# A canonical optimal stopping problem for American options under a double exponential jump-diffusion model

## Farid AitSahlia, Andreas Runnemo

#### Abstract

ABSTRACT

This paper presents a simple numerical approach to compute accurately the values and optimal exercise boundaries for American options when the underlying process is a double exponential jump-diffusion model that prices jump risk. The present work extends the canonical representation for American options initially developed in the Brownian motion set-up. Here, too, jump-diffusion pricing models can be reduced to a single optimal stopping problem, indexed by one more parameter, and linear spline approximations of the stopping boundary in the canonical scale with only a few knots are supported through numerical evidence. These approximations can then be exploited to solve the integral equation defining the early exercise boundary of an American option efficiently and accurately, thus leading to its efficient and accurate pricing and hedging.