossRefGoogle Scholar
  7. Bratley P., Fox B.L., Niederreiter H. (1992) Implementation and tests of low-discrepancy sequences. ACM Transactions on Modeling and Computer Simulation 2(3): 195–213CrossRefGoogle Scholar
  8. Broadie M., Detemple J. (1996) American option valuation: New bounds, approximation, and a comparison of existing methods. Review of Financial Studies 9(4): 1211–1250CrossRefGoogle Scholar
  9. Broadie M., Glasserman P. (1997) Pricing American-style securities using simulation. Journal of Economic Dynamics and Control 21(8): 1323–1352CrossRefGoogle Scholar
  10. Broadie M., Glasserman P., Jain G. (1997) Enhanced Monte Carlo estimates for American option prices. Journal of Derivatives 5(1): 25–44Google Scholar
  11. Clément E., Lamberton D., Protter P. (2002) An analysis of a least squares regression method for American option pricing. Finance and Stochastics 6(4): 449–471CrossRefGoogle Scholar
  12. Cox J.C., Ross S.M., Rubinstein M. (1979) Option pricing: A simplified approach. Journal of Financial Economics 7: 229–263CrossRefGoogle Scholar
  13. Diebold F.X., Mariano R.S. (1995) Comparing predictive accuracy. American Statistical Association 13(3): 253–263Google Scholar
  14. Faure H. (1982) Discrépance de suites associées à un système de numération (en dimension s). Acta Arithmetica 41(4): 337–351Google Scholar
  15. Gamba, A. (2003). Real options valuation: A Monte Carlo approach. University of Verona.Google Scholar
  16. Glasserman P., Yu B. (2004) Number of paths versus number of basis functions in American option pricing. The Annals of Applied Probability 14(4): 2090–2119Google Scholar
  17. Halton J.H. (1960) On the efficiency of certain quasi-random sequences of points in evaluating multi-dimensional integrals. Mumerische Mathematik 2: 84–90CrossRefGoogle Scholar
  18. Jackel, P. (2002). Monte Carlo methods in finance. Wiley.Google Scholar
  19. Joy C., Boyle P.P., Tan K.S. (1996) Quasi-Monte Carlo methods in numerical finance. Management Science 42(6): 926–938CrossRefGoogle Scholar
  20. L’Ecuyer P., Touzin R. (2000) Fast combined multiple recursive generators with multipliers of the form a = ± 2q ± 2r. In: Joines J. A., Barton R. R., Kang K., Fishwick P. A. (eds) Proceedings of the 2000 Winter Simulation Conference. IEEE Press, Piscataway, NJ, pp 683–689Google Scholar
  21. Lemieux C., La J. (2005) A study of variance reduction techniques for American option pricing. In: Kuhl M.E., Steiger N.M., Armstrong F.B., Joines J.A. (eds) Proceedings of the 2005 Winter Simulation Conference. IEEE Press, Piscataway, NJ, pp 1884–1891CrossRefGoogle Scholar
  22. Longstaff F.A., Schwartz E.S. (2001) Valuing American options by simulation: A simple least-squares approach. Review of Financial Studies 14(1): 113–147CrossRefGoogle Scholar
  23. Marsaglia G., Bray T.A. (1964) A convenient method for generating normal variables. SIAM Review 6(3): 260–264CrossRefGoogle Scholar
  24. Moreni N. (2004) A variance reduction technique for American option pricing. Physica A: Statistical Mechanics and its Applications 338(1–2): 292–295CrossRefGoogle Scholar
  25. Moreno M., Navas J.F. (2003) On the robustness of least-squares Monte Carlo (LSM) for pricing American derivatives. Review of Derivatives Research 6(2): 107–128CrossRefGoogle Scholar
  26. Moro B. (1995) The full Monte. Risk 8(2): 57–58Google Scholar
  27. Morokoff W.J., Caflisch R.E. (1995) Quasi-Monte Carlo integration. Journal of Computational Physics 122(2): 218–230CrossRefGoogle Scholar
  28. Moskowitz B., Caflish R.E. (1996) Smoothness and dimension reduction in quasi-Monte Carlo methods. Mathematical and Computer Modelling 23(8/9): 37–54CrossRefGoogle Scholar
  29. Niederreiter H. (1988) Low-discrepancy and low-dispersion sequences. Journal of Number Theory 30(1): 51–70CrossRefGoogle Scholar
  30. Papageorgiou A. (2002) The brownian bridge does not offer a consistent advantage in quasi-Monte Carlo integration. Journal of Complexity 18(1): 171–186CrossRefGoogle Scholar
  31. Paskov S., Traub J. (1995) Faster valuation of financial derivatives. Journal of Portfolio Management 22(1): 113–120CrossRefGoogle Scholar
  32. Press W.H., Teukolsky S.A., Vetterling W.T., Flanney B.P. (1992) Numerical recipes in C: The Art of scientific computing. Cambridge University Press, CambridgeGoogle Scholar
  33. Silva, M. E., & Barbe, T. (2003). Quasi Monte Carlo in finance: Extending for high dimensional problems, Universidade de São Paulo.Google Scholar
  34. Sobol I.M. (1967) On the distribution of points in a cube and the approximate evaluation of integrals. USSR Computational Mathematics and Mathematical Physics 7(4): 86–112CrossRefGoogle Scholar
  35. Stentoft L. (2004a) Assessing the least squares Monte-Carlo approach to American option valuation. Review of Derivatives Research 7(2): 129–168CrossRefGoogle Scholar
  36. Stentoft L. (2004b) Convergence of the least squares Monte Carlo approach to American option valuation. Management Science 50(9): 1193–1203CrossRefGoogle Scholar
  37. Tian T., Burrage K. (2003) Accuracy issues of Monte-Carlo methods for valuing American options. The ANZIAM Journal (Australian & New Zealand Industrial and Applied Mathematics Journal) Electronic Part C: 739–C758Google Scholar
  38. Tsitsiklis J.N, Van Roy B. (2001) Regression methods for pricing complex American-style options. IEEE Transactions on Neural Networks 12(4): 694–703CrossRefGoogle Scholar
  39. van Resenburg E.J.J., Torrie G.M. (1993) Estimation of multidimensional integrals: Is Monte Carlo the best method?. Journal of Physics A: Mathematics and General 26(4): 943–953CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2008

Authors and Affiliations

  • Nelson Areal
    • 1
    Email author
  • Artur Rodrigues
    • 1
  • Manuel R. Armada
    • 1
  1. 1.NEGE, School of Economics and ManagementUniversity of MinhoBragaPortugal

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