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Arbitrage-free market models for option prices: the multi-strike case

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  • Martin Schweizer

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  • Johannes Wissel

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Abstract

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Suggested Citation

  • Martin Schweizer & Johannes Wissel, 2008. "Arbitrage-free market models for option prices: the multi-strike case," Finance and Stochastics, Springer, vol. 12(4), pages 469-505, October.
  • Handle: RePEc:spr:finsto:v:12:y:2008:i:4:p:469-505
    DOI: 10.1007/s00780-008-0068-6
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    References listed on IDEAS

    as
    1. Wissel, Johannes, 2007. "Some results on strong solutions of SDEs with applications to interest rate models," Stochastic Processes and their Applications, Elsevier, vol. 117(6), pages 720-741, June.
    2. Rama Cont & Jose da Fonseca, 2002. "Dynamics of implied volatility surfaces," Quantitative Finance, Taylor & Francis Journals, vol. 2(1), pages 45-60.
    3. Breeden, Douglas T & Litzenberger, Robert H, 1978. "Prices of State-contingent Claims Implicit in Option Prices," The Journal of Business, University of Chicago Press, vol. 51(4), pages 621-651, October.
    4. H. Berestycki & J. Busca & I. Florent, 2002. "Asymptotics and calibration of local volatility models," Quantitative Finance, Taylor & Francis Journals, vol. 2(1), pages 61-69.
    5. Merton, Robert C., 1976. "Option pricing when underlying stock returns are discontinuous," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 125-144.
    6. 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.
    7. Carr, Peter & Madan, Dilip B., 2005. "A note on sufficient conditions for no arbitrage," Finance Research Letters, Elsevier, vol. 2(3), pages 125-130, September.
    8. Brace, Alan & Fabbri, Giorgio & Goldys, Benjamin, 2007. "An Hilbert space approach for a class of arbitrage free implied volatilities models," MPRA Paper 6321, University Library of Munich, Germany.
    9. Ledoit, Olivier & Santa-Clara, Pedro & Yan, Shu, 2002. "Relative Pricing of Options with Stochastic Volatility," University of California at Los Angeles, Anderson Graduate School of Management qt7jp8f42t, Anderson Graduate School of Management, UCLA.
    10. David Heath & Robert Jarrow & Andrew Morton, 2008. "Bond Pricing And The Term Structure Of Interest Rates: A New Methodology For Contingent Claims Valuation," World Scientific Book Chapters,in: Financial Derivatives Pricing Selected Works of Robert Jarrow, chapter 13, pages 277-305 World Scientific Publishing Co. Pte. Ltd..
    11. Martin Schweizer & Johannes Wissel, 2008. "Term Structures Of Implied Volatilities: Absence Of Arbitrage And Existence Results," Mathematical Finance, Wiley Blackwell, vol. 18(1), pages 77-114.
    12. Hull, John C & White, Alan D, 1987. " The Pricing of Options on Assets with Stochastic Volatilities," Journal of Finance, American Finance Association, vol. 42(2), pages 281-300, June.
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    Citations

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    Cited by:

    1. Pietro Siorpaes, 2013. "Optimal investment and price dependence in a semi-static market," Papers 1303.0237, arXiv.org, revised Oct 2013.
    2. Tehranchi, Michael R., 2009. "Symmetric martingales and symmetric smiles," Stochastic Processes and their Applications, Elsevier, vol. 119(10), pages 3785-3797, October.
    3. Anja Richter & Josef Teichmann, 2014. "Discrete Time Term Structure Theory and Consistent Recalibration Models," Papers 1409.1830, arXiv.org.
    4. Sebastian Herrmann & Johannes Muhle-Karbe, 2017. "Model Uncertainty, Recalibration, and the Emergence of Delta-Vega Hedging," Papers 1704.04524, arXiv.org.
    5. Rene Carmona & Yi Ma & Sergey Nadtochiy, 2015. "Simulation of Implied Volatility Surfaces via Tangent Levy Models," Papers 1504.00334, arXiv.org.
    6. Pietro Siorpaes, 2015. "Optimal investment and price dependence in a semi-static market," Finance and Stochastics, Springer, vol. 19(1), pages 161-187, January.
    7. Jan Kallsen & Paul Krühner, 2015. "On a Heath–Jarrow–Morton approach for stock options," Finance and Stochastics, Springer, vol. 19(3), pages 583-615, July.
    8. René Carmona & Sergey Nadtochiy, 2012. "Tangent Lévy market models," Finance and Stochastics, Springer, vol. 16(1), pages 63-104, January.
    9. repec:spr:finsto:v:21:y:2017:i:4:d:10.1007_s00780-017-0342-6 is not listed on IDEAS
    10. Valdo Durrleman, 2010. "From implied to spot volatilities," Finance and Stochastics, Springer, vol. 14(2), pages 157-177, April.
    11. S. Kindermann & P. Mayer, 2011. "On the calibration of local jump-diffusion asset price models," Finance and Stochastics, Springer, vol. 15(4), pages 685-724, December.
    12. Jean Jacod & Philip Protter, 2010. "Risk-neutral compatibility with option prices," Finance and Stochastics, Springer, vol. 14(2), pages 285-315, April.
    13. Henrik Hult & Filip Lindskog & Johan Nykvist, 2013. "A simple time-consistent model for the forward density process," Papers 1301.4869, arXiv.org.

    More about this item

    Keywords

    Option prices; Market model; Implied volatility; Static arbitrage; Dynamic arbitrage; Drift restrictions; Existence result; 60H10; 91B28; C60; G13;

    JEL classification:

    • C60 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - General
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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