Pricing of some exotic options with NIG-Lévy input

Sebastian Rasmus*, Søren Asmussen** and Magnus Wiktorsson*

* Centre for Mathematical Sciences, University of Lund, Box 118, 221 00 Lund, Sweden
{rasmus,magnusw}@maths.lth.se

** Theoretical Statistics, University of Aarhus, Ny Munkegade, 8000 Aarhus C, Denmark
asmus@imf.au.dk

Abstract

 We study the problem of pricing barrier options and Russian options
 driven by exponential NIG L evy 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.