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Feller processes of normal inverse Gaussian type


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  • O. E. Barndorff-Nielsen
  • S. Z. Levendorskii
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    We consider the construction of normal inverse Gaussian (NIG) (and some related) Levy processes from the probabilistic viewpoint and from that of the theory of pseudo-differential operators; we then introduce and analyse natural generalizations of these constructions. The resulting Feller processes are somewhat similar to the NIG Levy process but may, for instance, possess mean-reverting features. Possible applications to financial mathematics are discussed, and approximations to solutions of corresponding generalizations of the Black-Scholes equation are derived.

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    Bibliographic Info

    Article provided by Taylor & Francis Journals in its journal Quantitative Finance.

    Volume (Year): 1 (2001)
    Issue (Month): 3 ()
    Pages: 318-331

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    Handle: RePEc:taf:quantf:v:1:y:2001:i:3:p:318-331

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    Cited by:
    1. Lim, Dongjae & Li, Lingfei & Linetsky, Vadim, 2012. "Evaluating callable and putable bonds: An eigenfunction expansion approach," Journal of Economic Dynamics and Control, Elsevier, vol. 36(12), pages 1888-1908.
    2. Ole E. Barndorff-Nielsen & Neil Shephard, 2012. "Basics of Levy processes," Economics Papers 2012-W06, Economics Group, Nuffield College, University of Oxford.
    3. McCulloch, James, 2012. "Fractal market time," Journal of Empirical Finance, Elsevier, Elsevier, vol. 19(5), pages 686-701.
    4. Jir\^o Akahori & Takahiro Tsuchiya, 2006. "What is the natural scale for a L\'evy process in modelling term structure of interest rates?," Papers math/0612341,
    5. Young Kim & Svetlozar Rachev & Michele Bianchi & Frank Fabozzi, 2009. "Computing VAR and AVaR in Infinitely Divisible Distributions," Yale School of Management Working Papers, Yale School of Management amz2569, Yale School of Management.
    6. Lin, Zuodong & Rachev, Svetlozar T. & Kim, Young Shin & Fabozzi, Frank J., 2012. "Option pricing with regime switching tempered stable processes," Working Paper Series in Economics 43, Karlsruhe Institute of Technology (KIT), Department of Economics and Business Engineering.
    7. James McCulloch, 2012. "Fractal Market Time," Research Paper Series, Quantitative Finance Research Centre, University of Technology, Sydney 311, Quantitative Finance Research Centre, University of Technology, Sydney.
    8. Florian Kleinert & Kees van Schaik, 2013. "A variation of the Canadisation algorithm for the pricing of American options driven by L\'evy processes," Papers 1304.4534,


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