Analysis of Higher Order Error in the Binomial Model
Date Issued
2011
Date
2011
Author(s)
Huang, Kuan-Min
Abstract
In this paper, we study the rate of convergence of the European call option price by the binomial model to the Black-Scholes price as the number of period n tends to
infinity. The binomial option pricing is determined by the jump sizes u and d and the risk-neutral probability p. Chang and Palmer [1] gives an explicit formula for the coefficient of 1/n in the expansion of the error. This paper discusses the higher order in the expansion of the error. We consider more general u and d to prove
the Main Theorem and apply it to strengthen the Chang-Palmer result, expanding up to the higher term in the expansion of the error and also giving an explicit formula for the coefficient of the higher term. We use the strengthened Chang-Palmer result to prove the error between the binomial price and the Black-Scholes price in Joshi''s model [4]. We also use the Main Theorem to obtain a proof of the convergence rate in Leiser-Reimer''s model [5] and a new theorem in Tian''s model [7].
Subjects
binomial model
option value
Black-Scholes price
digital call option
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