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Computation of Greeks using binomial trees in a jump-diffusion model

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  • Suda, Shintaro
  • Muroi, Yoshifumi

Abstract

We propose a new algorithm for computing the Greeks in jump-diffusion settings using binomial trees. We further demonstrate that the Greeks for European options converge to the Malliavin Greeks in the continuous time model. Our proposed algorithm is efficient, because the price and the Greeks (Delta, Gamma, Vega, and Rho) can be computed simultaneously. Computation of the Greeks for American options is also discussed.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:dyncon:v:51:y:2015:i:c:p:93-110
    DOI: 10.1016/j.jedc.2014.09.032
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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. S. G. Kou, 2002. "A Jump-Diffusion Model for Option Pricing," Management Science, INFORMS, vol. 48(8), pages 1086-1101, August.
    3. Fang, Fang & Oosterlee, Kees, 2008. "A Novel Pricing Method For European Options Based On Fourier-Cosine Series Expansions," MPRA Paper 9319, University Library of Munich, Germany.
    4. Amin, Kaushik I, 1993. "Jump Diffusion Option Valuation in Discrete Time," Journal of Finance, American Finance Association, vol. 48(5), pages 1833-1863, December.
    5. Bally Vlad & Caramellino Lucia & Zanette Antonino, 2005. "Pricing and hedging American options by Monte Carlo methods using a Malliavin calculus approach," Monte Carlo Methods and Applications, De Gruyter, vol. 11(2), pages 97-133, June.
    6. 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.
    7. Merton, Robert C., 1976. "Option pricing when underlying stock returns are discontinuous," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 125-144.
    8. Yoshifumi Muroi & Shintaro Suda, 2014. "Computation of Greeks using Binomial Tree," TMARG Discussion Papers 117, Graduate School of Economics and Management, Tohoku University.
    9. 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.
    10. 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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    Cited by:

    1. 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.
    2. Duy Nguyen, 2018. "A hybrid Markov chain-tree valuation framework for stochastic volatility jump diffusion models," International Journal of Financial Engineering (IJFE), World Scientific Publishing Co. Pte. Ltd., vol. 5(04), pages 1-30, December.

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    More about this item

    Keywords

    Options; Greeks; Jump-diffusion model; Binomial tree;
    All these keywords.

    JEL classification:

    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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