Finance and Stochastics

, Volume 5, Issue 3, pp 357–367 | Cite as

Discrete time hedging errors for options with irregular payoffs

  • Emmanuel Gobet
  • Emmanuel Temam
Original Paper


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.

Key words: Discrete time hedging, approximation of stochastic integral, rate of convergence. 
JEL Classification: G11, G12, D4, C0 
Mathematics Subject Classification (1991): 65U05, 60H05,90A09 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Emmanuel Gobet
    • 1
  • Emmanuel Temam
    • 2
  1. 1.CMAP-Ecole Polytechnique, 91128 Palaiseau Cedex, France (e-mail: FR
  2. 2.Université Paris VI - CERMICS, Ecole Nationale des Ponts et Chaussées, 6 et 8 avenue Blaise Pascal, 77455 Marne La Vallée, France (e-mail: FR

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