Pricing of Some Exotic Options with NIG-Lévy Input

We study the problem of pricing barrier options and Russian options driven by exponential NIG Levy processes by simulation. Simulating at a discrete grid creates a systematic bias because the minimum and maximum in between grid points is neglected. The proposed solution is to simulate the large jumps only and use a Brownian approximation for the rest combined with explicit formulas for Brownian minima and maxima.