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Discrete Malliavin calculus and computations of greeks in the binomial tree

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  • Muroi, Yoshifumi
  • Suda, Shintaro

Abstract

This paper proposes new methods for computation of greeks using the binomial tree and the discrete Malliavin calculus. In the last decade, the Malliavin calculus has come to be considered as one of the main tools in financial mathematics. It is particularly important in the computation of greeks using Monte Carlo simulations. In previous studies, greeks were usually represented by expectation formulas that are derived from the Malliavin calculus and these expectations are computed using Monte Carlo simulations. On the other hand, the binomial tree approach can also be used to compute these expectations. In this article, we employ the discrete Malliavin calculus to obtain expectation formulas for greeks by the binomial tree method. All the results are obtained in an elementary manner.

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  • Muroi, Yoshifumi & Suda, Shintaro, 2013. "Discrete Malliavin calculus and computations of greeks in the binomial tree," European Journal of Operational Research, Elsevier, vol. 231(2), pages 349-361.
    • Handle: RePEc:eee:ejores:v:231:y:2013:i:2:p:349-361
    DOI: 10.1016/j.ejor.2013.05.038
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    1. Eric Fournié & Jean-Michel Lasry & Pierre-Louis Lions & Jérôme Lebuchoux & Nizar Touzi, 1999. "Applications of Malliavin calculus to Monte Carlo methods in finance," Finance and Stochastics, Springer, vol. 3(4), pages 391-412.
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    Cited by:

    1. Suda, Shintaro & Muroi, Yoshifumi, 2015. "Computation of Greeks using binomial trees in a jump-diffusion model," Journal of Economic Dynamics and Control, Elsevier, vol. 51(C), pages 93-110.
    2. Muroi, Yoshifumi & Suda, Shintaro, 2017. "Computation of Greeks in jump-diffusion models using discrete Malliavin calculus," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 140(C), pages 69-93.
    3. Gambaro, Anna Maria & Kyriakou, Ioannis & Fusai, Gianluca, 2020. "General lattice methods for arithmetic Asian options," European Journal of Operational Research, Elsevier, vol. 282(3), pages 1185-1199.

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