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A Shot Noise Model For Financial Assets

Author

Listed:
  • 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)

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.

Suggested Citation

  • Timo Altmann & Thorsten Schmidt & Winfried Stute, 2008. "A Shot Noise Model For Financial Assets," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 11(01), pages 87-106.
    • Handle: RePEc:wsi:ijtafx:v:11:y:2008:i:01:n:s0219024908004737
    DOI: 10.1142/S0219024908004737
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    References listed on IDEAS

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    1. Dothan, Michael U., 1990. "Prices in Financial Markets," OUP Catalogue, Oxford University Press, number 9780195053128, Decembrie.
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    Cited by:

    1. 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.
    2. Baranovski, Alexander L., 2012. "Calibration of factor models with equity data: parade of correlations," MPRA Paper 36300, University Library of Munich, Germany.
    3. Oleksandra Putyatina & Jörn Sass, 2018. "Approximation for portfolio optimization in a financial market with shot-noise jumps," Computational Management Science, Springer, vol. 15(2), pages 161-186, June.
    4. 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.
    5. Kai Kopperschmidt & Winfried Stute, 2009. "Purchase timing models in marketing: a review," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 93(2), pages 123-149, June.
    6. Liang, Xiaoqing & Lu, Yi, 2017. "Indifference pricing of a life insurance portfolio with risky asset driven by a shot-noise process," Insurance: Mathematics and Economics, Elsevier, vol. 77(C), pages 119-132.
    7. Angelos Dassios & Xin Dong, 2014. "Stationarity of Bivariate Dynamic Contagion Processes," Papers 1405.5842, arXiv.org.
    8. Thorsten Schmidt, 2014. "Catastrophe Insurance Modeled by Shot-Noise Processes," Risks, MDPI, vol. 2(1), pages 1-22, February.
    9. Shuang Li & Yanli Zhou & Yonghong Wu & Xiangyu Ge, 2017. "Equilibrium approach of asset and option pricing under Lévy process and stochastic volatility," Australian Journal of Management, Australian School of Business, vol. 42(2), pages 276-295, May.

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