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Local risk-minimization for Lévy markets

Author

Listed:
  • Takuji Arai

    (Department of Economics, Keio University, 2-15-45 Mita, Minato-ku, Tokyo, 108-8345, Japan)

  • Ryoichi Suzuki

    (Department of Mathematics, Keio University, 3-14-1 Hiyoshi, Kohoku-ku, Yokohama, 223-8522, Japan)

Abstract

In this paper, we aim to obtain explicit representations of locally risk-minimizing by using Malliavin calculus for Lévy processes. For incomplete market models whose asset price is described by a solution to a stochastic differential equation driven by a Lévy process, we derive general formulas of locally risk-minimizing including Malliavin derivatives; and calculate its concrete expressions for call options, Asian options and lookback options.

Suggested Citation

  • Takuji Arai & Ryoichi Suzuki, 2015. "Local risk-minimization for Lévy markets," International Journal of Financial Engineering (IJFE), World Scientific Publishing Co. Pte. Ltd., vol. 2(02), pages 1-28.
    • Handle: RePEc:wsi:ijfexx:v:02:y:2015:i:02:n:s2424786315500152
    DOI: 10.1142/S2424786315500152
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    Citations

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    Cited by:

    1. Takuji Arai, 2021. "Approximate option pricing formula for Barndorff-Nielsen and Shephard model," Papers 2104.10877, arXiv.org.
    2. Takuji Arai & Yuto Imai & Ryoichi Suzuki, 2016. "Numerical Analysis On Local Risk-Minimization For Exponential Lévy Models," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 19(02), pages 1-27, March.
    3. Masahiro Handa & Noriyoshi Sakuma & Ryoichi Suzuki, 2024. "A Girsanov transformed Clark-Ocone-Haussmann type formula for $$L^1$$ L 1 -pure jump additive processes and its application to portfolio optimization," Annals of Finance, Springer, vol. 20(3), pages 329-352, September.
    4. Takuji Arai, 2019. "Pricing And Hedging Of Vix Options For Barndorff-Nielsen And Shephard Models," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 22(08), pages 1-26, December.
    5. Takuji Arai & Ryoichi Suzuki, 2019. "A Clark-Ocone type formula via Ito calculus and its application to finance," Papers 1906.06648, arXiv.org.
    6. Takuji Arai, 2019. "Pricing and hedging of VIX options for Barndorff-Nielsen and Shephard models," Papers 1904.12260, arXiv.org.
    7. Takuji Arai & Yuto Imai & Ryo Nakashima, 2018. "Numerical analysis on quadratic hedging strategies for normal inverse Gaussian models," Papers 1801.05597, arXiv.org.
    8. Takuji Arai, 2020. "Al\`os type decomposition formula for Barndorff-Nielsen and Shephard model," Papers 2005.07393, arXiv.org, revised Sep 2020.

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