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Pricing exotic derivatives exploiting structure

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  • Sesana, Debora
  • Marazzina, Daniele
  • Fusai, Gianluca

Abstract

In this paper we introduce a new fast and accurate numerical method for pricing exotic derivatives when discrete monitoring occurs, and the underlying evolves according to a Markov one-dimensional stochastic processes. The approach exploits the structure of the matrix arising from the numerical quadrature of the pricing backward formulas to devise a convenient factorization that helps greatly in the speed-up of the recursion. The algorithm is general and is examined in detail with reference to the CEV (Constant Elasticity of Variance) process for pricing different exotic derivatives, such as Asian, barrier, Bermudan, lookback and step options for which up to date no efficient procedures are available. Extensive numerical experiments confirm the theoretical results. The MATLAB code used to perform the computation is available online at http://www1.mate.polimi.it/∼marazzina/BP.htm.

Suggested Citation

  • Sesana, Debora & Marazzina, Daniele & Fusai, Gianluca, 2014. "Pricing exotic derivatives exploiting structure," European Journal of Operational Research, Elsevier, vol. 236(1), pages 369-381.
    • Handle: RePEc:eee:ejores:v:236:y:2014:i:1:p:369-381
    DOI: 10.1016/j.ejor.2013.12.009
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    5. S. Corsaro & D. Marazzina & Z. Marino, 2015. "A parallel wavelet-based pricing procedure for Asian options," Quantitative Finance, Taylor & Francis Journals, vol. 15(1), pages 101-113, January.
    6. Fusai, Gianluca & Germano, Guido & Marazzina, Daniele, 2016. "Spitzer identity, Wiener-Hopf factorization and pricing of discretely monitored exotic options," European Journal of Operational Research, Elsevier, vol. 251(1), pages 124-134.
    7. Ning Cai & Yingda Song & Steven Kou, 2015. "A General Framework for Pricing Asian Options Under Markov Processes," Operations Research, INFORMS, vol. 63(3), pages 540-554, June.
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    9. Oleg L. Kritski & Vladimir F. Zalmezh, 2017. "Asymptotics for Greeks under the constant elasticity of variance model," Papers 1707.04149, arXiv.org, revised Jul 2017.
    10. Detemple, Jérôme & Laminou Abdou, Souleymane & Moraux, Franck, 2020. "American step options," European Journal of Operational Research, Elsevier, vol. 282(1), pages 363-385.
    11. Cui, Zhenyu & Lee, Chihoon & Liu, Yanchu, 2018. "Single-transform formulas for pricing Asian options in a general approximation framework under Markov processes," European Journal of Operational Research, Elsevier, vol. 266(3), pages 1134-1139.
    12. Kontosakos, Vasileios E. & Mendonca, Keegan & Pantelous, Athanasios A. & Zuev, Konstantin M., 2021. "Pricing discretely-monitored double barrier options with small probabilities of execution," European Journal of Operational Research, Elsevier, vol. 290(1), pages 313-330.
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