Analysis of Error with Malliavin Calculus: Application to Hedging

Author: Temam, E.

Source: Mathematical Finance, Volume 13, Number 1, January 2003 , pp. 201-214(14)

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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 dXⁱ_t=Xⁱ_t(bⁱ(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.

Keywords: discrete time hedging; approximation of stochastic integral; Malliavin calculus

Document Type: Research article

DOI: http://dx.doi.org/10.1111/1467-9965.00014

Publication date: 2003-01-01