Smooth convergence in the binomial model
LB Chang, K Palmer - Finance and stochastics, 2007 - Springer
LB Chang, K Palmer
Finance and stochastics, 2007•SpringerIn 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.
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.
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.
Springer
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