Articlegreen2003

Analysis of Error with Malliavin Calculus: Application to Hedging

18 citations0/0 files storedMathematical Finance

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Stochastic processes and financial applications Financial Markets and Investment Strategies Risk and Portfolio Optimization

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.

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References

1995The Malliavin Calculus and Related Topics 1981Stochastic Differential Equations and Diffusion Processes 1984Applications of the Malliavin Calculus, Part I 1980Limit Distributions for the Error in Approximations of Stochastic Integrals 2001Discrete time hedging errors for options with irregular payoffs 1999Couverture approchée des options européennes

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