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Two Exotic Lookback Options

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  • Hans-Peter Bermin
  • Peter Buchen
  • Otto Konstandatos

Abstract

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.

Suggested Citation

  • Hans-Peter Bermin & Peter Buchen & Otto Konstandatos, 2008. "Two Exotic Lookback Options," Applied Mathematical Finance, Taylor & Francis Journals, vol. 15(4), pages 387-402.
    • Handle: RePEc:taf:apmtfi:v:15:y:2008:i:4:p:387-402
    DOI: 10.1080/13504860802012824
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    References listed on IDEAS

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    1. Robert C. Merton, 2005. "Theory of rational option pricing," World Scientific Book Chapters, in: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 8, pages 229-288, World Scientific Publishing Co. Pte. Ltd..
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    5. Peter Buchen & Otto Konstandatos, 2005. "A New Method Of Pricing Lookback Options," Mathematical Finance, Wiley Blackwell, vol. 15(2), pages 245-259, April.
    6. 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 401-413, May.
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    Cited by:

    1. Konstandatos, Otto, 2020. "Fair-value analytical valuation of reset executive stock options consistent with IFRS9 requirements," Annals of Actuarial Science, Cambridge University Press, vol. 14(1), pages 188-218, March.
    2. Kim, Geonwoo & Jeon, Junkee, 2018. "Closed-form solutions for valuing partial lookback options with random initiation," Finance Research Letters, Elsevier, vol. 24(C), pages 321-327.
    3. Peter Buchen & Otto Konstandatos, 2009. "A New Approach to Pricing Double-Barrier Options with Arbitrary Payoffs and Exponential Boundaries," Applied Mathematical Finance, Taylor & Francis Journals, vol. 16(6), pages 497-515.
    4. Lee, Hangsuck & Kim, Eunchae & Ko, Bangwon, 2022. "Valuing lookback options with barrier," The North American Journal of Economics and Finance, Elsevier, vol. 60(C).

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