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Semi-analytic pricing of double barrier options with time-dependent barriers and rebates at hit

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  • Andrey Itkin
  • Dmitry Muravey

Abstract

We continue a series of papers devoted to construction of semi-analytic solutions for barrier options. These options are written on underlying following some simple one-factor diffusion model, but all the parameters of the model as well as the barriers are time-dependent. We managed to show that these solutions are systematically more efficient for pricing and calibration than, eg., the corresponding finite-difference solvers. In this paper we extend this technique to pricing double barrier options and present two approaches to solving it: the General Integral transform method and the Heat Potential method. Our results confirm that for double barrier options these semi-analytic techniques are also more efficient than the traditional numerical methods used to solve this type of problems.

Suggested Citation

  • Andrey Itkin & Dmitry Muravey, 2020. "Semi-analytic pricing of double barrier options with time-dependent barriers and rebates at hit," Papers 2009.09342, arXiv.org, revised Oct 2020.
    • Handle: RePEc:arx:papers:2009.09342
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    References listed on IDEAS

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    1. A. Itkin & A. Lipton & D. Muravey, 2020. "From the Black-Karasinski to the Verhulst model to accommodate the unconventional Fed's policy," Papers 2006.11976, arXiv.org, revised Jan 2021.
    2. Alexander Lipton & Vadim Kaushansky, 2018. "On the First Hitting Time Density of an Ornstein-Uhlenbeck Process," Papers 1810.02390, arXiv.org, revised Oct 2018.
    3. Peter Carr & Andrey Itkin & Dmitry Muravey, 2020. "Semi-closed form prices of barrier options in the time-dependent CEV and CIR models," Papers 2005.05459, arXiv.org.
    4. Peter Carr & Andrey Itkin, 2020. "Semi-closed form solutions for barrier and American options written on a time-dependent Ornstein Uhlenbeck process," Papers 2003.08853, arXiv.org, revised Mar 2020.
    5. Andrey Itkin & Dmitry Muravey, 2020. "Semi-closed form prices of barrier options in the Hull-White model," Papers 2004.09591, arXiv.org, revised Sep 2020.
    6. Alexander Lipton & Marcos Lopez de Prado, 2020. "A closed-form solution for optimal mean-reverting trading strategies," Papers 2003.10502, arXiv.org.
    7. Aleksandar Mijatović, 2010. "Local time and the pricing of time-dependent barrier options," Finance and Stochastics, Springer, vol. 14(1), pages 13-48, January.
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    Cited by:

    1. A. Itkin & A. Lipton & D. Muravey, 2021. "Multilayer heat equations: application to finance," Papers 2102.08338, arXiv.org.

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