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Discrete time hedging errors for options with irregular payoffs

Author

Listed:
  • 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)

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.

Suggested Citation

  • Emmanuel Temam & Emmanuel Gobet, 2001. "Discrete time hedging errors for options with irregular payoffs," Finance and Stochastics, Springer, vol. 5(3), pages 357-367.
    • 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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    More about this item

    Keywords

    Discrete time hedging; approximation of stochastic integral; rate of convergence.;
    All these keywords.

    JEL classification:

    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • D4 - Microeconomics - - Market Structure, Pricing, and Design
    • C0 - Mathematical and Quantitative Methods - - General

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