CONVERGENCE OF BARRIER OPTION PRICES IN THE BINOMIAL MODEL

Authors


  • Ken Palmer is partially supported by NSC (Taiwan) 97-2115-M-002 -011 -MY2.

Ken Palmer, Providence University—Financial and Computational Mathematics, 200 Chung-Chi Road, Salu Dist., Taichung City 43301, Taiwan; e-mail: palmer@math.ntu.edu.tw.

Abstract

In this paper, we study the rate of convergence of the European barrier call option price given by the CRR binomial model to the Black–Scholes price as the number of periods n tends to infinity. In general the error is of order inline image and we give explicit formulas for the coefficients of inline image and 1/n in the asymptotic expansion of the error. These coefficients depend on the positions of the barrier and strike in the binomial lattice and enable us to give a rigorous explanation of the observed fact that the error is of order 1/n when n is chosen in an appropriate way.

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