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Computation of Greeks in jump-diffusion models using discrete Malliavin calculus

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  • Muroi, Yoshifumi
  • Suda, Shintaro

Abstract

In the last decade, many studies have investigated the computation of Greeks (sensitivity of options) for European options, American options, exotic options, and so on using Malliavin calculus. Moreover, many studies have derived Greeks using jump-diffusion models. In this paper, we investigate a new computation scheme to derive Greeks in a jump-diffusion model using discrete Malliavin calculus. This method enables us to obtain Greeks for European options using the binomial tree approach.

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  • 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.
    • Handle: RePEc:eee:matcom:v:140:y:2017:i:c:p:69-93
    DOI: 10.1016/j.matcom.2017.03.002
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. 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.
    4. Eric Benhamou, 2003. "Optimal Malliavin Weighting Function for the Computation of the Greeks," Mathematical Finance, Wiley Blackwell, vol. 13(1), pages 37-53, January.
    5. Merton, Robert C., 1976. "Option pricing when underlying stock returns are discontinuous," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 125-144.
    6. Yoshifumi Muroi & Shintaro Suda, 2014. "Computation of Greeks using Binomial Tree," TMARG Discussion Papers 117, Graduate School of Economics and Management, Tohoku University.
    7. Montero, Miquel & Kohatsu-Higa, Arturo, 2003. "Malliavin Calculus applied to finance," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 320(C), pages 548-570.
    8. Reiichiro Kawai & Atsushi Takeuchi, 2013. "Computation of Greeks for asset price dynamics driven by stable and tempered stable processes," Quantitative Finance, Taylor & Francis Journals, vol. 13(8), pages 1303-1316, July.
    9. Guillaume Bernis & Emmanuel Gobet & Arturo Kohatsu‐Higa, 2003. "Monte Carlo Evaluation of Greeks for Multidimensional Barrier and Lookback Options," Mathematical Finance, Wiley Blackwell, vol. 13(1), pages 99-113, January.
    10. Paul Glasserman & Zongjian Liu, 2010. "Sensitivity Estimates from Characteristic Functions," Operations Research, INFORMS, vol. 58(6), pages 1611-1623, December.
    11. Davis, Mark H.A. & Johansson, Martin P., 2006. "Malliavin Monte Carlo Greeks for jump diffusions," Stochastic Processes and their Applications, Elsevier, vol. 116(1), pages 101-129, January.
    12. Kawai, Reiichiro & Takeuchi, Atsushi, 2010. "Sensitivity analysis for averaged asset price dynamics with gamma processes," Statistics & Probability Letters, Elsevier, vol. 80(1), pages 42-49, January.
    13. Reiichiro Kawai & Arturo Kohatsu-Higa, 2010. "Computation of Greeks and Multidimensional Density Estimation for Asset Price Models with Time-Changed Brownian Motion," Applied Mathematical Finance, Taylor & Francis Journals, vol. 17(4), pages 301-321.
    14. Amin, Kaushik I, 1993. "Jump Diffusion Option Valuation in Discrete Time," Journal of Finance, American Finance Association, vol. 48(5), pages 1833-1863, December.
    15. San‐Lin Chung & Mark Shackleton, 2002. "The Binomial Black–Scholes model and the Greeks," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 22(2), pages 143-153, February.
    16. San‐Lin Chung & Weifeng Hung & Han‐Hsing Lee & Pai‐Ta Shih, 2011. "On the rate of convergence of binomial Greeks," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 31(6), pages 562-597, June.
    17. El-Khatib, Youssef & Abdulnasser, Hatemi-J, 2011. "On the calculation of price sensitivities with jump-diffusion structure," MPRA Paper 30596, University Library of Munich, Germany.
    18. Cox, John C. & Ross, Stephen A. & Rubinstein, Mark, 1979. "Option pricing: A simplified approach," Journal of Financial Economics, Elsevier, vol. 7(3), pages 229-263, September.
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    1. Muroi, Yoshifumi & Suda, Shintaro, 2022. "Binomial tree method for option pricing: Discrete cosine transform approach," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 198(C), pages 312-331.

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