The concept of a jump, which is usually interpreted as a sudden change in the value either of an underlying asset or of a derivative security, provides a suitable framework that can be generalized to solve a number of problems involving unanticipated signals. In this paper we discuss the practical implementation of jump models in a partial differential equation framework for pricing derivatives under a known and unknown number of jumps, regime changes, and reorganization. The framework lends itself ideally to treatment with finite differences, and allows complex contingencies to be introduced in a straightforward manner.

[First published in issue 27 of Wilmott - July 2006]