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Optimal hedging in discrete time

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  • Bruno R\'emillard

    (GERAD)

  • Sylvain Rubenthaler

    (JAD)

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    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.

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    File URL: http://arxiv.org/pdf/1211.5035
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    Paper provided by arXiv.org in its series Papers with number 1211.5035.

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    Date of creation: Nov 2012
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    Handle: RePEc:arx:papers:1211.5035

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    1. René Garcia & �ric Renault, 1998. "A Note on Hedging in ARCH and Stochastic Volatility Option Pricing Models," Mathematical Finance, Wiley Blackwell, Wiley Blackwell, vol. 8(2), pages 153-161.
    2. Boyle, Phelim P. & Emanuel, David, 1980. "Discretely adjusted option hedges," Journal of Financial Economics, Elsevier, Elsevier, vol. 8(3), pages 259-282, September.
    3. Jin-Chuan Duan, 1995. "The Garch Option Pricing Model," Mathematical Finance, Wiley Blackwell, Wiley Blackwell, vol. 5(1), pages 13-32.
    4. Ale\v{s} \v{C}ern\'y & Jan Kallsen, 2007. "On the structure of general mean-variance hedging strategies," Papers 0708.1715, arXiv.org.
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