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A COST-EFFECTIVE MODIFICATION OF THE TRINOMIAL METHOD FOR OPTION PRICING

  • Received : 2010.12.22
  • Accepted : 2010.12.31
  • Published : 2011.03.25

Abstract

A new method for option pricing based on the trinomial tree method is introduced. The new method calculates the local average of option prices around a node at each time, instead of computing prices at each node of the trinomial tree. Local averaging has a smoothing effect to reduce oscillations of the tree method and to speed up the convergence. The option price and the hedging parameters are then obtained by the compact scheme and the Richardson extrapolation. Computational results for the valuation of European and American vanilla and barrier options show superiority of the proposed scheme to several existing tree methods.

Acknowledgement

Supported by : National Research Foundation of Korea(NRF), Kyungwon University

References

  1. T. Achdou, O. Pironneau. Computational methods for option pricing. SIAM Philadelphia, 2005.
  2. P. Boyle. A lattice framework for option pricing with two state variables. Journal of Financial and Quantitative Analysis, 23(1):1-12, 1988. https://doi.org/10.2307/2331019
  3. P. Boyle, J. Evnine, and S. Gibbs. Numerical evaluation of multivariate contingent claims. The Review of Financial Studies, 2(2):241-250, 1989. https://doi.org/10.1093/rfs/2.2.241
  4. P. Boyle, and S. H. Lau. Bumping up against the barrier with the binomial method. Journal of Derivatives, 1:6-14, 1994.
  5. M. Broadie and J. Detemple. American option valuation: new bounds, approximations, and a comparison of existing methods. Review of Financial Studies, 9:1211-1250, 1996. https://doi.org/10.1093/rfs/9.4.1211
  6. T. H. F. Cheuk and T. C. F. Vorst. Complex barrier options. Journal of Derivatives, 4:8-22, 1996.
  7. J. Cox, S. Ross, and M. Rubinstein. Option pricing: A simplified approach. Journal of Financial Economics, 7:229-263, 1979.
  8. E. Derman, I. Kani, D. Ergener and I. Bardhan. Enhanced Numerical Methods for Options with Barriers. Financial Analysts Journal, 51(6):65-74, 1995. https://doi.org/10.2469/faj.v51.n6.1951
  9. S. Figlewski and B. Gao. The adaptive mesh model: a new approach to efficient option pricing. Journal of Financial Economics, 53:313-351, 1999.
  10. M. Gaudenzi and M. A. Lepellere. Pricing and hedging American barrier options by a modified binomial method. International Journal of Theoretical and Applied Finance, 9(4):533-553, 2006. https://doi.org/10.1142/S0219024906003664
  11. M. Gaudenzi and F. Pressacco. An efficient binomial method for pricing american options. Decisions in Economics and finance, 26:1-17, 2003.
  12. E. G. Haug. The complete guide to option pricing formulas. McGraw-Hill, 1997.
  13. D.J. Higham. An introduction to financial option valuation. Cambridge University Press, 2004.
  14. B. Kamrad and P. Ritchken. Multinomial approximating models for options with k state variables. Management science, 37(12), 1991.
  15. Y. K. Kwok. Mathematical models of financial derivatives. Springer-Verlag, Singapore, 1998.
  16. Y. D. Lyuu. Financial Engineering and Computation. Cambridge, 2002.
  17. B. Oksendal. Stochastic differential equations. Springer, Berlin, 1998.
  18. E. Reimer and M. Rubinstein. Unscrambling the binary code. Risk Magazine, 4, 1991.
  19. P. Ritchken. On pricing barrier options. Journal of Derivatives, 3:19-28, 1995.
  20. P.Wilmott, J. Dewynne, S. Howison. Option Pricing: Mathematical Models and Computation. Oxford Financial Press, 1993.