Junichi Imai
ABSTRACT
In recent years, the quasi-Monte Carlo approach for pricing high-dimensional derivative securities has been used widely relative to other competitive approaches such as the Monte Carlo methods. Such success can be, in part, attributed to the notion of effective dimension of the finance problems. In this paper, we provide additional insight on the connection between the effective dimension and the quasi-Monte Carlo method. We also propose a dimension reduction technique which further enhances the quasi-Monte Carlo method for derivative pricing. The efficiency of the proposed method is illustrated by applying it to high-dimensional multi-factor path-dependent derivative securities.
- Acworth, P., M. Broadie, and P. Glasserman. 1998. A comparison of some Monte Carlo and quasi-Monte Carlo methods for option pricing. In Monte and quasi-Monte-Carlo Methods 1996: Proceedings of a conference at the University of Salzburg, Austria, July 9--12, 1996, ed. H. Niederreiter, P. Hellekalek, G. Larcher and P. Zinterhof. Lecture Notes in Statistics 127. Springer-Verlag, New York.Google Scholar
- Boyle, P. 1977. Options: A Monte Carlo Approach. Journal of Financial Economics, 4:323--338.Google ScholarCross Ref
- Bratley, P., B. Fox, and H. Niederreiter. 1992. Implementation and tests of low-discrepancy sequences. ACM Transactions on Modeling and Computer Simulation 2 (3):195--213. Google ScholarDigital Library
- Caflisch, R., W. Morokoff, and A. Owen. 1997. Valuation of mortgage-backed securities using Brownian bridges to reduce effective dimension. Journal of Computational Finance 1 (1):27--46.Google ScholarCross Ref
- Joy, C., P. Boyle, and K. S. Tan. 1996. Quasi-Monte Carlo methods in numerical finance. Management Science 42 (6):926--938. Google ScholarDigital Library
- Moskowitz, B. and R. Caflisch. 1996. Smoothness and dimension reduction in quasi-Monte Carlo methods. Mathematical and Computer Modelling 23 (8--9):37--54. Google ScholarDigital Library
- Owen, A. 1995. Randomly permuted (t, m, s)-nets and (t, s)-sequences. In Monte and quasi-Monte-Carlo Methods in Scientific Computing: Proceedings of a conference at the University of Nevada, Las Vegas, Nevada, USA, June 23--25, 1994, ed. H. Niederreiter, and P.-S. Shiue. Lecture Notes in Statistics 106, pages 299--317. Springer-Verlag, New York.Google Scholar
- Owen, A. 1998. Latin supercube sampling for very high-dimensional simulations. ACM Transactions on Modeling and Computer Simulation 8 (1):71--102. Google ScholarDigital Library
- Paskov, S. and J. Traub. 1995. Faster valuation of financial derivatives. Journal of Portfolio Management 22 (1):113--120.Google ScholarCross Ref
- Sobol′, I. 1967. The distribution of points in a cube and the approximate evaluation of integrals. U.S.S.R Computational Mathematics and Mathematical Physics 7 (4):86--112.Google ScholarCross Ref
- Derivatives and credit risk: enhanced quasi-monte carlo methods with dimension reduction
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