Sensitivity Estimates from Characteristic Functions

The likelihood ratio method (LRM) is a technique for estimating derivatives of expectations through simulation. LRM estimators are constructed from the derivatives of probability densities of inputs to a simulation. We investigate the application of the likelihood ratio method for sensitivity estimation when the relevant densities for the underlying model are known only through their characteristic functions or Laplace transforms. This problem arises in financial applications, where sensitivities are used for managing risk and where a substantial class of models have transition densities known only through their transforms. We quantify various sources of errors arising when numerical transform inversion is used to sample through the characteristic function and to evaluate the density and its derivative, as required in LRM. This analysis provides guidance for setting parameters in the method to accelerate convergence.