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Optimal hedging in discrete time

Author

Listed:
  • Bruno R'emillard

    (GERAD)

  • Sylvain Rubenthaler

    (JAD)

Abstract

Building on the work of Schweizer (1995) and Cern and Kallseny (2007), we present discrete time formulas minimizing the mean square hedging error for multidimensional assets. In particular, we give explicit formulas when a regime-switching random walk or a GARCH-type process is utilized to model the returns. Monte Carlo simulations are used to compare the optimal and delta hedging methods.

Suggested Citation

  • Bruno R'emillard & Sylvain Rubenthaler, 2012. "Optimal hedging in discrete time," Papers 1211.5035, arXiv.org.
    • Handle: RePEc:arx:papers:1211.5035
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    References listed on IDEAS

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    1. Martin Schweizer, 1995. "Variance-Optimal Hedging in Discrete Time," Mathematics of Operations Research, INFORMS, vol. 20(1), pages 1-32, February.
    2. Alev{s} v{C}ern'y & Jan Kallsen, 2007. "On the Structure of General Mean-Variance Hedging Strategies," Papers 0708.1715, arXiv.org, revised Jul 2017.
    3. René Garcia & Èric Renault, 1998. "A Note on Hedging in ARCH and Stochastic Volatility Option Pricing Models," Mathematical Finance, Wiley Blackwell, vol. 8(2), pages 153-161, April.
    4. Lorenzo Cornalba & Jean-Philippe Bouchaud & Marc Potters, 2002. "Option Pricing And Hedging With Temporal Correlations," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 5(03), pages 307-320.
    5. Boyle, Phelim P. & Emanuel, David, 1980. "Discretely adjusted option hedges," Journal of Financial Economics, Elsevier, vol. 8(3), pages 259-282, September.
    6. Jin‐Chuan Duan, 1995. "The Garch Option Pricing Model," Mathematical Finance, Wiley Blackwell, vol. 5(1), pages 13-32, January.
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