Skip to main content
SpringerLink
Log in

On the methods of pricing American options: case study

  • S.I.: Advances of OR in Commodities and Financial Modelling
  • Published:
Annals of Operations Research Aims and scope Submit manuscript

Abstract

In this study, a comparative analysis of numerical and approximation methods for pricing American options is performed. Binomial and finite difference approximations are discussed; furthermore, Roll-Geske-Whaley, Barone-Adesi and Whaley and Bjerksund-Stensland analytical approximations as well as the least-squares Monte Carlo method of Longstaff and Schwartz are presented. Applicability and efficiency in almost all circumstances, numerical solutions of the corresponding free boundary problem is emphasized. Methods used in pricing American options are also compared on dividend and non-dividend paying assets; and their pros and cons are discussed along with numerical experiments.

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

Fig. 1
Fig. 2
Fig. 3
Fig. 4

Similar content being viewed by others

References

  • Andersen, L., & Broadie, M. (2004). Primal-dual simulation algorithm for pricing multidimensional American options. Management Science, 50, 1222–1234.

    Article  Google Scholar 

  • Averbukh, V.: Pricing American options using Monte Carlo simulation. Ph.D. dissertation, Cornell University (1997)

  • Barone-Adesi, G., & Whaley, R. E. (1987). Efficient analytic approximation of American options values. The Journal of Finance, 42(2), 301–320.

    Article  Google Scholar 

  • Barraquand, J., & Martineau, D. (1995). Numerical valuation of high dimensional multivariate American securities. Journal of Financial and Quantitative Analysis, 30, 383–405.

    Article  Google Scholar 

  • Bjerksund, P., Stensland, G. (1992). American exchange options and a put-call transformation. Working paper no. 4/92, Institute of Finance and Management Science, Norwegian School of Economics and Business Administration.

  • Bjerksund, P., & Stensland, G. (1993). Closed-form approximation of American options. Scandinavian Journal of Management, 9, 87–99.

    Article  Google Scholar 

  • Bjerksund, P., Stensland, G. (2002). Closed-form valuation of American options. Working Paper NHH.

  • Black, F. (1975). Fact and fantasy in the use of options. Financial Analysts Journal, 31(4), 36–72.

    Article  Google Scholar 

  • Bossaerts, P. (1989). Simulation estimators of optimal early exercise. Working paper, Carnegie-Mellon University.

  • Boyle, P. P. (1988). A lattice framework for option pricing with two state variables. Journal of Financial and Quantitative Analysis, 23, 1–12.

    Article  Google Scholar 

  • Brennan, M., & Schwartz, E. (1978). Finite difference methods and jump processes arising in the pricing of contingent claims: A synthesis. Journal of Financial and Quantitative Analysis, 13(3), 461–474.

    Article  Google Scholar 

  • Carr, P. (1998). Randomization and the American put. Review of Financial Studies, 11, 597–626.

    Article  Google Scholar 

  • Carriere, J. (1996). Valuation of early-exercise price of options using simulations and nonparametric regression. Insurance: Mathematics and Economics, 19, 19–30.

    Google Scholar 

  • Courtadon, G. (1982). A more accurate finite difference approximation for the valuation of options. Journal of Financial and Quantitative Analysis, 17, 697–705.

    Article  Google Scholar 

  • Cox, J. C., Ross, S. A., & Rubinstein, M. (1979). On the valuation of American call options on stocks with known dividends. Journal of Financial Economics, 7, 229–264.

    Article  Google Scholar 

  • Crank, J., & Nicolson, P. (1947). A practical method for numerical evaluation of solutions of partial differential equations of the heat conduction type. Proceedings of the Cambridge Philosophical Society, 43(1), 50–67.

    Article  Google Scholar 

  • Cryer, C. W. (1971). The solution of a quadratic programming problem using systematic overrelaxation. SIAM Journal on Control and Optimization, 9(3), 385–392.

