Abstract
In this article, we consider a general class of binomial models with an additional parameter λ. We show that in the case of a European call option the binomial price converges to the Black–Scholes price at the rate 1/n and, more importantly, give a formula for the coefficient of 1/n in the expansion of the error. This enables us, by making special choices for λ, to prove that convergence is smooth in Tian’s flexible binomial model and also in a new center binomial model which we propose.
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Ken Palmer was supported by NSC grant 93-2118-M-002-002.
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Chang, LB., Palmer, K. Smooth convergence in the binomial model. Finance Stoch 11, 91–105 (2007). https://doi.org/10.1007/s00780-006-0020-6
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DOI: https://doi.org/10.1007/s00780-006-0020-6