Affiliation:
1. Department of Mathematics and Statistics, American University of Sharjah, Sharjah, P. O. Box 26666, UAE
2. Department of Mathematics, National Taiwan University, Taipei, Taiwan
Abstract
In the [Formula: see text]-period Cox, Ross, and Rubinstein (CRR) model, we achieve smooth convergence of European vanilla options to their Black–Scholes limits simply by altering the probability at one node, in fact, at the preterminal node between the closest neighbors of the strike in the terminal layer. For barrier options, we do even better, obtaining order [Formula: see text] convergence by altering the probability just at the node nearest the barrier, but only the first time it is hit. First-order smooth convergence for vanilla options was already achieved in Tian’s flexible model but here we show how second order smooth convergence can be achieved by changing one probability, leading to convergence of order [Formula: see text] with Richardson extrapolation. We illustrate our results with examples and provide numerical evidence of our results.
Funder
American University of Sharjah Faculty Research Travel Grant
Publisher
World Scientific Pub Co Pte Lt
Subject
General Economics, Econometrics and Finance,Finance
Cited by
2 articles.
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