SFB 303 Discussion Paper No. B-272

Author: Sandmann, K., and M. Reimer

Title: A Discrete Time Approach for European and American Barrier Options

Abstract: The extension of the Black-Scholes option pricing theory to the valuation of barrier options is reconsidered. Working in the binomial framework of CRR we show how various types of barrier options can be priced either by backward induction or by closed binomial formulas. We also consider analytically and numerically the convergence of the prices in discrete time to their continuous-time limits. The arising numerical problems are solved by quadratic interpolation. Furthermore, the case of American barrier options is analyzed in detail. For American barrier call options, binomial formulae and their limit results are given. Finally, the binomial approach is applied to contracts with local and partial barrier checks.(Completely revised version march 1995)

Keywords: Arbitrage, Barrier Option, Option Pricing, Pathment payoff

JEL-Classification-Number: G13

Creation-Date: March 1995
URL: ../1995/b/bonnsfb272.pdf

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