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Discrete time hedging errors for options with irregular payoffs

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  • Emmanuel Temam

    ()
    (Université Paris VI - CERMICS, Ecole Nationale des Ponts et Chaussées, 6 et 8 avenue Blaise Pascal, 77455 Marne La Vallée, France Manuscript)

  • Emmanuel Gobet

    ()
    (CMAP-Ecole Polytechnique, 91128 Palaiseau Cedex, France)

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    Abstract

    In a complete market with a constant interest rate and a risky asset, which is a linear diffusion process, we are interested in the discrete time hedging of a European vanilla option with payoff function f. As regards the perfect continuous hedging, this discrete time strategy induces, for the trader, a risk which we analyze w.r.t. n, the number of discrete times of rebalancing. We prove that the rate of convergence of this risk (when $n \rightarrow + \infty$) strongly depends on the regularity properties of f: the results cover the cases of standard options.

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    Bibliographic Info

    Article provided by Springer in its journal Finance and Stochastics.

    Volume (Year): 5 (2001)
    Issue (Month): 3 ()
    Pages: 357-367

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    Handle: RePEc:spr:finsto:v:5:y:2001:i:3:p:357-367

    Note: received: July 1999; final version received: September 2000
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    Web page: http://www.springerlink.com/content/101164/

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    Related research

    Keywords: Discrete time hedging; approximation of stochastic integral; rate of convergence.;

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    Cited by:
    1. Clément, Emmanuelle & Delattre, Sylvain & Gloter, Arnaud, 2013. "An infinite dimensional convolution theorem with applications to the efficient estimation of the integrated volatility," Stochastic Processes and their Applications, Elsevier, vol. 123(7), pages 2500-2521.
    2. Geiss, Christel & Geiss, Stefan & Gobet, Emmanuel, 2012. "Generalized fractional smoothness and Lp-variation of BSDEs with non-Lipschitz terminal condition," Stochastic Processes and their Applications, Elsevier, vol. 122(5), pages 2078-2116.
    3. Tankov, Peter & Voltchkova, Ekaterina, 2009. "Asymptotic analysis of hedging errors in models with jumps," Stochastic Processes and their Applications, Elsevier, vol. 119(6), pages 2004-2027, June.
    4. Ale\v{s} \v{C}ern\'y & Stephan Denkl & Jan Kallsen, 2013. "Hedging in L\'evy models and the time step equivalent of jumps," Papers 1309.7833, arXiv.org, revised Nov 2013.
    5. Emmanuel Denis & Yuri Kabanov, 2010. "Mean square error for the Leland–Lott hedging strategy: convex pay-offs," Finance and Stochastics, Springer, vol. 14(4), pages 625-667, December.
    6. Mats Brod\'en & Magnus Wiktorsson, 2010. "Hedging Errors Induced by Discrete Trading Under an Adaptive Trading Strategy," Papers 1004.4526, arXiv.org.

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