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Static replications with traffic light options

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  • Michael Schmutz
  • Thomas Zurcher

Abstract

It is well known that any sufficiently regular one-dimensional payoff function has an explicit static hedge by bonds, forward contracts and lots of vanilla options. We show that the natural extension of the corresponding representation leads to a static hedge based on the same instruments along with traffic light options, which have recently been introduced in the market. One big advantage of these replication strategies is the easy structure of the hedge. Hence, traffic light options are particularly powerful building blocks for more complicated bivariate options. While it is well known that the second strike derivative of non-discounted prices of vanilla options are related to the risk-neutral density of the underlying asset price in the corresponding absolutely continuous settings, similar statements hold for traffic light options in sufficiently regular bivariate settings.

Suggested Citation

  • Michael Schmutz & Thomas Zurcher, 2010. "Static replications with traffic light options," Papers 1011.4795, arXiv.org.
    • Handle: RePEc:arx:papers:1011.4795
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    References listed on IDEAS

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    1. Baxter, Martin, 1998. "Hedging in Financial Markets," ASTIN Bulletin, Cambridge University Press, vol. 28(1), pages 5-16, May.
    2. David C. Nachman, 1988. "Spanning and Completeness with Options," The Review of Financial Studies, Society for Financial Studies, vol. 1(3), pages 311-328.
    3. Stephen A. Ross, 1976. "Options and Efficiency," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 90(1), pages 75-89.
    4. Jorgensen, Peter Lochte, 2007. "Traffic light options," Journal of Banking & Finance, Elsevier, vol. 31(12), pages 3698-3719, December.
    5. Ernst Eberlein & Kathrin Glau & Antonis Papapantoleon, 2010. "Analysis of Fourier Transform Valuation Formulas and Applications," Applied Mathematical Finance, Taylor & Francis Journals, vol. 17(3), pages 211-240.
    6. Thomas Kokholm, 2009. "Pricing Of Traffic Light Options And Other Hybrid Products," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 12(05), pages 687-707.
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    Cited by:

    1. Yukihiro Tsuzuki, 2013. "On Optimal Super-Hedging And Sub-Hedging Strategies," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 16(06), pages 1-17.
    2. Thorsten Rheinländer & Jenny Sexton, 2011. "Hedging Derivatives," World Scientific Books, World Scientific Publishing Co. Pte. Ltd., number 8062, December.
    3. Ilya Molchanov & Michael Schmutz, 2009. "Exchangeability type properties of asset prices," Papers 0901.4914, arXiv.org, revised Apr 2011.

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