Computations of Greeks in a market with jumps via the Malliavin calculus (Q1887269)

The authors deal with Asian options in a market model with jumps, and present formulas for the computation of Greeks using a particular version of the Malliavin calculus on a Poisson space. The family of jump processes includes sums of independent Poisson processes with arbitrary jump sizes. A version of the operator is used that has the derivation property and its adjoint coincides with the Poisson stochastic integral, which provides a natural way to make explicit computation of weights. The integration by parts formula is presented which is the main tool for computing Greeks using a random variable called a weight. They consider the Delta of a binary Asian option and the Gamma of a standard Asian option with numerical simulations. These simulations show that the Malliavin approach applied to Asian options in the case of a market driven by a Poisson process is more efficient than the finite difference method.