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Pricing discrete double barrier options under Lévy processes: An extension of the method by Milev and Tagliani

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  • Xiao, Shuang
  • Ma, Shihua

Abstract

We investigate pricing issue of discrete-double barrier options under Lévy processes. We first derive an analytical pricing formula, which is no longer applicable when the monitoring frequency becomes large. Therefore, we present a numerical algorithm based on the idea of using discrete variables to approximate continuous ones initiated by Milev and Tagliani (2010) and utilizing adaptive Gauss–Lobatto quadrature with five points to address the integration problem. The method applies for all types of Lévy processes whose probability density function of the increment is available in closed form. Numerical experiments confirm that our algorithm is both effective and efficient.

Suggested Citation

  • Xiao, Shuang & Ma, Shihua, 2016. "Pricing discrete double barrier options under Lévy processes: An extension of the method by Milev and Tagliani," Finance Research Letters, Elsevier, vol. 19(C), pages 67-74.
    • Handle: RePEc:eee:finlet:v:19:y:2016:i:c:p:67-74
    DOI: 10.1016/j.frl.2016.06.004
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    References listed on IDEAS

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    1. Fajardo, José, 2015. "Barrier style contracts under Lévy processes: An alternative approach," Journal of Banking & Finance, Elsevier, vol. 53(C), pages 179-187.
    2. M. Broadie & Y. Yamamoto, 2005. "A Double-Exponential Fast Gauss Transform Algorithm for Pricing Discrete Path-Dependent Options," Operations Research, INFORMS, vol. 53(5), pages 764-779, October.
    3. Ornthanalai, Chayawat, 2014. "Lévy jump risk: Evidence from options and returns," Journal of Financial Economics, Elsevier, vol. 112(1), pages 69-90.
    4. Hsu, Pao-Peng & Chen, Ying-Hsiu, 2012. "Barrier option pricing for exchange rates under the Levy–HJM processes," Finance Research Letters, Elsevier, vol. 9(3), pages 176-181.
    5. Sam Howison & Mario Steinberg, 2007. "A Matched Asymptotic Expansions Approach to Continuity Corrections for Discretely Sampled Options. Part 1: Barrier Options," Applied Mathematical Finance, Taylor & Francis Journals, vol. 14(1), pages 63-89.
    6. Liming Feng & Vadim Linetsky, 2008. "Pricing Discretely Monitored Barrier Options And Defaultable Bonds In Lévy Process Models: A Fast Hilbert Transform Approach," Mathematical Finance, Wiley Blackwell, vol. 18(3), pages 337-384, July.
    7. A. Golbabai & L. Ballestra & D. Ahmadian, 2014. "A Highly Accurate Finite Element Method to Price Discrete Double Barrier Options," Computational Economics, Springer;Society for Computational Economics, vol. 44(2), pages 153-173, August.
    8. Sam Howison, 2007. "A Matched Asymptotic Expansions Approach to Continuity Corrections for Discretely Sampled Options. Part 2: Bermudan Options," Applied Mathematical Finance, Taylor & Francis Journals, vol. 14(1), pages 91-104.
    9. Kleinert, Florian & van Schaik, Kees, 2015. "A variation of the Canadisation algorithm for the pricing of American options driven by Lévy processes," Stochastic Processes and their Applications, Elsevier, vol. 125(8), pages 3234-3254.
    10. Dingeç, Kemal Dinçer & Hörmann, Wolfgang, 2012. "A general control variate method for option pricing under Lévy processes," European Journal of Operational Research, Elsevier, vol. 221(2), pages 368-377.
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    Cited by:

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    2. Braouezec, Yann, 2017. "How fundamental is the one-period trinomial model to European option pricing bounds. A new methodological approach," Finance Research Letters, Elsevier, vol. 21(C), pages 92-99.
    3. Lee, Hangsuck & Jeong, Himchan & Lee, Minha, 2022. "Multi-step double barrier options," Finance Research Letters, Elsevier, vol. 47(PA).

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    More about this item

    Keywords

    European option pricing; Discrete double-barrier option; Lévy process; Milev and Tagliani algorithm; Adaptive Gauss–Lobatto quadrature;
    All these keywords.

    JEL classification:

    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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