Analysis of Error with Malliavin Calculus: Application to Hedging |
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Authors: | E Temam |
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Institution: | Laboratoire de Probabilités et Modèles Aléatoires, UniversitéParis VI Ecole Nationals des Ponts et Chaussées, CERMICS |
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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 +σ i , 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/ n 1/4 for options with irregular payoff. |
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Keywords: | discrete time hedging approximation of stochastic integral Malliavin calculus |
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