In this paper we study the tracking error resulting from the discrete-time application of continuous-time delta-hedging procedures for European options. We characterize the asymptotic distribution of the tracking error as the number of discrete time periods increases, and its joint distribution with other assets. We introduce the notion of temporal granularity of the continuous-time stochastic model that enables us to characterize the degree to which discrete-time approximations of continuous time models track the payoff of the option. We derive closed form expressions for the granularity for a put and call option on a stock that follows a geometric Brownian motion and a mean-reverting process. These expressions offer insight into the tracking error involved in applying continuous-time delta-hedging in discrete time. We also introduce alternative measures of the tracking error and analyze their properties.

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