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On the calculation of price sensitivities with jump-diffusion structure

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  • El-Khatib, Youssef
  • Abdulnasser, Hatemi-J

Abstract

We provide a new theoretical framework for estimating the price sensitivities of a trading position with regard to five underlying factors in jump-diffusion models using jump times Poisson noise. The proposition that results in a general solution is mathematically proved. The general solution that this paper offers can be applied to compute each price sensitivity. The suggested modeling approach deals with the shortcomings of the Black-Scholes formula such as the jumps that can occur at any time in the stock's price. Via the Malliavin calculus we show that differentiation can be transformed into integration, which makes the price sensitivities operational and more efficient. Thus, the solution that is provided in this paper is expected to make decision making under uncertainty more efficient.

Suggested Citation

  • 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.
    • Handle: RePEc:pra:mprapa:30596
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    File URL: https://mpra.ub.uni-muenchen.de/45328/1/MPRA_paper_30596.pdf
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    References listed on IDEAS

    as
    1. Elliott, R. J. & Tsoi, A. H., 1993. "Integration by Parts for Poisson Processes," Journal of Multivariate Analysis, Elsevier, vol. 44(2), pages 179-190, February.
    2. Jan Ubøe & Bernt Øksendal & Knut Aase & Nicolas Privault, 2000. "White noise generalizations of the Clark-Haussmann-Ocone theorem with application to mathematical finance," Finance and Stochastics, Springer, vol. 4(4), pages 465-496.
    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. Youssef El-Khatib & Nicolas Privault, 2004. "Computations of Greeks in a market with jumps via the Malliavin calculus," Finance and Stochastics, Springer, vol. 8(2), pages 161-179, May.
    5. 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.
    6. 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.
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    Cited by:

    1. Abdulnasser Hatemi-J & Youssef El-Khatib, 2018. "Valuation of Currency Options in Markets with a Crunch," Papers 1801.08346, arXiv.org.
    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.

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    More about this item

    Keywords

    Malliavin Calculus; Asset Pricing; Price Sensitivity; Jump-diffusion Models; Jump Times Poisson Noise; European Options.;
    All these keywords.

    JEL classification:

    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • G10 - Financial Economics - - General Financial Markets - - - General (includes Measurement and Data)
    • C60 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - General

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