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Numerical analysis on local risk-minimization forexponential L\'evy models

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  • Takuji Arai
  • Yuto Imai
  • Ryoichi Suzuki

Abstract

We illustrate how to compute local risk minimization (LRM) of call options for exponential L\'evy models. We have previously obtained a representation of LRM for call options; here we transform it into a form that allows use of the fast Fourier transform method suggested by Carr & Madan. In particular, we consider Merton jump-diffusion models and variance gamma models as concrete applications.

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  • Takuji Arai & Yuto Imai & Ryoichi Suzuki, 2015. "Numerical analysis on local risk-minimization forexponential L\'evy models," Papers 1506.03898, arXiv.org.
  • Handle: RePEc:arx:papers:1506.03898
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    File URL: http://arxiv.org/pdf/1506.03898
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    References listed on IDEAS

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    1. Ewald, Christian-Oliver & Nawar, Roy & Siu, Tak Kuen, 2013. "Minimal variance hedging of natural gas derivatives in exponential Lévy models: Theory and empirical performance," Energy Economics, Elsevier, vol. 36(C), pages 97-107.
    2. P. Leoni & N. Vandaele & M. Vanmaele, 2014. "Hedging strategies for energy derivatives," Quantitative Finance, Taylor & Francis Journals, vol. 14(10), pages 1725-1737, October.
    3. Merton, Robert C., 1976. "Option pricing when underlying stock returns are discontinuous," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 125-144.
    4. Kiseop Lee & Seongjoo Song, 2007. "Insiders' hedging in a jump diffusion model," Quantitative Finance, Taylor & Francis Journals, vol. 7(5), pages 537-545.
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    Cited by:

    1. Takuji Arai & Yuto Imai, 2016. "On the difference between locally risk-minimizing and delta hedging strategies for exponential L\'evy models," Papers 1610.09085, arXiv.org.

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