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Pricing bounds for discrete arithmetic Asian options under Lévy models

Author

Listed:
  • Lemmens, D.
  • Liang, L.Z.J.
  • Tempere, J.
  • De Schepper, A.

Abstract

Analytical bounds for Asian options are almost exclusively available in the Black–Scholes framework. In this paper we derive bounds for the price of a discretely monitored arithmetic Asian option when the underlying asset follows an arbitrary Lévy process. Explicit formulas are given for Kou’s model, Merton’s model, the normal inverse Gaussian model, the CGMY model and the variance gamma model. The results are compared with the comonotonic upper bound, existing numerical results, Monte carlo simulations and in the case of the variance gamma model with an existing lower bound. The method outlined here provides lower and upper bounds that are quick to evaluate, and more accurate than existing bounds.

Suggested Citation

  • Lemmens, D. & Liang, L.Z.J. & Tempere, J. & De Schepper, A., 2010. "Pricing bounds for discrete arithmetic Asian options under Lévy models," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(22), pages 5193-5207.
    • Handle: RePEc:eee:phsmap:v:389:y:2010:i:22:p:5193-5207
    DOI: 10.1016/j.physa.2010.07.026
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    Cited by:

    1. Alexander Novikov & Nino Kordzakhia, 2013. "On lower and upper bounds for Asian-type options: a unified approach," Papers 1309.2383, arXiv.org.
    2. Gianluca Fusai & Ioannis Kyriakou, 2016. "General Optimized Lower and Upper Bounds for Discrete and Continuous Arithmetic Asian Options," Mathematics of Operations Research, INFORMS, vol. 41(2), pages 531-559, May.
    3. Salazar Celis, Oliver & Liang, Lingzhi & Lemmens, Damiaan & Tempère, Jacques & Cuyt, Annie, 2015. "Determining and benchmarking risk neutral distributions implied from option prices," Applied Mathematics and Computation, Elsevier, vol. 258(C), pages 372-387.
    4. Luca Spadafora & Marco Dubrovich & Marcello Terraneo, 2014. "Value-at-Risk time scaling for long-term risk estimation," Papers 1408.2462, arXiv.org.
    5. Ruggero Caldana & Gianluca Fusai & Alessandro Gnoatto & Martino Grasselli, 2016. "General closed-form basket option pricing bounds," Quantitative Finance, Taylor & Francis Journals, vol. 16(4), pages 535-554, April.
    6. Pingping Zeng & Yue Kuen Kwok, 2016. "Pricing bounds and approximations for discrete arithmetic Asian options under time-changed Lévy processes," Quantitative Finance, Taylor & Francis Journals, vol. 16(9), pages 1375-1391, September.
    7. Geon Ho Choe & Minseok Kim, 2021. "Closed‐form lower bounds for the price of arithmetic average Asian options by multiple conditioning," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 41(12), pages 1916-1932, December.
    8. Alexander Novikov & Scott Alexander & Nino Kordzakhia & Timothy Ling, 2016. "Pricing of Asian-type and Basket Options via Upper and Lower Bounds," Papers 1612.08767, arXiv.org.

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