    Article  Google Scholar 

  • Garcia, D. (1999). A Monte Carlo method for pricing American options. Working paper, University of California, Berkeley.

  • Geske, R. (1979). The valuation of compound options. Journal of Financial Economics, 7, 63–81.

    Article  Google Scholar 

  • Geske, R. (1981). Comments on Whaley’s note. Journal of Financial Economics, 9(2), 213–215.

    Article  Google Scholar 

  • Gilli, M., Schumann, E. (2009). Implementing binomial trees. Comisef Working Paper Series.

  • Haug, E. G., Haug, J., & Lewis, A. (2003). Back to basics: A new approach to the discrete dividend problem. London: Wilmott Magazine.

    Google Scholar 

  • Haugh, M., & Kogan, L. (2004). Pricing American options: A duality approach. Operations Research, 52, 258–270.

    Article  Google Scholar 

  • Ibanez, A., Zapatero, F. (1998). Monte Carlo valuation of American options through computation of the optimal exercise frontier. Working paper, University of Southern California.

  • Kozpinar, S. (2013). Pricing American options under discrete and continuous time setting. M.Sc. Thesis, Middle East Technical University.

  • Kwok, Y. K. (2008). Mathematical Models of Financial Derivatives. Berlin: Springer Finance.

    Google Scholar 

  • Longstaff, F. A., & Schwartz, E. S. (2001). Valuing American options by simulation: A simple least-squares approach. The Society for Financial Studies, 14(1), 113–147.

    Article  Google Scholar 

  • Morton, K. W., & Mayers, D. F. (1995). Numerical solutions of partial differential equations. Cambridge: Cambridge University Press.

    Google Scholar 

  • Protter, P., Clement, E., & Lamberton, D. (2002). An analysis of a least squares regression method for American option pricing. Finance and Stochastics, 6(4), 449–471.

    Article  Google Scholar 

  • Rogers, L. (2002). Monte Carlo valuation of American options. Mathematical Finance, 3, 271–286.

    Article  Google Scholar 

  • Roll, R. (1977). An analytic valuation formula for unprotected American call options on stocks with known dividends. Journal of Financial Economics, 5, 251–258.

    Article  Google Scholar 

  • Schwartz, E. S. (1977). The valuation of warrants: Implementing a new approach. Journal of Financial Economics, 13, 79–93.

    Article  Google Scholar 

  • Tilley, J. A. (1993). Valuing American options in a path simulation model. Transactions of the Society of the Actuaries, 45, 83–104.

    Google Scholar 

  • Tsitsiklis, J., & Van Roy, B. (1999). Optimal stopping of Markov processes: Hilbert space theory, approximation algorithms, and an application to pricing high-dimensional financial derivatives. IEEE Transactions on Automatic Control, 44, 1840–1851.

    Article  Google Scholar 

  • Uğur, Ö. (2009). An introduction to computational finance. London: Imperial College Press.

    Google Scholar 

  • Whaley, R. E. (1981). On the valuation of American call options on stocks with known dividends. Journal of Financial Economics, 9, 207–211.

    Article  Google Scholar 

  • Wu, Z. (2012). Pricing American options using Monte Carlo method. M.Sc. Thesis, University of Oxford.

Download references

Author information

Authors and Affiliations

  1. Institute of Applied Mathematics, Middle East Technical University, 06800, Çankaya, Ankara, Turkey

    Burcu Aydoğan & Ömür Uğur

  2. Department of Mathematics, Atilim University, 06836, Incek Gölbaşı, Ankara, Turkey

    Ümit Aksoy

Authors
  1. Burcu Aydoğan
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ümit Aksoy
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Ömür Uğur
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Burcu Aydoğan.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Aydoğan, B., Aksoy, Ü. & Uğur, Ö. On the methods of pricing American options: case study. Ann Oper Res 260, 79–94 (2018). https://doi.org/10.1007/s10479-016-2267-4

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10479-016-2267-4

Keywords

Search

Navigation