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On improving the least squares Monte Carlo option valuation method

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Abstract

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.

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References

  • Black F., Scholes M. (1973) The pricing of options and corporate liabilities. Journal of Political Economy 81(3): 637–654

    Article  Google Scholar 

  • 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 604–611

    Google Scholar 

  • Box G., Muller M. (1958) A note on the generation of random normal deviates. Annals of Mathematical Statistics 29(2): 610–611

    Article  Google Scholar 

  • Boyle P.P. (1977) Options: A Monte Carlo approach. Journal of Financial Economics 4: 323–338

    Article  Google Scholar 

  • Boyle P.P., Broadie M., Glasserman P. (1997) Monte Carlo methods for security pricing. Journal of Economic Dynamics and Control 21(8): 1267–1321

    Article  Google Scholar 

  • Bratley P., Fox B.L. (1988) Algorithm 659: Implementing sobol’s quasirandom sequence generator. ACM Transaction on Mathematical Software 14(1): 88–100

    Article  Google Scholar 

  • Bratley P., Fox B.L., Niederreiter H. (1992) Implementation and tests of low-discrepancy sequences. ACM Transactions on Modeling and Computer Simulation 2(3): 195–213

    Article  Google Scholar 

  • Broadie M., Detemple J. (1996) American option valuation: New bounds, approximation, and a comparison of existing methods. Review of Financial Studies 9(4): 1211–1250

    Article  Google Scholar 

  • Broadie M., Glasserman P. (1997) Pricing American-style securities using simulation. Journal of Economic Dynamics and Control 21(8): 1323–1352

    Article  Google Scholar 

  • Broadie M., Glasserman P., Jain G. (1997) Enhanced Monte Carlo estimates for American option prices. Journal of Derivatives 5(1): 25–44

    Google Scholar 

  • Clément E., Lamberton D., Protter P. (2002) An analysis of a least squares regression method for American option pricing. Finance and Stochastics 6(4): 449–471

    Article  Google Scholar 

  • Cox J.C., Ross S.M., Rubinstein M. (1979) Option pricing: A simplified approach. Journal of Financial Economics 7: 229–263

    Article  Google Scholar 

  • Diebold F.X., Mariano R.S. (1995) Comparing predictive accuracy. American Statistical Association 13(3): 253–263

    Google Scholar 

  • Faure H. (1982) Discrépance de suites associées à un système de numération (en dimension s). Acta Arithmetica 41(4): 337–351

    Google Scholar 

  • Gamba, A. (2003). Real options valuation: A Monte Carlo approach. University of Verona.

  • Glasserman P., Yu B. (2004) Number of paths versus number of basis functions in American option pricing. The Annals of Applied Probability 14(4): 2090–2119

    Google Scholar 

  • Halton J.H. (1960) On the efficiency of certain quasi-random sequences of points in evaluating multi-dimensional integrals. Mumerische Mathematik 2: 84–90

    Article  Google Scholar 

  • Jackel, P. (2002). Monte Carlo methods in finance. Wiley.

  • Joy C., Boyle P.P., Tan K.S. (1996) Quasi-Monte Carlo methods in numerical finance. Management Science 42(6): 926–938

    Article  Google Scholar 

  • 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 683–689

    Google Scholar 

  • 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 1884–1891

    Chapter  Google Scholar 

  • Longstaff F.A., Schwartz E.S. (2001) Valuing American options by simulation: A simple least-squares approach. Review of Financial Studies 14(1): 113–147

    Article  Google Scholar 

  • Marsaglia G., Bray T.A. (1964) A convenient method for generating normal variables. SIAM Review 6(3): 260–264

    Article  Google Scholar 

  • Moreni N. (2004) A variance reduction technique for American option pricing. Physica A: Statistical Mechanics and its Applications 338(1–2): 292–295

    Article  Google Scholar 

  • 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): 107–128

    Article  Google Scholar 

  • Moro B. (1995) The full Monte. Risk 8(2): 57–58

    Google Scholar 

  • Morokoff W.J., Caflisch R.E. (1995) Quasi-Monte Carlo integration. Journal of Computational Physics 122(2): 218–230

    Article  Google Scholar 

  • Moskowitz B., Caflish R.E. (1996) Smoothness and dimension reduction in quasi-Monte Carlo methods. Mathematical and Computer Modelling 23(8/9): 37–54

    Article  Google Scholar 

  • Niederreiter H. (1988) Low-discrepancy and low-dispersion sequences. Journal of Number Theory 30(1): 51–70

    Article  Google Scholar 

  • Papageorgiou A. (2002) The brownian bridge does not offer a consistent advantage in quasi-Monte Carlo integration. Journal of Complexity 18(1): 171–186

    Article  Google Scholar 

  • Paskov S., Traub J. (1995) Faster valuation of financial derivatives. Journal of Portfolio Management 22(1): 113–120

    Article  Google Scholar 

  • 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, Cambridge

    Google Scholar 

  • Silva, M. E., & Barbe, T. (2003). Quasi Monte Carlo in finance: Extending for high dimensional problems, Universidade de São Paulo.

  • 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): 86–112

    Article  Google Scholar 

  • Stentoft L. (2004a) Assessing the least squares Monte-Carlo approach to American option valuation. Review of Derivatives Research 7(2): 129–168

    Article  Google Scholar 

  • Stentoft L. (2004b) Convergence of the least squares Monte Carlo approach to American option valuation. Management Science 50(9): 1193–1203

    Article  Google Scholar 

  • 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–C758

    Google Scholar 

  • Tsitsiklis J.N, Van Roy B. (2001) Regression methods for pricing complex American-style options. IEEE Transactions on Neural Networks 12(4): 694–703

    Article  Google Scholar 

  • 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): 943–953

    Article  Google Scholar 

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Authors and Affiliations

  1. NEGE, School of Economics and Management, University of Minho, 4710-057, Braga, Portugal

    Nelson Areal, Artur Rodrigues & Manuel R. Armada

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  1. Nelson Areal
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  2. Artur Rodrigues
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  3. Manuel R. Armada
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Correspondence to Nelson Areal.

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Areal, N., Rodrigues, A. & Armada, M.R. On improving the least squares Monte Carlo option valuation method. Rev Deriv Res 11, 119–151 (2008). https://doi.org/10.1007/s11147-008-9026-x

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