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Two Exotic Lookback Options

  • Hans-Peter Bermin
  • Peter Buchen
  • Otto Konstandatos

This paper formally analyses two exotic options with lookback features, referred to as extreme spread lookback options and look-barrier options, first introduced by Bermin. The holder of such options receives partial protection from large price movements in the underlying, but at roughly the cost of a plain vanilla contract. This is achieved by increasing the leverage through either floating the strike price (for the case of extreme spread options) or introducing a partial barrier window (for the case of look-barrier options). We show how to statically replicate the prices of these hybrid exotic derivatives with more elementary European binary options and their images, using new methods first introduced by Buchen and Konstandatos. These methods allow considerable simplification in the analysis, leading to closed-form representations in the Black-Scholes framework.

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Article provided by Taylor & Francis Journals in its journal Applied Mathematical Finance.

Volume (Year): 15 (2008)
Issue (Month): 4 ()
Pages: 387-402

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Handle: RePEc:taf:apmtfi:v:15:y:2008:i:4:p:387-402
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  1. Goldman, M Barry & Sosin, Howard B & Gatto, Mary Ann, 1979. "Path Dependent Options: "Buy at the Low, Sell at the High"," Journal of Finance, American Finance Association, vol. 34(5), pages 1111-27, December.
  2. Goldman, M Barry & Sosin, Howard B & Shepp, Lawrence A, 1979. "On Contingent Claims That Insure Ex-post Optimal Stock Market Timing," Journal of Finance, American Finance Association, vol. 34(2), pages 401-13, May.
  3. Robert C. Merton, 1973. "Theory of Rational Option Pricing," Bell Journal of Economics, The RAND Corporation, vol. 4(1), pages 141-183, Spring.
  4. Peter Buchen, 2004. "The pricing of dual-expiry exotics," Quantitative Finance, Taylor & Francis Journals, vol. 4(1), pages 101-108.
  5. Peter Buchen & Otto Konstandatos, 2005. "A New Method Of Pricing Lookback Options," Mathematical Finance, Wiley Blackwell, vol. 15(2), pages 245-259.
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