A New Approach to Sensitivity Analysis Based on Dirac Delta Family Methods

In this paper, we propose a new approach to sensitivity analysis by utilizing the Dirac Delta family method. In a novel way, we combine it with the classical infinitesimal perturbation analysis (IPA) estimator, and propose a new class of Dirac-Delta based sensitivity estimators, which we name as the Delta-Family IPA estimators. We establish an explicitly computable error bound for the Delta-Family IPA estimators, which bypasses the usual technical assumption of interchangeability of limit and differentiation as in the literature of IPA stochastic derivatives estimators. Numerical examples of Greeks computations in the case of European call options and Asian digital options illustrate the improved efficiency of the proposed method as compared to the IPA method.