Partial Integro‐Differential Equations (PIDES)

Abstract

Option pricing in models with jumps leads to the solution of partial integro‐differential equations (PIDEs). We present the specific features of the PIDEs compared with the partial differential equations. In particular, we highlight the difficulties that arise for the numerical solution of these equations. We show that the use of standard methods, such as finite differences or finite elements, is not straightforward. We then present a simple explicit–implicit finite difference scheme for pricing European vanilla and barrier options in exponential Lévy models and survey the other existing numerical techniques. We also discuss American option pricing, which leads to variational inequalities with the same integro‐differential operator.