BibTeX
@MISC{Kevin04continuoustime,
author = {Timothy Kevin and Kuria Kamanu},
title = {Continuous time limit of the Binomial Model},
year = {2004}
}
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Abstract
I would like to acknowledge my sponsors, The African Institute for Mathematical Sciences, and it donors for giving me an opportunity to undertake the Diploma programme, my supervisor, Dr. Diane Wilcox (UCT), for her advice and kindness with reading materials, my fellow col-leagues; special regards to Ikleel, academic and non-academic staff for creating and enabling environment for study. A.I.M.S 2003/04 The limit of the Cox, Ross and Rubinstein formula as the length of time-steps goes to zero is the Black-Scholes formula. In this paper we use the de Moivre Laplace central limit theorem to demonstrate the convergence of option prices in the binomial model to the price given by the latter. We also show the convergence of option prices to the geometric Weiner process which is a pre-assumption of the Black-Scholes model by relating the parameters of the binomial model (up and down return) with the parameters of the log-normal distribution of the stock prices (drift and volatility). In addition, we show that the option price given by the Black-Scholes formula satises the partial differ-ential equation of Black-Scholes using the continuous time limit of the binomial model.
Keyphrases
binomial model continuous time limit option price black-scholes formula african institute diploma programme log-normal distribution special regard geometric weiner process reading material partial differ-ential equation fellow col-leagues diane wilcox moivre laplace central limit theorem stock price non-academic staff mathematical science black-scholes model rubinstein formula
