Abstract

http://ssrn.com/abstract=1514025
 
 

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Citations (18)



 


 



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


Mitya Boyarchenko


University of Michigan - Department of Mathematics

Marco De Innocentis


University of Leicester - Department of Mathematics

Sergei Levendorskii


University of Leicester - Department of Mathematics

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.

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


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Date posted: November 28, 2009  

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: http://ssrn.com/abstract=1514025 or http://dx.doi.org/10.2139/ssrn.1514025

Contact Information

Mitya Boyarchenko
University of Michigan - Department of Mathematics ( email )
530 Church Street
2074 East Hall
Ann Arbor, MI 48109
United States
Marco De Innocentis
University of Leicester - Department of Mathematics ( email )
University Road
Leicester, LE1 7RG
United Kingdom
Sergei Z. Levendorskii (Contact Author)
University of Leicester - Department of Mathematics ( email )
University Road
Leicester, TX LE1 7RH
United Kingdom
+44(0)1162231794 (Phone)
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