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Computation of Greeks for asset price dynamics driven by stable and tempered stable processes

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  • Reiichiro Kawai
  • Atsushi Takeuchi

Abstract

The purpose of this paper is to derive the Greeks formulas of Delta, Gamma, Vega and Theta for derivative securities with both continuous and discontinuous payoff structures under asset price dynamics described by stable and tempered stable processes with presentation of their practical simulation methods. Our approach is based on the representation of stable distributions using an exponential distribution whose scaling property with respect to the Girsanov transform is used in the Malliavin calculus framework on the Poisson space. Numerical results are presented to illustrate the effectiveness of our formulas in Monte Carlo simulations relative to the finite difference method.

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  • 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.
    • Handle: RePEc:taf:quantf:v:13:y:2013:i:8:p:1303-1316
    DOI: 10.1080/14697688.2011.589403
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    References listed on IDEAS

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    1. Peter Carr & Liuren Wu, 2003. "The Finite Moment Log Stable Process and Option Pricing," Journal of Finance, American Finance Association, vol. 58(2), pages 753-777, April.
    2. Peter Carr & Helyette Geman, 2002. "The Fine Structure of Asset Returns: An Empirical Investigation," The Journal of Business, University of Chicago Press, vol. 75(2), pages 305-332, April.
    3. Peter Carr & Liuren Wu, 2003. "The Finite Moment Log Stable Process and Option Pricing," Journal of Finance, American Finance Association, vol. 58(2), pages 753-778, April.
    4. Benoit Mandelbrot, 2015. "The Variation of Certain Speculative Prices," World Scientific Book Chapters, in: Anastasios G Malliaris & William T Ziemba (ed.), THE WORLD SCIENTIFIC HANDBOOK OF FUTURES MARKETS, chapter 3, pages 39-78, World Scientific Publishing Co. Pte. Ltd..
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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.

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