The main goal of this paper is to generalize the results of Fournie et al.  for markets generated by Lévy processes. For this reason we extend the theory of Malliavin calculus to provide the tools that are necessary for the calculation of the sensitivities, such as differentiability results for the solution of a stochastic differential equation.
Evangelia Petrou. "Malliavin Calculus in Lévy spaces and Applications to Finance.." Electron. J. Probab. 13 852 - 879, 2008. https://doi.org/10.1214/EJP.v13-502