Analysis of Error with Malliavin Calculus: Application to Hedging

The aim of this paper is to compute the quadratic error of a discrete time‐hedging strategy in a complete multidimensional model. This result extends that of Gobet and Temam (2001) and Zhang (1999). More precisely, our basic assumption is that the asset prices satisfy the d ‐dimensional stochastic differential equation dX i t = X i t ( b i ( X t ) dt +σ i , j ( X t ) dW j t ) . We precisely describe the risk of this strategy with respect to n , the number of rebalancing times. The rates of convergence obtained are for any options with Lipschitz payoff and 1/ n 1/4 for options with irregular payoff.