Static Hedging with Traffic Light Options

Authors

  • Michael Schmutz,

    Corresponding author
    1. Dr. Michael Schmutz is at the Department of Mathematical Statistics and Actuarial Science, University of Bern, Bern, Switzerland
    • Correspondence author, Department of Mathematical Statistics and Actuarial Science, University of Bern, Sidlerstrasse 5, Bern 3012, Switzerland. Tel: +41(0)31 631 88 18, Fax: +41(0)31 631 38 70, e-mail: michael.schmutz@stat.unibe.ch

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  • Thomas Zürcher

    1. Dr. Thomas Zürcher is at the Department of Mathematics and Statistics, University of Jyväskylä, Jyväskylä, Finland. A large part of the research was done when he was a postdoc at the Mathematical Institute, University of Bern
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  • The authors are grateful to Rolf Burgermeister and Markus Liechti for useful hints from practice, to Peter L. Jørgensen, Thomas Kokholm, Thorsten Rheinländer, and an anonymous referee for theoretical hints, to Gabriel Maresch and Christoph Haberl for very helpful discussions, and to Peter Carr for drawing our attention to the problematics in this area. Our final special thanks go out to Ilya Molchanov for his support in all areas.

Abstract

It is well known that sufficiently regular, one-dimensional payoff functions have an explicit static hedge by bonds, forward contracts, and options in a continuum of strikes. An easy and natural extension of the corresponding representation leads to static hedges based on the same instruments along with traffic light options, which have recently been introduced in the market. It is well known that the second strike derivative of non-discounted prices of vanilla options is 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. © 2013 Wiley Periodicals, Inc. Jrl Fut Mark 34:690–702, 2014

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