Sensitivity estimates from characteristic functions

Authors:
Paul Glasserman;Zongjian Liu
Affiliations:
Columbia Business School, Uris Hall, Broadway, New York, N.Y.;Columbia University, New York, N.Y.
Venue:
Proceedings of the 39th conference on Winter simulation: 40 years! The best is yet to come
Year:
2007

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Abstract

We investigate the application of the likelihood ratio method (LRM) for sensitivity estimation when the relevant density for the underlying model is known only through its characteristic function or Laplace transform. 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.