Skip to main content
SpringerLink
Log in

Applications of Monte Carlo/Quasi-Monte Carlo Methods in Finance: Option Pricing

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

Abstract

The pricing of options is a very important problem encountered in financial markets today. The famous Black-Scholes model provides explicit closed form solutions for the values of certain (European style) call and put options. But for many other options, either there are no closed form solutions, or if such closed form solutions exist, the formulas exhibiting them are complicated and difficult to evaluate accurately by conventional methods. In this case, Monte Carlo methods may prove to be valuable.

In this paper, we illustrate two separate applications of Monte Carlo and/or quasi-Monte Carlo methods to the pricing of options: first, the method is used to estimate multiple integrals related to the evaluation of European style options; second, an adaptive Monte Carlo method is applied to a finite difference approximation of a partial differential equation formulation of a class of finance problems. Some of the advantages in using the Monte Carlo method for such problems are discussed.

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. . Barrett, J., Moore, G., Wilmott, P.: Inelegant Efficiency.Risk Magazine 5(1995) 82–84

    Google Scholar 

  2. . Black, F., Scholes, M.: The Pricing of Options and Corporate Liabilities.J. Pol and Econ. 81(1973) 637–659

    Article  Google Scholar 

  3. . Boyle, P.P.: Options: a Monte Carlo Approach.J. Finan. Econ. 4(1977) 323–338

    Article  Google Scholar 

  4. . Chance, D. M.:An Introduction to Derivatives, (third edition) The Dryden Press 1995

    Google Scholar 

  5. . Cox, J. C., Rubinstein, M.:Options Markets. Prentice Hall 1985

    Google Scholar 

  6. . Cox, J. C. Ross, S. A., Rubinstein, M.: Option Pricing: a Simplified Approach.J. Fin. Econ. 71979 229–263

    Article  MATH  Google Scholar 

  7. . Duffie, D.:Dynamic Asset Pricing Theory. Princeton 1992

    Google Scholar 

  8. . Duffie, D.:Security Markets: Stochastic Models. Academic Press, Inc. 1988

    MATH  Google Scholar 

  9. . Gemmili, G.:Options Pricing. McGraw-Hill 1992

    Google Scholar 

  10. . Hull, J. C.:Options, Futures, and other Derivative Securities. Prentice-Hall, Inc. 1993

    Google Scholar 

  11. . Paskov, S.: Computing High Dimensional Integrals with Applications to Finance. preprint Columbia Univ. (1994)

    Google Scholar 

  12. . Wilmott, P., Dewynne, J., Howison, S.:Option Pricing: Mathematical Models and Computation. Oxford University Press 1995

    MATH  Google Scholar 

  13. . Harrison, J. M., Kresps, D.: Martingales and Arbitrage in Multiperiod Securities Markets.J. Econ. Theory 20(1979) 381–408

    Article  MATH  Google Scholar 

  14. . Niederreiter, H.:Random Number Generation and Quasi-Monte Carlo Methods. SIAM 1992

    Book  MATH  Google Scholar 

  15. . Harrison, J. M., Pliska, S. R.: Martingales and Stochastic Integrals in the Theory of Continuous Trading.Stoch. Proc. Appi 11(1981) 261–271

    Article  MathSciNet  Google Scholar 

  16. . Halton, J.: Sequential Monte Carlo. Proc. Camb. Phil. Soc.58(1962) 57–73

    Article  MATH  MathSciNet  Google Scholar 

  17. . Halton, J.: Sequential Monte Carlo Techniques for the Solution of Linear Systems.J. Sei. Comp. 9(1994) 213–257

    MATH  MathSciNet  Google Scholar 

  18. . Li, L., Spanier, J.: Approximation of Transport Equations by Matrix Equations and Sequential Sampling.Monte Carlo Methods and Appi 3(1997) 171–198

    MATH  MathSciNet  Google Scholar 

  19. . Lai, Y.: Monte Carlo and Quasi-Monte Carlo Methods and Their Applications. Ph.D. dissertation Claremont Graduate University 1998

    Google Scholar 

  20. . Broadie, M., Glasserman, P.: Pricing American-style Securities Using Simulation.J. of Economic Dynamics and Control 21(1997) 1323–1352

    Article  MATH  MathSciNet  Google Scholar 

  21. . Spanier, J., Gelbard, E. M.:Monte Carlo Principles and Neutron Transport Problems. Addison-Wesley 1969

    MATH  Google Scholar 

  22. . Karatzas, I.:Lectures on the Mathematics of Finance. American Mathematical Society 1998

    Google Scholar 

  23. . Joy, C., Boyle, P. P., Tan, K. S.: Quasi-Monte Carlo Methods in Numerical Finance.Management ScienceVol. 42 No. 6 June 1996

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Claremont Graduate University, 925 N. Dartmouth Ave., Claremont, CA, 91711, USA

    Yongzeng Lai & Jerome Spanier

Authors
  1. Yongzeng Lai
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jerome Spanier
    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

Lai, Y., Spanier, J. (2000). Applications of Monte Carlo/Quasi-Monte Carlo Methods in Finance: 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_19

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-59657-5_19

  • 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