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Semi-analytical prices for lookback and barrier options under the Heston model

Author

Listed:
  • Luca De Gennaro Aquino

    (Université Grenoble Alpes ComUE)

  • Carole Bernard

    (Université Grenoble Alpes ComUE
    Vrije Universiteit Brussel (VUB))

Abstract

Under the Heston stochastic volatility model, we derive semi-analytical formulas for the prices of path-dependent options with payoffs linked to the maximum or minimum value of the underlying asset price over a certain period of time. In particular, we obtain prices of lookback and barrier options in the Heston model, but the methodology applies more generally. By conditioning with respect to the variance path, we obtain pricing formulas that can be related to their counterparts in the Black–Scholes model.

Suggested Citation

  • Luca De Gennaro Aquino & Carole Bernard, 2019. "Semi-analytical prices for lookback and barrier options under the Heston model," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 42(2), pages 715-741, December.
    • Handle: RePEc:spr:decfin:v:42:y:2019:i:2:d:10.1007_s10203-019-00254-x
    DOI: 10.1007/s10203-019-00254-x
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    References listed on IDEAS

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    5. Wong, Hoi Ying & Chan, Chun Man, 2007. "Lookback options and dynamic fund protection under multiscale stochastic volatility," Insurance: Mathematics and Economics, Elsevier, vol. 40(3), pages 357-385, May.
    6. Anthonie W. Van Der Stoep & Lech A. Grzelak & Cornelis W. Oosterlee, 2014. "The Heston Stochastic-Local Volatility Model: Efficient Monte Carlo Simulation," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 17(07), pages 1-30.
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    11. Phelan, Carolyn E. & Marazzina, Daniele & Fusai, Gianluca & Germano, Guido, 2018. "Fluctuation identities with continuous monitoring and their application to the pricing of barrier options," European Journal of Operational Research, Elsevier, vol. 271(1), pages 210-223.
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    Cited by:

    1. P. Carr & A. Itkin & D. Muravey, 2022. "Semi-analytical pricing of barrier options in the time-dependent Heston model," Papers 2202.06177, arXiv.org.
    2. Elisa Alòs & Maria Elvira Mancino & Tai-Ho Wang, 2019. "Volatility and volatility-linked derivatives: estimation, modeling, and pricing," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 42(2), pages 321-349, December.
    3. Lazar, Emese & Qi, Shuyuan, 2022. "Model risk in the over-the-counter market," European Journal of Operational Research, Elsevier, vol. 298(2), pages 769-784.
    4. Alexander Lipton & Artur Sepp, 2022. "Toward an efficient hybrid method for pricing barrier options on assets with stochastic volatility," Papers 2202.07849, arXiv.org.
    5. Cai, Ning & Li, Chenxu & Shi, Chao, 2021. "Pricing discretely monitored barrier options: When Malliavin calculus expansions meet Hilbert transforms," Journal of Economic Dynamics and Control, Elsevier, vol. 127(C).

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    More about this item

    Keywords

    Derivatives pricing; Lookback options; Barrier options; Path-dependent options; Heston model; Stochastic volatility;
    All these keywords.

    JEL classification:

    • C65 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Miscellaneous Mathematical Tools
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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