Download this Paper Open PDF in Browser

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

63 Pages Posted: 28 Nov 2009  

Mitya Boyarchenko

University of Michigan - Department of Mathematics

Marco de Innocentis

Credit Suisse Securities (Europe) Limited; University of Leicester

Sergei Levendorskii

Calico Science Consulting

Date Written: November 26, 2009

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.

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

Suggested Citation

Boyarchenko, Mitya and de Innocentis, Marco and Levendorskii, Sergei, Prices of Barrier and First-Touch Digital Options in Levy-Driven Models, Near Barrier (November 26, 2009). Available at SSRN: https://ssrn.com/abstract=1514025 or http://dx.doi.org/10.2139/ssrn.1514025

Mitya Boyarchenko

University of Michigan - Department of Mathematics ( email )

530 Church Street
2074 East Hall
Ann Arbor, MI 48109
United States

Marco De Innocentis

Credit Suisse Securities (Europe) Limited ( email )

1 Cabot Square
London, E14 4QJ
United Kingdom

University of Leicester ( email )

Department of Mathematics
University Road
Leicester, LE1 7RG
United Kingdom

Sergei Z. Levendorskii (Contact Author)

Calico Science Consulting ( email )

Austin, TX
United States

Paper statistics

Downloads
133
Rank
183,030
Abstract Views
751