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Pricing double barrier options using Laplace transforms


  • Antoon Pelsser

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


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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    Cited by:

    1. 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.
    2. 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.
    3. Amirhossein Sobhani & Mariyan Milev, 2017. "A Numerical Method for Pricing Discrete Double Barrier Option by Legendre Multiwavelet," Papers 1703.09129,, revised Mar 2017.
    4. Amirhossein Sobhani & Mariyan Milev, 2017. "A Numerical Method for Pricing Discrete Double Barrier Option by Lagrange Interpolation on Jacobi Node," Papers 1712.01060,, revised Feb 2018.
    5. 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.
    6. 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.
    7. 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.
    8. 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.
    9. José 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.
    10. 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.
    11. Jean-Pierre Fouque & Sebastian Jaimungal & Matthew Lorig, 2010. "Spectral Decomposition of Option Prices in Fast Mean-Reverting Stochastic Volatility Models," Papers 1007.4361,, revised Apr 2012.
    12. Aleksandar Mijatović, 2010. "Local time and the pricing of time-dependent barrier options," Finance and Stochastics, Springer, vol. 14(1), pages 13-48, January.
    13. 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.
    14. J. C. Ndogmo & D. B. Ntwiga, 2007. "High-order accurate implicit methods for the pricing of barrier options," Papers 0710.0069,
    15. Giacomo Bormetti & Giorgia Callegaro & Giulia Livieri & Andrea Pallavicini, 2015. "A backward Monte Carlo approach to exotic option pricing," Papers 1511.00848,
    16. Vanden, Joel M., 2005. "Equilibrium analysis of volatility clustering," Journal of Empirical Finance, Elsevier, vol. 12(3), pages 374-417, June.
    17. 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.

    More about this item


    Option pricing; Laplace transform; contour integration;

    JEL classification:

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


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