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A Shot Noise Model For Financial Assets

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Author Info

  • TIMO ALTMANN

    (Mathematical Insitute, University of Giessen, Arndtstr. 2, D-35392 Giessen, Germany)

  • THORSTEN SCHMIDT

    ()
    (Mathematical Insitute, University of Leipzig, D-04081 Leipzig, Germany)

  • WINFRIED STUTE

    ()
    (Mathematical Insitute, University of Giessen, Arndtstr. 2, D-35392 Giessen, Germany)

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    Abstract

    In this article we propose and study a model for stock prices which allows for shot-noise effects. This means that abrupt changes caused by jumps may fade away as time goes by. This model is incomplete. We derive the minimal martingale measure in discrete and continuous time and discuss the associated hedging strategy. Finally, a simulation study is included to show that our model is able to produce smile effects.

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    Bibliographic Info

    Article provided by World Scientific Publishing Co. Pte. Ltd. in its journal International Journal of Theoretical and Applied Finance.

    Volume (Year): 11 (2008)
    Issue (Month): 01 ()
    Pages: 87-106

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    Handle: RePEc:wsi:ijtafx:v:11:y:2008:i:01:p:87-106

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    Related research

    Keywords: Shot-noise component; jump diffusion; minimal martingale measure;

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    Cited by:
    1. Moreno, Manuel & Serrano, Pedro & Stute, Winfried, 2011. "Statistical properties and economic implications of jump-diffusion processes with shot-noise effects," European Journal of Operational Research, Elsevier, vol. 214(3), pages 656-664, November.
    2. Fu, Jun & Yang, Hailiang, 2012. "Equilibruim approach of asset pricing under Lévy process," European Journal of Operational Research, Elsevier, vol. 223(3), pages 701-708.
    3. Thorsten Schmidt, 2014. "Catastrophe Insurance Modeled by Shot-Noise Processes," Risks, MDPI, Open Access Journal, vol. 2(1), pages 3-24, February.
    4. Baranovski, Alexander L., 2012. "Calibration of factor models with equity data: parade of correlations," MPRA Paper 36300, University Library of Munich, Germany.
    5. Kai Kopperschmidt & Winfried Stute, 2009. "Purchase timing models in marketing: a review," AStA Advances in Statistical Analysis, Springer, vol. 93(2), pages 123-149, June.
    6. Angelos Dassios & Xin Dong, 2014. "Stationarity of Bivariate Dynamic Contagion Processes," Science & Finance (CFM) working paper archive 1405.5842, Science & Finance, Capital Fund Management.

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