Pricing of Occupation Time Derivatives: Continuous and Discrete Monitoring

Gianluca Fusai, Aldo Tagliani

Abstract

ABSTRACT

In the present work we use different numerical methods (multidimensional inverse Laplace transform, numerical solution of a PDE by finite difference scheme, Monte Carlo simulation) for pricing occupation time derivatives in order to examine the effect of continuous and discrete time monitoring of the underlying asset. In particular we treat the problem of the numerical inversion of a multidimensional Laplace transform and we show that it can be performed very fast and with great accuracy. We conduct also an analysis of the numerical method for the solution of the PDE with discrete monitoring and we show that the proposed method avoids unwanted oscillations in the solution arising near the monitoring dates due to the updating of the occupation time.