Improved multilevel monte carlo convergence using the milstein scheme

Monte Carlo and Quasi-Monte Carlo Methods 2006

Volumn , Issue , 2008, Pages 343-358

  Giles, Mike ^a  

^a UNIVERSITY OF OXFORD   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

DIFFERENTIAL EQUATIONS; MEAN SQUARE ERROR; STOCHASTIC SYSTEMS;

COMPUTATIONAL COSTS; NUMERICAL RESULTS; ROOT MEAN SQUARE ERRORS; STOCHASTIC DIFFERENTIAL EQUATIONS;

MONTE CARLO METHODS;

EID: 84892272601     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1007/978-3-540-74496-2_20     Document Type: Conference Paper

References (13)

1. [BGK97] M. Broadie, P. Glasserman, and S. Kou. A continuity correction for discrete barrier options. Mathematical Finance, 7(4):325-348, 1997.
2. [BT95] V. Bally and D. Talay. The law of the Euler scheme for stochastic differential equations, I: convergence rate of the distribution function. Probability Theory and Related Fields, 104(1):43-60, 1995.
3. [Ecu04] P. L'Ecuyer. Quasi-Monte Carlo methods in finance. In R.G. Ingalls, M.D. Rossetti, J.S. Smith, and B.A. Peters, editors, Proceedings of the 2004 Winter Simulation Conference, pages 1645-1655. IEEE Press, 2004.
4. [ES02] M. Emsermann and B. Simon. Improving simulation efficiency with quasi control variates. Stochastic Models, 18(3):425-448, 2002.
5. [GL94] J.G. Gaines and T.J. Lyons. Random generation of stochastic integrals. SIAM J. Appl. Math., 54(4):1132-1146, 1994.
6. [Gla04] P. Glasserman. Monte Carlo Methods in Financial Engineering. Springer-Verlag, New York, 2004.
7. [Hei01] S. Heinrich. Multilevel Monte Carlo Methods, volume 2179 of Lecture Notes in Computer Science, pages 58-67. Springer-Verlag, 2001.
8. [Keb05] A. Kebaier. Statistical Romberg extrapolation: a new variance reduction method and applications to options pricing. Annals of Applied Probability, 14(4):2681-2705, 2005.
9. [KP92] P.E. Kloeden and E. Platen. Numerical Solution of Stochastic Differential Equations. Springer-Verlag, Berlin, 1992.
10. [KS05] F.Y. Kuo and I.H. Sloan. Lifting the curse of dimensionality. Notices of the AMS, 52(11):1320-1328, 2005.
11. [Nie92] H. Niederreiter. Random Number Generation and Quasi-Monte Carlo Methods. SIAM, 1992.
12. [Spe05] A. Speight. A multilevel approach to control variates. Working paper, Georgia State University, 2005.
13. [TT90] D. Talay and L. Tubaro. Expansion of the global error for numerical schemes solving stochastic differential equations. Stochastic Analysis and Applications, 8:483-509, 1990.