Discrete time hedging errors for options with irregular payoffs

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.