Option Pricing in Some Non-Levy Jump Models

Abstract

This paper considers pricing European options in a large class of one-dimensional Markovian jump processes known as subordinate diffusions, which are obtained by time changing a diffusion process with an independent Levy or additive random clock. These jump processes are non-Levy in general, and they can be viewed as a natural generalization of many popular Levy processes used in finance. Subordinate diffusions offer richer jump behavior than Levy processes and they have found a variety of applications in financial modeling. The pricing problem for these processes presents unique challenges, as existing numerical PIDE schemes fail to be efficient and the applicability of transform methods to many subordinate diffusions is unclear. We develop a novel method based on a finite difference approximation of spatial derivatives and matrix eigendecomposition, and it can deal with diffusions that exhibit various types of boundary behavior. Since financial payoffs are typically not smooth, we apply a smoothing tech...