Discrete time hedging errors for options with irregular payoffs

Emmanuel Temam () and Emmanuel Gobet ()
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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

Finance and Stochastics, 2001, vol. 5, issue 3, pages 357-367

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.

Keywords: Discrete time hedging; approximation of stochastic integral; rate of convergence. (search for similar items in EconPapers)
JEL-codes: G11 G12 D4 C0 (search for similar items in EconPapers)
Date: 2001-07-12
Note: received: July 1999; final version received: September 2000

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