Skip to main content

Parallel Monte Carlo Methods for Derivative Security Pricing

  • Conference paper
  • First Online:
Numerical Analysis and Its Applications (NAA 2000)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1988))

Included in the following conference series:

Abstract

Monte Carlo (MC) methods have proved to be flexible, robust and very useful techniques in computational finance. Several studies have investigated ways to achieve greater efficiency of such methods for serial computers. In this paper, we concentrate on the parallelization potentials of the MC methods. While MC is generally thought to be “embarrassingly parallel”, the results eventually depend on the quality of the underlying parallel pseudo-random number generators. There are several methods for obtaining pseudo-random numbers on a parallel computer and we briefly present some alternatives. Then, we turn to an application of security pricing where we empirically investigate the pros and cons of the different generators. This also allows us to assess the potentials of parallel MC in the computational finance framework.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 109.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 139.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Boyle, P. (1977). “Options: a Monte Carlo approach”, Journal of Financial Economics 4, 323–338.

    Article  Google Scholar 

  2. Boyle, P., M. Broadie and P. Glasserman (1997). “Monte Carlo methods for security pricing”, Journal of Economic Dynamics and Control 21, 1267–1321.

    Article  MATH  MathSciNet  Google Scholar 

  3. Carverhill, A. and K. Pang (1995). “Efficient and flexible bond option valuation in the Heath, Jarrow and Morton framework”, Journal of Fixed Income 5, 70–77.

    Google Scholar 

  4. Coddington, P. D. (1994). “Analysis of random number generators using Monte Carlo simulation”, International Journal of Modern Physics

    Article  Google Scholar 

  5. Cox, J. C. and S. A. Ross (1976). “The valuation of options for alternative stochastic processes”, Journal of Financial Economics 3, 145–166.

    Article  Google Scholar 

  6. De Matteis, A., J. Eichenauer-Herrmann and H. Grothe (1992). “Computation of critical distances within multiplicative congruential pseudorandom number sequences”, Journal of Computational and Applied Mathematics 39, 49–55.

    Article  MATH  MathSciNet  Google Scholar 

  7. Eddy, W. F. (1990). “Random number generators for parallel processors”, Journal of Computational and Applied Mathematics 31, 63–71.

    Article  MATH  MathSciNet  Google Scholar 

  8. Entacher, K., A. Uhl and S. Wegenkittl (1999). “Parallel random number generation: long-range correlations among multiple processors”, in P. Zinterhof, M. Vajteršic and A. Uhl (eds) ACPC’99, LNCS 1557, Springer-Verlag, 107–116.

    Google Scholar 

  9. Ferrenberg, A. M. and Landau D. P. Landau (1992). “Monte Carlo simulations: hidden errors from ‘good’ random number generators”, Physical Review Letters 69(23), 3382–3384.

    Article  Google Scholar 

  10. Hammersley, J. M. and D. C. Handscomb (1964). Monte Carlo Methods, Methuen’s Monographs and Applied Probability and Statistics, Wiley, New York, NY.

    Google Scholar 

  11. Hull, J. and A. White (1987). “The pricing of options on assets with stochastic volatilities”, Journal of Finance 42, 281–300.

    Article  Google Scholar 

  12. Johnson, H. (1987). “Option on the maximum or the minimum of several assets”, Journal of Financial and Quantitative Analysis 22, 227–283.

    Article  Google Scholar 

  13. Knuth, D. E. (1981). The Art of Computer Programming, Volume 2: Seminumerical Algorithms, 2nd edition, Addison-Wesley, Reading, MA.

    Google Scholar 

  14. L’Ecuyer, P. (1998). “Random number generation”, in J. Banks (ed.) Handbook on Simulation, Chapter 4, Wiley, New York, NY.

    Google Scholar 

  15. L’Ecuyer, P. (1999). “Good Parameter Sets for Combined Multiple Recursive Random Number Generators”, Operations Research, 47, 1, 159–164.

    Article  MATH  MathSciNet  Google Scholar 

  16. L’Ecuyer, P. and P. Côté (1991). “Implementing a random number package with splitting facilities”, ACM Transactions on Mathematical Software 17 (1), 98–111.

    Article  MATH  Google Scholar 

  17. Mascagni M. (1997). “Some Methods of Parallel Pseudorandom Number Generation”, in Proceedings of the IMA Workshop on Algorithms for Parallel Processing, R. Schreiber, M. Heath and A. Ranade (eds), Springer Verlag, New York.

    Google Scholar 

  18. Metropolis, N. and S. Ulam (1949). “The Monte Carlo Method”, Journal of the American Statistical Association 247 (44), 335–341.

    Article  MathSciNet  Google Scholar 

  19. Park, S. K. and K. W. Miller (1988). “Random number generators: good ones are hard to find”, Communications of the ACM 31(10), 1192–1201.

    Article  MathSciNet  Google Scholar 

  20. Vattulainen, I., T. Ala-Nissila and K. Kankaala (1995). “Physical models as tests of randomness”, Physical Review E 52(3), 3205–3214.

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2001 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Pauletto, G. (2001). Parallel Monte Carlo Methods for Derivative Security Pricing. In: Vulkov, L., Yalamov, P., Waśniewski, J. (eds) Numerical Analysis and Its Applications. NAA 2000. Lecture Notes in Computer Science, vol 1988. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45262-1_77

Download citation

  • DOI: https://doi.org/10.1007/3-540-45262-1_77

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-41814-6

  • Online ISBN: 978-3-540-45262-1

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics