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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Manuscript received: July 1999; final version received: September 2000
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Gobet, E., Temam, E. Discrete time hedging errors for options with irregular payoffs. Finance Stochast 5, 357–367 (2001). https://doi.org/10.1007/PL00013539
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DOI: https://doi.org/10.1007/PL00013539