GPU based sparse grid technique for solving multidimensional options pricing PDEs

Proceedings of the 2nd Workshop on High Performance Computational Finance, WHPCF '09

Volumn , Issue , 2009, Pages

  Gaikwad, Abhijeet ^a   Toke, Ioane Muni ^a  

^a Ecole Centrale de Paris   (France)

Author keywords

Conjugate gradient squared; Iterative solvers; Multidimensional option pricing; NVIDIA CUDA; Sparse linear iterative solvers; Stabilized biconjugate gradient

Indexed keywords

BI-CGSTAB; CONJUGATE GRADIENT; DIRECT METHOD; DISCRETIZATIONS; EFFICIENT IMPLEMENTATION; FINITE DIFFERENCE; GENERAL PURPOSE; GRAPHICS PROCESSING UNIT; HIGH-DIMENSIONAL; ITERATIVE SOLUTIONS; ITERATIVE SOLVERS; KRYLOV SUBSPACE; MASSIVE PARALLELISM; OPTION PRICING; OPTIONS PRICING; SPARSE GRID; STABILIZED BICONJUGATE GRADIENT; STANDARD FINITE ELEMENT;

AIRCRAFT ENGINES; CONJUGATE GRADIENT METHOD; COSTS; DATA STRUCTURES; HIERARCHICAL SYSTEMS; LINEAR SYSTEMS; PROGRAM PROCESSORS;

ECONOMICS;

EID: 74049120824     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1145/1645413.1645419     Document Type: Conference Paper

References (25)

1. H. J. Bungartz, M. Griebel, D. R. Oschke, and C. Zenger. Pointwise convergence of the combination technique for the laplace equation. East-West J. Numer. Math, 1994.
2. M. Griebel, T. Gerstner, and S. Wahl. Method and device for evaluation of financial derivatives using sparse grids. US Patent App. 09/994,114.
3. M. Griebel, M. Schneider, and C. Zenger. A combination technique for the solution of sparse grid problems. Iterative Methods in Linear Algebra, pages 263-281, 1992.
4. M. Griebel and V. Thurner. Efficient solution of fluid dynamics problems by the combination technique. International Journal of Numerical Methods for Heat and Fluid Flow, 5(3):251-269, 1995.
5. C. Pflaum. Convergence of the combination technique for Second-Order elliptic differential equations. SIAM J. on Num. Ana., 34(6):2431-2455, Dec. 1997.
6. C. Pflaum and A. Zhou. Error analysis of the combination technique. Numerische Mathematik, 84(2):327-350, Dec. 1999.
7. J. Garcke, M. Griebel, and M. Thess. Data mining with sparse grids. Computing, 67(3):225-253, Oct. 2001.
8. O. Pironneau and Y. Achdou. Computational Methods for Option Pricing. Society for Industrial & Applied Mathematics, U.S., illustrated edition edition, 2008.
9. C. Reisinger. Analysis of linear difference schemes in the sparse grid combination technique. SIAM Journal on Numerical Analysis, 2006.
10. C. Reisinger and G. Wittum. Efficient hierarchical approximation of high-dimensional option pricing problems. SIAM J. on Scientific Computing, 29(1):440, 2008.
11. L. Buatois , G. Caumon and B. Levy. Concurrent number cruncher - A GPU implementation of a general sparse linear solver. Intl. Journal of Parallel, Emergent and Distributed Systems, to appear.
12. M. Baskaran and R. Bordawekar. Optimizing Sparse Matrix-Vector Multiplication on GPUs. IBM Technical Report RC24704., 2008.
13. J. Hull Options, Futures, and Other Derivative Securities Prentice Hall, 4th Edition 2000., 2nd Edition, 1993.
14. A. Brandt. Multilevel adaptive solutions to boundary-value problems. Math. Comp., 31:311329, 1977.
15. R. Barrett et al. Templates for the Solution of Linear Systems: Building Blocks for Iterative Methods. SIAM, Philadelphia, 1994.
16. N. Bell and M. Garland Efficient Sparse Matrix-Vector Multiplication on CUDA. NVIDIA Technical Report, Dec. 2008.
17. S. Williams, L. Oliker , R. Vuduc amd J. Shalf , K. Yelick, and J. Demmel. Optimization of sparse matrix-vector multiplication on emerging multicore platforms. Proc. of the 2007 ACM/IEEE conf. Supercomputing, 1-12, 2007.
18. J. Bolz, I. Farmer, E. Grinspun, and P. Schörder. Sparse matrix solvers on the GPU: conjugate gradients and multigrid. ACM Trans. Graph., 22(3):917-924, July 2003.
19. J. Krüger and R. Westermann. Linear algebra operators for GPU implementation of numerical algorithms. ACM Trans. on Graphics (TOG), 22(3):908-916, 2003.
20. V. Volkov and J. W. Demmel. Benchmarking GPUs to tune dense linear algebra. Proc. of the 2008 ACM/IEEE conference on Supercomputing, 2008, pp. 1-11.
21. N. Galoppo , N. K. Govindaraju , M. Henson, and D. Manocha. LU-GPU: Efficient algorithms for solving dense linear systems on graphics hardware. Proc. of the 2005 ACM/IEEE conference on Supercomputing, 2005.
22. G. Quintana-Orti , F. D. Igual , E. S. Quintana-Orti, and R. van de Geijn. Solving dense linear algebra problems on platforms with multiple hardware accelerators. Proc. of the 14th ACM SIGPLAN Sym. PPPP, 2009.
23. A. Cevahir , A. Nukada, and S. Matsuoka. Fast Conjugate Gradients with Multiple GPUs. Computational Science, ICCS, Vol.5544 Springer (2009), p.893-903.
24. D. Göddeke , R. Strzodka , J. Mohd-Yusof , P. McCormick , H. Wobker , C. Becker, and S. Türek. Using GPUs to Improve Multigrid Solver Performance on a Cluster. Intl. Journal of CSE, 2008.
25. http://www.nvidia.com/object/product-tesla-c1060-us.html