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Barrier options

In: Non-Gaussian Merton-Black-Scholes Theory

Author

Listed:
  • Svetlana I. Boyarchenko

    (University of Texas at Austin, USA)

  • Sergei Z. Levendorskiĭ

    (Rostov State University of Economics, Russia)

Abstract

AbstractThe following sections are included:Types of barrier optionsStandard barrier optionsOptions with a rebateDown-and-out call option without a rebateReduction to the boundary problem for the Generalized Black-Scholes equationReduction to the Cauchy problem for an ordinary differential operator with the operator-valued coefficientConstruction of the resolvent, and the Wiener-Hopf factorization with a parameterProof of Eq. (8.17) and continuity of the RHS in Eq. (8.19)Asymptotics of the option price near the barrierCommentary

Suggested Citation

  • Svetlana I. Boyarchenko & Sergei Z. Levendorskiĭ, 2002. "Barrier options," World Scientific Book Chapters,in: Non-Gaussian Merton-Black-Scholes Theory, chapter 8, pages 185-198 World Scientific Publishing Co. Pte. Ltd..
  • Handle: RePEc:wsi:wschap:9789812777485_0008
    as

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    Citations

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    Cited by:

    1. Ernst Eberlein & Kathrin Glau & Antonis Papapantoleon, 2009. "Analyticity of the Wiener-Hopf factors and valuation of exotic options in L\'evy models," Papers 0911.0373, arXiv.org, revised Oct 2010.
    2. N. Reich & C. Schwab & C. Winter, 2010. "On Kolmogorov equations for anisotropic multivariate Lévy processes," Finance and Stochastics, Springer, vol. 14(4), pages 527-567, December.
    3. Jos'e E. Figueroa-L'opez & Peter Tankov, 2012. "Small-time asymptotics of stopped L\'evy bridges and simulation schemes with controlled bias," Papers 1203.2355, arXiv.org, revised Jul 2014.
    4. Sergei Levendorskii, 2002. "Pseudo-diffusions and Quadratic term structure models," Papers cond-mat/0212249, arXiv.org, revised Apr 2004.
    5. Denis Belomestny, 2009. "Spectral estimation of the fractional order of a Lévy process," SFB 649 Discussion Papers SFB649DP2009-021, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.

    More about this item

    Keywords

    Non-Gaussian Models; Merton-Black-Scholes Theory; Levy Processes; American Options; European Options; Feller Processes;

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • A1 - General Economics and Teaching - - General Economics
    • A2 - General Economics and Teaching - - Economic Education and Teaching of Economics
    • E6 - Macroeconomics and Monetary Economics - - Macroeconomic Policy, Macroeconomic Aspects of Public Finance, and General Outlook

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