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Pricing double barrier options using Laplace transforms

Author

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  • Antoon Pelsser

    (ABN-Amro Bank, Structured Products Group , P.O.Box 283 1000 EA Amsterdam, The Netherlands (Tel:)

Abstract

In this paper we address the pricing of double barrier options. To derive the density function of the first-hit times of the barriers, we analytically invert the Laplace transform by contour integration. With these barrier densities, we derive pricing formulÖfor new types of barrier options: knock-out barrier options which pay a rebate when either one of the barriers is hit. Furthermore we discuss more complicated types of barrier options like double knock-in options.

Suggested Citation

  • Antoon Pelsser, 2000. "Pricing double barrier options using Laplace transforms," Finance and Stochastics, Springer, vol. 4(1), pages 95-104.
    • Handle: RePEc:spr:finsto:v:4:y:2000:i:1:p:95-104
    Note: received: August 1997; final version received: October 1998
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    Citations

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    Cited by:

    1. Jun, Doobae & Ku, Hyejin, 2015. "Static hedging of chained-type barrier options," The North American Journal of Economics and Finance, Elsevier, vol. 33(C), pages 317-327.
    2. Aleksandar Mijatović, 2010. "Local time and the pricing of time-dependent barrier options," Finance and Stochastics, Springer, vol. 14(1), pages 13-48, January.
    3. Igor V. Kravchenko & Vladislav V. Kravchenko & Sergii M. Torba & Jos'e Carlos Dias, 2017. "Pricing double barrier options on homogeneous diffusions: a Neumann series of Bessel functions representation," Papers 1712.08247, arXiv.org.
    4. Jos� Carlos Dias & João Pedro Vidal Nunes & João Pedro Ruas, 2015. "Pricing and static hedging of European-style double barrier options under the jump to default extended CEV model," Quantitative Finance, Taylor & Francis Journals, vol. 15(12), pages 1995-2010, December.
    5. Rahman Farnoosh & Hamidreza Rezazadeh & Amirhossein Sobhani & M. Hossein Beheshti, 2016. "A Numerical Method for Discrete Single Barrier Option Pricing with Time-Dependent Parameters," Computational Economics, Springer;Society for Computational Economics, vol. 48(1), pages 131-145, June.
    6. Shiyu Song & Yongjin Wang, 2017. "Pricing double barrier options under a volatility regime-switching model with psychological barriers," Review of Derivatives Research, Springer, vol. 20(3), pages 255-280, October.
    7. Hardy Hulley & Eckhard Platen, 2007. "Laplace Transform Identities for Diffusions, with Applications to Rebates and Barrier Options," Research Paper Series 203, Quantitative Finance Research Centre, University of Technology, Sydney.
    8. Andrew Ming-Long Wang & Yu-Hong Liu & Yi-Long Hsiao, 2009. "Barrier option pricing: a hybrid method approach," Quantitative Finance, Taylor & Francis Journals, vol. 9(3), pages 341-352.
    9. C. Atkinson & S. Kazantzaki, 2009. "Double knock-out Asian barrier options which widen or contract as they approach maturity," Quantitative Finance, Taylor & Francis Journals, vol. 9(3), pages 329-340.
    10. Giacomo Bormetti & Giorgia Callegaro & Giulia Livieri & Andrea Pallavicini, 2015. "A backward Monte Carlo approach to exotic option pricing," Papers 1511.00848, arXiv.org.
    11. Amirhossein Sobhani & Mariyan Milev, 2017. "A Numerical Method for Pricing Discrete Double Barrier Option by Lagrange Interpolation on Jacobi Node," Papers 1712.01060, arXiv.org, revised Feb 2018.
    12. Marcos Escobar & Peter Hieber & Matthias Scherer, 2014. "Efficiently pricing double barrier derivatives in stochastic volatility models," Review of Derivatives Research, Springer, vol. 17(2), pages 191-216, July.
    13. Choe, Geon Ho & Koo, Ki Hwan, 2014. "Probability of multiple crossings and pricing of double barrier options," The North American Journal of Economics and Finance, Elsevier, vol. 29(C), pages 156-184.
    14. Feng, Yun & Huang, Bing-hua & Young, Martin & Zhou, Qi-yuan, 2015. "Decomposing and valuing convertible bonds: A new method based on exotic options," Economic Modelling, Elsevier, vol. 47(C), pages 193-206.
    15. Amirhossein Sobhani & Mariyan Milev, 2017. "A Numerical Method for Pricing Discrete Double Barrier Option by Legendre Multiwavelet," Papers 1703.09129, arXiv.org, revised Mar 2017.
    16. J. C. Ndogmo & D. B. Ntwiga, 2007. "High-order accurate implicit methods for the pricing of barrier options," Papers 0710.0069, arXiv.org.
    17. Jean-Pierre Fouque & Sebastian Jaimungal & Matthew Lorig, 2010. "Spectral Decomposition of Option Prices in Fast Mean-Reverting Stochastic Volatility Models," Papers 1007.4361, arXiv.org, revised Apr 2012.
    18. Bernard, Carole & Le Courtois, Olivier & Quittard-Pinon, François, 2008. "Pricing derivatives with barriers in a stochastic interest rate environment," Journal of Economic Dynamics and Control, Elsevier, vol. 32(9), pages 2903-2938, September.
    19. Vanden, Joel M., 2005. "Equilibrium analysis of volatility clustering," Journal of Empirical Finance, Elsevier, vol. 12(3), pages 374-417, June.

    More about this item

    Keywords

    Option pricing; Laplace transform; contour integration;
    All these keywords.

    JEL classification:

    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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