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Revisiting the Greeks for European and American Options

In: Stochastic Processes And Applications To Mathematical Finance

Author

Listed:
  • Emmanuel Gobet

    (Ecole Polytechnique, Centre de Mathématiques Appliquées, 91128 Palaiseau Cedex, France)

Abstract

In this paper, we address the problem of the Greeks' evaluation for European and American options, when the model is defined by a general stochastic differential equation. We represent the Greeks as expectations, in order to allow their computations using Monte Carlo simulations. We avoid the use of Malliavin calculus techniques since in general, it leads to random variables whose simulations are costly in terms of computational time. We take advantage of the Markovian structure to derive simple formulas in a great generality. Moreover, they appear to be efficient in practice.

Suggested Citation

  • Emmanuel Gobet, 2004. "Revisiting the Greeks for European and American Options," World Scientific Book Chapters, in: Jiro Akahori & Shigeyoshi Ogawa & Shinzo Watanabe (ed.), Stochastic Processes And Applications To Mathematical Finance, chapter 3, pages 53-71, World Scientific Publishing Co. Pte. Ltd..
    • Handle: RePEc:wsi:wschap:9789812702852_0003
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    Citations

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    Cited by:

    1. Kloeden Peter E. & Sanz-Chacón Carlos, 2011. "Efficient price sensitivity estimation of financial derivatives by weak derivatives," Monte Carlo Methods and Applications, De Gruyter, vol. 17(1), pages 47-75, January.
    2. Ankush Agarwal & Stefano de Marco & Emmanuel Gobet & Gang Liu, 2017. "Rare event simulation related to financial risks: efficient estimation and sensitivity analysis," Working Papers hal-01219616, HAL.
    3. Jazaerli, Samy & F. Saporito, Yuri, 2017. "Functional Itô calculus, path-dependence and the computation of Greeks," Stochastic Processes and their Applications, Elsevier, vol. 127(12), pages 3997-4028.
    4. E. Benhamou & E. Gobet & M. Miri, 2009. "Smart expansion and fast calibration for jump diffusions," Finance and Stochastics, Springer, vol. 13(4), pages 563-589, September.
    5. Agarwal, Ankush & Claisse, Julien, 2020. "Branching diffusion representation of semi-linear elliptic PDEs and estimation using Monte Carlo method," Stochastic Processes and their Applications, Elsevier, vol. 130(8), pages 5006-5036.
    6. Samy Jazaerli & Yuri F. Saporito, 2013. "Functional Ito Calculus, Path-dependence and the Computation of Greeks," Papers 1311.3881, arXiv.org, revised Jun 2018.
    7. Emmanuel Gobet, 2009. "Advanced Monte Carlo methods for barrier and related exotic options," Post-Print hal-00319947, HAL.
    8. Jean-François Chassagneux & Romuald Elie & Idris Kharroubi, 2015. "When terminal facelift enforces delta constraints," Finance and Stochastics, Springer, vol. 19(2), pages 329-362, April.
    9. Joshi, Mark & Tang, Robert, 2014. "Effective sub-simulation-free upper bounds for the Monte Carlo pricing of callable derivatives and various improvements to existing methodologies," Journal of Economic Dynamics and Control, Elsevier, vol. 40(C), pages 25-45.
    10. Nan Chen & Yanchu Liu, 2014. "American Option Sensitivities Estimation via a Generalized Infinitesimal Perturbation Analysis Approach," Operations Research, INFORMS, vol. 62(3), pages 616-632, June.
    11. Nakatsu, Tomonori, 2023. "On density functions related to discrete time maximum of some one-dimensional diffusion processes," Applied Mathematics and Computation, Elsevier, vol. 441(C).
    12. D. Baños & T. Meyer-Brandis & F. Proske & S. Duedahl, 2017. "Computing deltas without derivatives," Finance and Stochastics, Springer, vol. 21(2), pages 509-549, April.
    13. Jean-Franc{c}ois Chassagneux & Romuald Elie & Idris Kharroubi, 2013. "When terminal facelift enforces Delta constraints," Papers 1307.6020, arXiv.org.

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