Quasi-monte Carlo methods in finance

Proceedings - Winter Simulation Conference

Volumn 2, Issue , 2004, Pages 1645-1655

  L'Ecuyer, Pierre ^a  

^a UNIVERSITÉ DE MONTRÉAL   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

APPROXIMATION THEORY; ASYMPTOTIC STABILITY; ERROR ANALYSIS; FINANCE; FUNCTIONS; INTEGRATION; RANDOM PROCESSES;

DETERMINISTIC NUMERICAL TECHNIQUES; QUASI-MONTE CARLO (QMC) METHODS; RANDOM POINTS; STOCHASTIC SIMULATIONS;

MONTE CARLO METHODS;

EID: 17744370571     PISSN: 08917736     EISSN: None     Source Type: Conference Proceeding    
DOI: None     Document Type: Conference Paper

References (41)

1. Acworth, P., M. Broadie, and P. Glasserman. 1997. A comparison of some Monte Carlo and quasi-Monte Carlo techniques for option pricing. In Monte Carlo and Quasi-Monte Carlo Methods 1996, ed. P. Hellekalek and H. Niederreiter, Lecture Notes in Statistics 127, 1-18. Springer-Verlag.
2. Avramidis, T., P. L'Ecuyer, and P.-A. Tremblay. 2003. Efficient simulation of gamma and variance-gamma processes. In Proceedings of the 2003 Winter Simulation Conference, ed. S. Chick, P. J. Sánchez, D. Ferrin, and D. J. Morrice, 319-326. Piscataway, New Jersey: IEEE Press.
3. Caflisch, R. E., W. Morokoff, and A. Owen. 1997. Valuation of mortgage-backed securities using Brownian bridges to reduce effective dimension. The Journal of Computational Finance 1 (1): 27-46.
4. Faure, H. 1982. Discrepance des suites associées à un système de numération en dimension s. Acta Arithmetica 61:337-351.
5. Faure, H., and S. Tezuka. 2002. Another random scrambling of digital (t, s)-sequences. In Monte Carlo and Quasi-Monte Carlo Methods 2000, ed. K.-T. Fang, F. J. Hickernell, and H. Niederreiter, 242-256. Berlin: Springer-Verlag.
6. Fox, B. L. 1999. Strategies for quasi-Monte Carlo. Boston, MA: Kluwer Academic.
7. Glasserman, P. 2004. Monte Carlo methods in financial engineering. New York: Springer-Verlag.
8. Halton, J. H. 1960. On the efficiency of certain quasi-random sequences of points in evaluating multi-dimensional integrals. Numerische Mathematik 2:84-90.
9. Hammersley, J. M. 1960. Monte Carlo methods for solving multivariate problems. Annals of the New York Academy of Science 86:844-874.
10. Heinrich, S., F. J. Hickernell, and R. X. Yue. 2004. Optimal quadrature for Haar wavelet spaces. Mathematics of Computation 73:259-277.
11. Hickernell, F. J. 1998a. A generalized discrepancy and quadrature error bound. Mathematics of Computation 67:299-322.
12. Hickernell, F. J. 1998b. Lattice rules: How well do they measure up? In Random and Quasi-Random Point Sets, ed. P. Hellekalek and G. Larcher, Lecture Notes in Statistics 138, 109-166. New York: Springer.
13. -2+ε) convergence for lattice quadrature rules. In Monte Carlo and QuasiMonte Carlo Methods 2000, ed. K.-T. Fang, F. J. Hickernell, and H. Niederreiter, 274-289. Berlin: Springer-Verlag.
14. Hickernell, F. J., C. Lemieux, and A. B. Owen. 2004. Control variates for quasi-Monte Carlo. Statistical Science, to appear.
15. Hickernell, F. J., and H. Wózniakowski. 2001. The price of pessimism for multidimensional quadrature. Journal of Complexity 17:625-659.
16. Hong, H. S., and F. H. Hickernell. 2003. Algorithm 823: Implementing scrambled digital sequences. ACM Transactions on Mathematical Software 29:95-109.
17. Imai, J., and K. S. Tan. 2002. Enhanced quasi-Monte Carlo methods with dimension reduction. In Proceedings of the 2002 Winter Simulation Conference, ed. E. Yücesan, C. H. Chen, J. L. Snowdon, and J. M. Charnes, 1502-1510. Piscataway, New Jersey: IEEE Press.
18. Imai, J., and K. S. Tan. 2004. Minimizing effective dimension using linear transformation. In Monte Carlo and QuasiMonte Carlo Methods 2002, ed. H. Niederreiter, 275-292. Berlin: Springer-Verlag.
