A Closer Look at Barrier Exchange Options

Authors

  • Christine A. Brown,

    1. Christine A. Brown is a Professor of Finance at the Department of Accounting and Finance, Monash University, Victoria, Australia
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  • John C. Handley,

    Corresponding author
    1. John C. Handley is an Associate Professor of Finance at the Department of Finance, University of Melbourne, Melbourne, Victoria, Australia
    • Christine A. Brown is a Professor of Finance at the Department of Accounting and Finance, Monash University, Victoria, Australia
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  • Ken Palmer

    1. Ken Palmer is a Professor of Mathematics at the Department of Financial and Computational Mathematics, Providence University, Taichung, Taiwan and an Adjunct Professor of Mathematics at the Department of Mathematics, National Taiwan University, Taipei, Taiwan
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  • Valuable comments from Michael Chng, Spencer Martin, Steve Easton, seminar participants at Deakin University, University of Melbourne, University of Newcastle and especially the referee are gratefully acknowledged.

Correspondence author, Department of Finance, University of Melbourne, Melbourne, VIC 3010, Australia. Tel: 61383447663, e-mail: handleyj@unimelb.edu.au.

Abstract

A barrier exchange option is an exchange option that is knocked out the first time the prices of two underlying assets become equal. Lindset, S., & Persson, S.-A. (2006) present a simple dynamic replication argument to show that, in the absence of arbitrage, the current value of the barrier exchange option is equal to the difference in the current prices of the underlying assets and that this pricing formula applies irrespective of whether the option is European or American. In this study, we take a closer look at barrier exchange options and show, despite the simplicity of the pricing formula presented by Lindset, S., & Persson, S.-A. (2006), that the barrier exchange option in fact involves a surprising array of key concepts associated with the pricing of derivative securities including: put–call parity, barrier in–out parity, static vs. dynamic replication, martingale pricing, continuous vs. discontinuous price processes, and numeraires. We provide valuable intuition behind the pricing formula which explains its apparent simplicity. © 2011 Wiley Periodicals, Inc. Jrl Fut Mark 33:29–43, 2013

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