Dimension Reduction Techniques in Quasi-Monte Carlo Methods for Option Pricing

References

• Acworth P., Broadie M., Glasserman P., Niederreiter H., Hellekalek P., Larcher G., Zinterhof P. A comparison of some Monte Carlo and quasi-Monte Carlo techniques for option pricing. Monte Carlo and Quasi-Monte Carlo Methods 1996 (1998) (Springer-Verlag, New York) 1–18Crossref, Google Scholar
• Åkesson F., Lehoczy J. P. Path generation for quasi-Monte Carlo simulation of mortgage-backed securities. Management Sci. (2000) 46(9):1171–1187Link, Google Scholar
• Caflisch R. E., Morokoff W., Owen A. Valuation of mortgage backed securities using Brownian bridges to reduce effective dimension. J. Comput. Finance (1997) 1(1):27–46Crossref, Google Scholar
• Chaudhary S. K. American options and the LSM algorithm: Quasi-random sequences and Brownian bridges. J. Comput. Finance (2005) 8(4):101–115Crossref, Google Scholar
• Glasserman P.Monte Carlo Methods in Financial Engineering (2004) (Springer-Verlag, New York) Crossref, Google Scholar
• Imai J., Tan K. S., Yucesan E., Chen C. H., Snowdon J. L., Charnes J. M. Enhanced quasi-Monte Carlo methods with dimension reduction. Proc. 2002 Winter Simulation Conf. (2002) (IEEE Press, Piscataway, NJ) 1502–1510Crossref, Google Scholar
• Joy C., Boyle P., Tan K. S. Quasi-Monte Carlo methods in numerical finance. Management Sci. (1996) 42(6):926–938Link, Google Scholar
• L'Ecuyer P., Ingalls R. G., Rossetti M. D., Smith J. S., Peters B. A. Quasi-Monte Carlo methods in finance. Proc. 2004 Winter Simulation Conf. (2004) (IEEE Press, Piscataway, NJ) 1645–1655Crossref, Google Scholar
• Lin J., Wang X. New Brownian bridge in quasi-Monte Carlo methods for computational finance. J. Complexity (2008) 24(2):109–133Crossref, Google Scholar
• Liu R., Owen A. Estimating mean dimensionality of analysis of variance decompositions. J. Amer. Statist. Assoc. (2006) 101(474):712–721Crossref, Google Scholar
• Longstaff F. A., Schwartz E. S. Valuing American options by simulation: A simple least-squares approach. Rev. Financial Stud. (2001) 14:113–148Crossref, Google Scholar
• Morokoff W. J. Generating quasi-random paths for stochastic processes. SIAM Rev. (1998) 40(4):765–788Crossref, Google Scholar
• Morokoff W. J., Caflisch R. E. Quasi-random sequences and their discrepancies. SIAM J. Sci. Comput. (1994) 15(6):1251–1279Crossref, Google Scholar
• Moskowitz B., Caflisch R. E. Smoothness and dimension reduction in quasi-Monte Carlo methods. Math. Comput. Modelling (1996) 23(8–9):37–54Crossref, Google Scholar
• Niederreiter H.Random Number Generation and Quasi-Monte Carlo Methods (1992) (SIAM, Philadelphia) Crossref, Google Scholar
• Owen A. B. The dimension distribution, and quadrature test functions. Statistica Sinica (2003) 13:1–17Google Scholar
• Paskov S. H., Traub J. F. Faster valuation of financial derivatives. J. Portfolio Management (1995) 22(1):113–120Crossref, Google Scholar
• Sloan I. H., Woźniakowski H. When are quasi-Monte Carlo algorithms efficient for high dimensional integrals? J. Complexity (1998) 14(1):1–33Crossref, Google Scholar
• Sloan I. H., Wang X., Woźniakowski H. Finite-order weights imply tractability of multivariate integration. J. Complexity (2004) 20(1):46–74Crossref, Google Scholar
• Sobol' I. M. On the distribution of points in a cube and the approximate evaluation of integrals. Zh. Vychisli. Mat. i Mat. Fiz. (1967) 7:784–802Google Scholar
• Sobol' I. M. Uniformly distributed sequences with additional uniform properties. Zh. Vychisli. Mat. i Mat. Fiz. (1976) 16:1332–1337Google Scholar
• Sobol' I. M. Sensitivity estimates for nonlinear mathematical models. Math. Model. Comput. Experiments (1993) 1:407–414Google Scholar
• Wang X. On the effects of dimension reduction techniques on high-dimensional problems in finance. Oper. Res. (2006) 54(6):1063–1078Link, Google Scholar
• Wang X. Constructing robust good lattice rules for computational finance. SIAM J. Sci. Comput. (2007) 29(2):598–621Crossref, Google Scholar
• Wang X., Fang K.-T. The effective dimensions and quasi-Monte Carlo integration. J. Complexity (2003) 19:101–124Crossref, Google Scholar
• Wang X., Sloan I. H. Why are high-dimensional finance problems often of low effective dimension? SIAM J. Sci. Comput. (2005) 27(1):159–183Crossref, Google Scholar
• Wang X., Sloan I. H. Efficient weighted lattice rules with application to finance. SIAM J. Sci. Comput. (2006) 28:728–750Crossref, Google Scholar
• Wang X., Sloan I. H. Brownian bridge and principal component analysis: Towards removing the curse of dimensionality. IMA J. Numer. Anal. (2007) 27(4):631–654Crossref, Google Scholar
• Wang X., Sloan I. H. Low discrepancy sequences in high dimensions: How well are their projections distributed? J. Comput. Appl. Math. (2008) 213(2):366–386Crossref, Google Scholar