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Continuity correction: on the pricing of discrete double barrier options

Author

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  • Sheng-Feng Luo

    (Chung Yuan Christian University)

  • Hsin-Chieh Wong

    (National Taipei University)

Abstract

This article deals with the pricing of double-barrier options monitored discretely. A continuity correction method is established to provide an analytical approximation for the price of such discrete options under the Black–Scholes model. We achieve this by applying the smooth-fit principle simultaneously to the two flat boundaries (barriers) associated. The resulting correction form still involves adjustments in the levels of barriers, but the amounts adjusted can be different for different boundaries. More interestingly, the shift for each boundary can also be in different directions, which depends largely on the position of the current level relative to the two boundaries. Numerical examples are provided as well which support our theoretical achievements.

Suggested Citation

  • Sheng-Feng Luo & Hsin-Chieh Wong, 2023. "Continuity correction: on the pricing of discrete double barrier options," Review of Derivatives Research, Springer, vol. 26(1), pages 51-90, April.
    • Handle: RePEc:kap:revdev:v:26:y:2023:i:1:d:10.1007_s11147-022-09193-z
    DOI: 10.1007/s11147-022-09193-z
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    References listed on IDEAS

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    1. Lian, Guanghua & Zhu, Song-Ping & Elliott, Robert J. & Cui, Zhenyu, 2017. "Semi-analytical valuation for discrete barrier options under time-dependent Lévy processes," Journal of Banking & Finance, Elsevier, vol. 75(C), pages 167-183.
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    4. 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.
    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.
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    Cited by:

    1. Guillaume Leduc, 2024. "The Boyle–Romberg Trinomial Tree, a Highly Efficient Method for Double Barrier Option Pricing," Mathematics, MDPI, vol. 12(7), pages 1-15, March.

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    More about this item

    Keywords

    Discrete option pricing; Double barrier option; Continuity correction; Principle of smooth fit; Overshoot;
    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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