IDEAS home Printed from https://ideas.repec.org/p/pra/mprapa/30596.html
   My bibliography  Save this paper

On the calculation of price sensitivities with jump-diffusion structure

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: https://mpra.ub.uni-muenchen.de/30596/1/MPRA_paper_30596.pdf
    File Function: original version
    Download Restriction: no

    File URL: https://mpra.ub.uni-muenchen.de/45328/1/MPRA_paper_30596.pdf
    File Function: revised version
    Download Restriction: no

    References listed on IDEAS

    as
    1. 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.
    2. 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.
    3. 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.
    4. 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.
    5. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. repec:eee:matcom:v:140:y:2017:i:c:p:69-93 is not listed on IDEAS

    More about this item

    Keywords

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

    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

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:pra:mprapa:30596. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Joachim Winter). General contact details of provider: http://edirc.repec.org/data/vfmunde.html .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.