Prices of Barrier and First-Touch Digital Options in Levy-Driven Models, Near Barrier

Abstract:     
We calculate the leading term of asymptotics of the prices of barrier options and first touch digitals near the barrier for wide classes of Levy processes with exponential jump densities, including Variance Gamma model, KoBoL (a.k.a. CGMY) model and Normal Inverse Gaussian processes. In the case of processes of infinite activity and finite variation, with the drift pointing from the barrier, we prove that the price is discontinuous at the boundary. In many cases, we calculate the second term of asymptotics as well.

Number of Pages in PDF File: 63

Keywords: barrier options, first-touch digitals, Levy processes,Carr's randomization, KoBoL processes, CGMY model,Normal Inverse Gaussian processes, Variance Gamma processes, Wiener-Hopf factorization, asymptotics

JEL Classification: G12

working papers series