Lévy Jumps

Abstract

Lévy processes are referred to as a large class of stationary processes with independent identical increments. Brownian motion and Poisson process can be regarded as two special cases of Lévy process, and have only finite activity in a finite time interval. In this chapter, we only consider Lévy processes with infinity activity in a finite time interval. With respect to jump event modeling in finance, compound Poisson jumps discussed in Chapter 7 are appropriate for capturing rare and large jumps such as market crashes, while Lévy processes with infinity activity may be better suited to describe many small jumps such as discontinuous information flows and discrete trading activities. To distinguish Poisson jump dynamics from jump dynamics with infinity activity, we label the latter jumps as Lévy jumps in this book.