We consider standard European as well as double-barrier European options for underlyings that are given by the superposition of a Guassian and a compound Poisson (jump) process with discrete values. We derive a formula for calculating such options and furthermore show that as the barriers tend to $\pm\infty$, the value of the double-barrier option tends asymptotically to that of the standard option. Numerical examples are provided.
"Asymptotics of European Double-Barrier Option with Compound Poisson Component." Commun. Math. Anal. 14 (2) 40 - 66, 2013.