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Static Hedging Of Barrier Options With A Smile: An Inverse Problem

Author

Listed:
  • Claude Bardos

    (LJLL - Laboratoire Jacques-Louis Lions - UPMC - Université Pierre et Marie Curie - Paris 6 - UPD7 - Université Paris Diderot - Paris 7 - CNRS - Centre National de la Recherche Scientifique)

  • Raphaël Douady

    (CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique)

  • Andrei Fursikov

    (Moscow State University)

Abstract

Let L be a parabolic second order differential operator on the domain ¯ Π = [0, T ] × ℝ. Given a function û : ℝ → R and ^x > 0 such that the support of of û is contained in (−∞, −ˆx], we let ˆy : ¯ Π → Ê be the solution to the equation: Lˆy= 0, ^ y| {0}× ℝ = û. Given positive bounds 0

Suggested Citation

  • Claude Bardos & Raphaël Douady & Andrei Fursikov, 2002. "Static Hedging Of Barrier Options With A Smile: An Inverse Problem," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-01477102, HAL.
    • Handle: RePEc:hal:cesptp:hal-01477102
    DOI: 10.1051/cocv:2002040
    Note: View the original document on HAL open archive server: https://hal.science/hal-01477102
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    References listed on IDEAS

    as
    1. Raphael Douady, 1999. "Closed Form Formulas For Exotic Options And Their Lifetime Distribution," World Scientific Book Chapters, in: Marco Avellaneda (ed.), Quantitative Analysis In Financial Markets Collected Papers of the New York University Mathematical Finance Seminar, chapter 6, pages 177-202, World Scientific Publishing Co. Pte. Ltd..
    2. Claude Bardos & Raphaël Douady & Andrei Fursikov, 2002. "Static Hedging Of Barrier Options With A Smile: An Inverse Problem," Post-Print hal-01477102, HAL.
    3. 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..
    4. David G. Hobson, 1998. "Robust hedging of the lookback option," Finance and Stochastics, Springer, vol. 2(4), pages 329-347.
    5. Peter Carr & Katrina Ellis & Vishal Gupta, 1998. "Static Hedging of Exotic Options," Journal of Finance, American Finance Association, vol. 53(3), pages 1165-1190, June.
    6. Gregory Koutmos, 1999. "Financial risk management: dynamic versus static hedging," Global Business and Economics Review, Inderscience Enterprises Ltd, vol. 1(1), pages 60-75.
    7. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
    8. Marco Avellaneda & Antonio ParAS, 1996. "Managing the volatility risk of portfolios of derivative securities: the Lagrangian uncertain volatility model," Applied Mathematical Finance, Taylor & Francis Journals, vol. 3(1), pages 21-52.
    9. Emanuel Derman & Iraj Kani, 1998. "Stochastic Implied Trees: Arbitrage Pricing with Stochastic Term and Strike Structure of Volatility," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 1(01), pages 61-110.
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    Cited by:

    1. Claude Bardos & Raphaël Douady & Andrei Fursikov, 2002. "Static Hedging Of Barrier Options With A Smile: An Inverse Problem," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-01477102, HAL.
    2. Priyanka Vashisht, 2012. "Ratio Spread with Calls- Creating a Zero Downside Risk Strategy in Stock Market," Acta Universitatis Danubius. OEconomica, Danubius University of Galati, issue 2(2), pages 48-60, April.
    3. Tim Leung & Matthew Lorig, 2016. "Optimal static quadratic hedging," Quantitative Finance, Taylor & Francis Journals, vol. 16(9), pages 1341-1355, September.

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    Keywords

    Barrier options; inverse problem;

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