Binomial Trees in Option Pricing—History, Practical Applications and Recent Developments

  • Ralf Korn
  • Stefanie Müller


We survey the history and application of binomial tree methods in option pricing. Further, we highlight some recent developments and point out problems for future research.


Stock Price Option Price American Option Binomial Tree Stock Price Process 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. Amin, K.I.: On the computation of continuous time option prices using discrete approximations. J. Financ. Quant. Anal. 26, 477–495 (1991) CrossRefGoogle Scholar
  2. Billingsley, P.: Convergence of Probability Measures. Wiley, New York (1968) MATHGoogle Scholar
  3. Bjoerk, T.: Arbitrage Theory in Continuous Time, 2nd edn. Oxford University Press, Oxford (2004) MATHGoogle Scholar
  4. Black, F., Scholes, M.S.: The pricing of options and corporate liabilities. J. Polit. Econ. 81, 637–654 (1973) CrossRefGoogle Scholar
  5. Boyle, P.P., Lau, S.H.: Bumping up against the barrier with the binomial method. J. Deriv. 1, 6–14 (1994) CrossRefGoogle Scholar
  6. Boyle, P.P., Evnine, J., Gibbs, S.: Numerical evaluation of multivariate contingent claims. Rev. Financ. Stud. 2, 241–250 (1989) CrossRefGoogle Scholar
  7. Chang, L.-B., Palmer, K.: Smooth convergence in the binomial model. Finance Stoch. 11, 91–105 (2007) MATHCrossRefMathSciNetGoogle Scholar
  8. Cox, J.C., Ross, S.A., Rubinstein, M.: Option pricing: a simplified approach. J. Financ. Econ. 7, 229–263 (1979) MATHCrossRefGoogle Scholar
  9. He, H.: Convergence from discrete- to continuous-time contingent claim prices. Rev. Financ. Stud. 3, 523–546 (1990) CrossRefGoogle Scholar
  10. Hull, J.C.: Options, Futures, and other Derivatives, 6th edn. Pearson/Prentice Hall, New Jersey (2006) Google Scholar
  11. Korn, R., Müller, S.: The decoupling approach to binomial pricing of multi-asset options. J. Comput. Finance 12, 1–30 (2009) MATHMathSciNetGoogle Scholar
  12. Leisen, D.P.J.: Pricing the American put option: a detailed convergence analysis for binomial models. J. Econ. Dyn. Control 22, 1419–1444 (1998) MATHCrossRefMathSciNetGoogle Scholar
  13. Leisen, D.P.J., Reimer, M.: Binomial models for option valuation—examining and improving convergence. Appl. Math. Finance 3, 319–346 (1996) CrossRefGoogle Scholar
  14. Rendleman, R.J., Bartter, B.J.: Two-state option pricing. J. Finance 34, 1093–1110 (1979) CrossRefGoogle Scholar
  15. Rogers, L.C.G., Stapleton, E.J.: Fast accurate binomial pricing. Finance Stoch. 2, 3–17 (1998) MATHCrossRefGoogle Scholar
  16. Rubinstein, M.: Guiding force. In: From Black-Scholes to Black Holes: New Frontiers in Options, Risk Magazine, November (1992) Google Scholar
  17. Tian, Y.S.: A Flexible Binomial option pricing model. J. Futures Mark. 19, 817–843 (1999) CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  1. 1.Center for Mathematical and Computational Modeling (CM)² and Department of MathematicsUniversity of KaiserslauternKaiserslauternGermany

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