Skip to main content
SpringerLink
Log in

Parallel Option Price Valuations with the Explicit Finite Difference Method

  • Published:
International Journal of Parallel Programming Aims and scope Submit manuscript

Abstract

We show how computations such as those involved in American or European-style option price valuations with the explicit finite difference method can be performed in parallel. Towards this we introduce a latency tolerant parallel algorithm for performing such computations efficiently that achieves optimal theoretical speedup p, where p is the number of processor of the parallel system. An implementation of the parallel algorithm has been undertaken, and an evaluation of its performance is carried out by performing an experimental study on a high-latency PC cluster, and at a smaller scale, on a multi-core processor using in addition the SWARM parallel computing framework for multi-core processors. Our implementation of the parallel algorithm is not only architecture but also communication library independent: the same code works under LAM-MPI and Open MPI and also BSPlib, two sets of library frameworks that facilitate parallel programming. The suitability of our approach to multi-core processors is also established.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Bader, D.A., Madduri, K.: SWARM: A Parallel Programming Framework for Multi-Core Processors, First Workshop on Multithreaded Architectures and Applications (MTAAP). Long Beach, CA, 30 March 2007

  2. Bader, D.A., Madduri, K., Sangani, R.H.: Multicore SWARM. http://www.multicore-swarm.sourceforge.net (2007)

  3. Black F., Scholes M.: The pricing of options and corporate liabilities. J. Polit. Econ. 81, 637–654 (1973)

    Article  Google Scholar 

  4. Blumofe, R.D., Joerg, C.F., Kuszmaul, B.C., Leiserson, C.E., Randall, K.H., Zhou, Y.: Proceedings, 5th ACM SIGPLAN Symposium on Principles and Practice of Parallel Programming (PPoPP), pp. 207–216 (1995)

  5. Boyle P.P.: Option valuation using a three jump process. Int. Options J. 3, 7–12 (1986)

    Google Scholar 

  6. Burns, G., Daoud, R., Vaigl, J.: LAM: An open cluster environment for MPI. In: Proceedings of Supercomputing Symposium ’94, pp. 379–386, University of Toronto, 1994

  7. Clewlow L., Strickland C.: Implementing Derivative Models. Wiley, New York (1998)

    Google Scholar 

  8. Gerbessiotis, A.V.: Trinomial-tree based parallel option price valuations. Parallel Algorithms Appl. 18(3), 181–196 (2003), Elsevier Science BV

    Google Scholar 

  9. Gerbessiotis, A.V.: Architecture independent parallel binomial tree option price valuations. Parallel Comput. J. 30(2), 303–318 (2004), Elsevier Science, BV

    Google Scholar 

  10. Gerbessiotis, A.V.: http://www.cs.njit.edu/~alexg/cluster/efdm.html (2009)

  11. Gerbessiotis A.V., Valiant L.G.: Direct bulk-synchronous parallel algorithms. J. Parallel Distrib. Comput. 22, 251–267 (1994)

    Article  Google Scholar 

  12. Ghuloum, A., Wu, G., Zhou, X., Guo, P., Fang, J.: Programming Option Pricing Financial Models with Qt. http://www.techresearch.intel.com/userfiles/en-us/File/terascale/Ct-appnote-option-pricing.pdf

  13. Goudreau, M.W., Hill, J.M.D., Lang, K., McColl, W.F., Rao, S.D., Stefanescu, D.C., Suel, T., Tsantilas, T.: A proposal for a BSP Worldwide standard. BSP Worldwide. http://www.bsp-worldwide.org/ (1996)

  14. Graham, R.L., Woodall, T.S., Squyres, J.M.: Open MPI: a flexible high performance MPI. In: Proceedings, 6th Annual International Conference on Parallel Processing and Applied Mathematics, September, Poznan, Poland, Springer Verlag Lecture Series in Computer Science, Springer, 2005

  15. Haug E.G.: The Complete Guide to Option Pricing Formulas. McGraw-Hill, New York (1998)

    Google Scholar 

  16. LAM/MPI Parallel computing: http://www.lam-mpi.org

  17. Mills, K., Vinson, M., Cheng, G.: A large scale comparison of option pricing models with historical market data. In: Proceedings, 4th Symposium on the Frontiers of Massively Parallel Computation (Frontiers 92), pp. 420–426, IEEE Computer Society Press, McLean, 1992

  18. Schwartz E.S.: The valuation of warrants: implementing a new approach. J. Financ. Econ. 4, 79–94 (1977)

    Article  Google Scholar 

  19. Sharpe W.F.: Investments. Prentice-Hall, Englewood Cliffs (1978)

    Google Scholar 

  20. Skillicorn D.B., Hill J.M.D., McColl W.F.: Questions and answers about BSP. Sci. Program. 6, 249–274 (1997)

    Google Scholar 

  21. Thulasiram, R.K., Litov, L., Nojumi, H., Downing, C.T., Gao, G.R.: Multithreaded algorithms for pricing a class of complex options. In: Proceedings of the 15th International Parallel and Distributed Processing Symposium, pp. 18–23, IEEE Computer Society Press, 2001

  22. Thulasiram, R.K., Thulasiraman, P., Adiele, C., Bondarenko, D.: Performance analysis of a multithreaded pricing algorithm on Cilk. In: Proceedings of the 16th Annual International Symposium on High Performance Computing Systems and Applications, pp. 251–257, IEEE Computer Society Press, 2002

  23. Valiant L.G.: A bridging model for parallel computation. Commun. ACM 33(8), 103–111 (1990)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. CS Department, New Jersey Institute of Technology, Newark, NJ, 07102, USA

    Alexandros V. Gerbessiotis

Authors
  1. Alexandros V. Gerbessiotis
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Alexandros V. Gerbessiotis.

Additional information

This work was supported in part by NSF/MRI NSF-9977508 and NSF/ITR IIS-0324816 grants.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Gerbessiotis, A.V. Parallel Option Price Valuations with the Explicit Finite Difference Method. Int J Parallel Prog 38, 159–182 (2010). https://doi.org/10.1007/s10766-009-0126-5

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10766-009-0126-5

Keywords

Search

Navigation