Option Replication in Discrete Time with Transaction Costs




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    • Harry A. Brandt, Visiting Professor, Department of Finance, College of Commerce, University of Illinois at Urbana-champaign, 340 Commerce-West, 1206 South Sixth Street, Champaign, Illinois 61820, and Professor of Mathematical Economics, Econometric Institute, Erasmus University Rotterdam, P.O. Box 1738, 3000 DR Rotterdam, The Netherlands, respectively. The authors are grateful to Antoon Pelsser, Jeroen de Munnik, Lijiang Fang, and Ruth Cornale for research assistance and to Philippe Artzner, Giovanni Barone-Adesi, Fischer Black, John E. Gilster Jr., D. C. Heath, Eric Reiner, and Stuart Turnbull for helpful suggestions. The authors thank the referee for useful comments. P. P. B. acknowledges research support from Erasmus University, the J. Page R. Wadsworth Chair at the University of Waterloo, and the Natural Sciences and Engineering Research Council of Canada.


Option replication is discussed in a discrete-time framework with transaction costs. The model represents an extension of the Cox-Ross-Rubinstein binomial option pricing model to cover the case of proportional transaction costs. The method proceeds by constructing the appropriate replicating portfolio at each trading interval. Numerical values of these prices are presented for a range of parameter values. The paper derives a simple Black-Scholes type approximation for the option prices with transaction costs and demonstrates numerically that it is quite accurate for plausible parameter values.