19. Kemna, A. G. Z., and A. C. F. Vorst. 1990. A pricing method for options based on average asset values. Journal of Banking and Finance 14:113-129.
20. L'Ecuyer, P. 2004. SSJ: A Java library for stochastic simulation. Available at 〈http://www.iro.umontreal.ca/~lecuyer〉.
21. L'Ecuyer, P., and C. Lemieux. 2000. Variance reduction via lattice rules. Management Science 46 (9): 1214-1235.
22. L'Ecuyer, P., and C. Lemieux. 2002. Recent advances in randomized quasi-Monte Carlo methods. In Modeling Uncertainty: An Examination of Stochastic Theory, Methods, and Applications, ed. M. Dror, P. L'Ecuyer, and F. Szidarovszki, 419-474. Boston: Kluwer Academic Publishers.
23. Lemieux, C., and P. L'Ecuyer. 2001. Selection criteria for lattice rules and other low-discrepancy point sets. Mathematics and Computers in Simulation 55 (1-3): 139-148.
24. Lemieux, C., M. Cieslak, and K. Luttmer. 2004. RandQMC User's Guide: A Package for Randomized Quasi-Monte Carlo Methods in C. Available at 〈http://www. math.ucalgary.ca/~lemieux〉.
25. Liu, R., and A. B. Owen. 2003. Estimating mean dimensionality, manuscript.
26. Madan, D. B., P. P. Carr, and E. C. Chang. 1998. The variance gamma process and option pricing. European Finance Review 2:79-105.
27. Matousek, J. 1999. Geometric discrepancy: An illustrated guide. Berlin: Springer-Verlag.
28. Morokoff, W. J. 1998. Generating quasi-random paths for stochastic processes. SIAM Review 40 (4): 765-788.
29. Moskowitz, B., and R. E. Caflisch. 1996. Smoothness and dimension reduction in quasi-Monte Carlo methods. Journal of Mathematical and Computer Modeling 23:37-54.
30. Niederreiter, H. 1987. Point sets and sequences with small discrepancy. Monatshefte für Mathematik 104:273-337.
31. Niederreiter, H. 1992b. Random number generation and quasi-Monte Carlo methods, Volume 63 of SIAM CBMS-NSF Regional Conference Series in Applied Mathematics. Philadelphia: SIAM.
32. Niederreiter, H., and C. Xing. 1997. The algebraic-geometry approach to low-discrepancy sequences. In Monte Carlo and Quasi-Monte Carlo Methods 1996, ed. P. Hellekalek, G. Larcher, H. Niederreiter, and P. Zinterhof, Volume 127 of Lecture Notes in Statistics, 139-160. New York: Springer-Verlag.
33. Owen, A. B. 1995. Randomly permuted (r, m, s)-nets and (t, s)-sequences. In Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing, ed. H. Nieder-reiter and P. J.-S. Shiue, Number 106 in Lecture Notes in Statistics, 299-317. Springer-Verlag.
34. Owen, A. B. 1997. Scrambled net variance for integrals of smooth functions. Annals of Statistics 25 (4): 1541-1562.
35. Owen, A. B. 1998. Latin supercube sampling for very high-dimensional simulations. ACM Transactions on Modeling and Computer Simulation 8 (1): 71-102.
36. Owen, A. B. 2003. Variance with alternative scramblings of digital nets. ACM Transactions on Modeling and Computer Simulation 13 (4): 363-378.
37. Ribeiro, C., and N. Webber. 2002, December. Valuing path-dependent options in the variance-gamma model by Monte Carlo with a gamma bridge, manuscript.
38. Sloan, I. H., and S. Joe. 1994. Lattice methods for multiple integration. Oxford: Clarendon Press.
39. Sobol', I. M. 1967. The distribution of points in a cube and the approximate evaluation of integrals. U.S.S.R. Jour nal of Computational Mathematics and Mathematical Physics 7:86-112.
40. Tezuka, S., and H. Faure. 2002. i-binomial scrambling of digital nets and sequences. Technical report, IBM Research, Tokyo Research Laboratory.
41. Wang, X., and F. J. Hickernell. 2000. Randomized Halton sequences. Mathematical and Computer Modelling 32:887-899.