A Discrete Time Approach for European and American Barrier Options

27 Pages Posted: 24 Apr 1998

See all articles by Matthias Reimer

Matthias Reimer

University of Bonn - Institute of Statistics

Klaus Sandmann

University of Bonn - The Bonn Graduate School of Economics

Date Written: 1995

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.

Keywords: Barrier option, binomial model, limit results

JEL Classification: G13

Suggested Citation

Reimer, Matthias and Sandmann, Klaus, A Discrete Time Approach for European and American Barrier Options (1995). Available at SSRN: https://ssrn.com/abstract=6075 or http://dx.doi.org/10.2139/ssrn.6075

Matthias Reimer (Contact Author)

University of Bonn - Institute of Statistics ( email )

Institut fuer Gesellschafts und Wirtschaftswissenschaften
Bonn, 53113
Germany
+49+228+739271 (Phone)
+49+228+739264 (Fax)

Klaus Sandmann

University of Bonn - The Bonn Graduate School of Economics ( email )

Adenauerallee 24-26
Bonn, D-53113
Germany

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