Premium
Analysis of Error with Malliavin Calculus: Application to Hedging
Author(s) -
Temam E.
Publication year - 2003
Publication title -
mathematical finance
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.98
H-Index - 81
eISSN - 1467-9965
pISSN - 0960-1627
DOI - 10.1111/1467-9965.00014
Subject(s) - mathematics , malliavin calculus , lipschitz continuity , stochastic differential equation , stochastic game , quadratic equation , mathematical economics , hedge , pure mathematics , calculus (dental) , differential equation , mathematical analysis , stochastic partial differential equation , medicine , geometry , dentistry , ecology , biology
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.