Abstract
This paper is dedicated to a new binomial lattice method called Moments and Strike Matching (MSM) consistent with the Black–Scholes model in the limit of an infinite step number and such that the Strike K is equal to one of the final nodes of the tree. The method is very easy to implement, since the parameters are explicitly given. Asymptotic expansions are obtained for the MSM European Put price and delta, which motivates the use of Richardson extrapolation. A numerical comparison with the best lattice based numerical methods known in literature, shows the efficiency of the proposed algorithm for pricing and hedging American Put options.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Black, F., Scholes, M.: The pricing of options and corporate liabilities. J. Polit. Econ. 81, 637–654 (1973)
Broadie, M., Detemple, J.: American option valuation: new bounds, approximations and a comparison of existing methods. Rev. Financ. Stud. 9(4), 1221–1250 (1996)
Cox, J., Ross, S.A., Rubinstein, M.: Option pricing: a simplified approach. J. Financ. Econ. 7, 229–264 (1979)
Diener, F., Diener, M.: Asymptotics of the price oscillations of a European Call option in a tree model. Math Finance 14(2), 271–293 (2004)
Figlewski, S., Gao, B.: The adaptive mesh model: a new approach to efficient option pricing. J. Financ. Econ. 53, 313–351 (1999)
Gaudenzi, M., Pressacco, F.: An efficient binomial method for pricing American put options. Decis. Econ. Finance. Springer, Heidelberg 4, No. 1, 1–17 (2003)
Gaudenzi, M., Pressacco, F., Zanette, A., Ziani, L.: High precision pricing and hedging of American put options: new insights. Eur. J. Oper. Res. 185(1), 235–254 (2008)
Jourdain, B., Martini, C.: Approximation of American put prices by European prices via an embedding method. Ann. Appl. Probab. 12, 196–223 (2002)
Kushner, H., Dupuis, P.G.: Numerical Methods for Stochastic Control Problems in Continous Time. Springer, Heidelberg (1992)
Lamberton, D.: Error estimates for the binomial approximation of American put options. Ann. Appl. Probab. 8(1), 206–233 (1998)
Lamberton, D.: Brownian optimal stopping and random walks. Appl. Math. Optim. 45, 283–324 (2002)
PREMIA: An Option Pricer, Mathfi Project (INRIA, CERMICS, UMLV). http://www.premia.fr/ (2005)
Walsh, J.B.: The rate of convergence of the binomial tree scheme. Financ. Stoch. 7, 337–361 (2003)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Jourdain, B., Zanette, A. A moments and strike matching binomial algorithm for pricing American Put options. Decisions Econ Finan 31, 33–49 (2008). https://doi.org/10.1007/s10203-007-0077-5
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10203-007-0077-5