Analysis of Error with Malliavin Calculus: Application to Hedging

E. Temam

Mathematical Finance, 2003, vol. 13, issue 1, 201-214

Abstract: 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 dXit=Xit(bi(Xt)dt+σi,j(Xt)dWjt). 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/n1/4 for options with irregular payoff.

Date: 2003
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