Skip to main content
SpringerLink
Log in

Applications of a Hybrid-Monte Carlo Sequence to Option Pricing

  • Conference paper
Monte-Carlo and Quasi-Monte Carlo Methods 1998

Abstract

The advantages of quasi-Monte Carlo methods diminish, mainly due to practical constraints, as the dimension of the problem grows. This phenomenon has been widely observed in several fields, especially in particle transport theory, and several methods have been proposed to provide remedies for the difficulties faced in high dimensional quasi-Monte Carlo simulation.

One of the methods that has been used successfully in various high dimensional problems will be presented. The advantages of this method will be illustrated when applied to selected problems from option pricing.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
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. A. B. Owen,“Latin Supercube Sampling for Very High Dimensional Simulations”, ACM Transactions on Modeling and Computer Simulation, Vol. 8, No. 1, 71–102, 1998.

    Article  MATH  MathSciNet  Google Scholar 

  2. N. Bouleau and D. Lépingle,Numerical Methods For Stochastic Processes, Wiley Series in Probability and Mathematical Statistics, 1994.

    Google Scholar 

  3. J. Spanier,“Quasi-Monte Carlo Methods for Particle Transport Problems”, Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing 1994, Lecture Notes in Statistics #106, Springer, 1995.

    Google Scholar 

  4. J. Spanier and L. Li, “Quasi-Monte Carlo Methods for Integral Equations”, Monte Carlo and Quasi-Monte Carlo Methods 1996, Lecture Notes in Statistics #127, Springer, 1998.

    Google Scholar 

  5. G. Ökten, “A Probabilistic Result on the Discrepancy of a Hybrid-Monte Carlo Sequence and Applications”, Monte Carlo Methods and Applications, Vol. 2, No. 4, 255–270, 1996.

    Article  MATH  MathSciNet  Google Scholar 

  6. P. Bratley, B. L. Fox, “ALGORITHM 659: Implementing Sobol’s Quasirandom Sequence Generator”, ACM Transactions on Mathematical Software, Vol. 14, No. 1, 88–99, 1988.

    Article  MATH  Google Scholar 

  7. B. L. Fox,“ALGORITHM 647: Implementation and Relative Efficiency of Quasirandom Sequence Generators”, ACM Transactions on Mathematical Software, Vol. 12, No. 4, 362–376, 1986.

    Article  MATH  Google Scholar 

  8. P. Bratley, B. L. Fox and H. Niederreiter,“Implementation and Tests of Low- Discrepancy Sequences”, ACM Transactions on Modelling and Computer Simulation, 2, 195–213, 1992.

    Article  MATH  Google Scholar 

  9. A. G. Z. Kemna and A. C. F. Vorst,“A Pricing Method for Options Based on Average Asset Values”, Journal of Banking and Finance, 14, 113–129, 1990.

    Article  Google Scholar 

  10. S. J. Taylor,“Modeling Stochastic Volatility: A Review And Comparative Study”, Mathematical Finance, Vol. 4, No. 2, 1994.

    Google Scholar 

  11. H. Johnson and D. Shanno, “Option Pricing when the Variance is Changing”Journal of Financial and Quantitative Analysis, Vol. 22, No. 2, 1987.

    Google Scholar 

  12. G. Ökten,Contributions to the Theory of Monte Carlo and Quasi-Monte Carlo Methods, Dissertation.Com, 1999 (www.dissertation.com/library/1120419a.htm www.dissertation.com/library/1120419a.htm).

    Google Scholar 

  13. G. Pages and Y. J. Xiao, “Sequences with low discrepancy and pseudo-random numbers: theoretical remarks and numerical tests”, J. Statist. Comput. Simul., Vol. 56, 163–188, 1997.

    Article  MATH  MathSciNet  Google Scholar 

  14. I. M. Sobol’, “Sensitivity Estimates for Nonlinear Mathematical Models”, MMCE, Vol. 1, No. 4, 407–414, 1993.

    MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematical Sciences, Ball State University, Muncie, IN, 47306, USA

    Giray Ökten

Authors
  1. Giray Ökten
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Institute of Discrete Mathematics, Austrian Academy of Sciences, Sonnenfelsgasse 19, 1010, Vienna, Austria

    Harald Niederreiter

  2. Claremont Graduate University, 925 N. Dartmouth Avenue, 91711, Claremont, CA, USA

    Jerome Spanier

Rights and permissions

Reprints and permissions

Copyright information

© 2000 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Ökten, G. (2000). Applications of a Hybrid-Monte Carlo Sequence to Option Pricing. In: Niederreiter, H., Spanier, J. (eds) Monte-Carlo and Quasi-Monte Carlo Methods 1998. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-59657-5_27

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-59657-5_27

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-66176-4

  • Online ISBN: 978-3-642-59657-5

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation