K. Amin, Jump Diffusion Option Valuation in Discrete Time, The Journal of Finance, vol.21, issue.5, pp.1833-1863, 1993.
DOI : 10.1111/j.1540-6261.1993.tb05130.x

O. E. Barndorff-nielsen, Processes of normal inverse Gaussian type, Processes of Normal Inverse Gaussian Type, pp.41-68, 1998.
DOI : 10.1007/s007800050032

O. E. Barndorff-nielsen and S. Levendorski?ilevendorski?levendorski?i, Feller processes of normal inverse Gaussian type, Feller Processes of Normal Inverse Gaussian type, pp.318-331, 2001.
DOI : 10.1088/1469-7688/1/3/303

M. Boyarchenko and S. Boyarchenko, Double Barrier Options in Regime-Switching Hyper-Exponential Jump-Diffusion Models Available at SSRN: http://ssrn, International Journal of Theoretical and Applied Finance, 2011.

S. I. Boyarchenko and S. Z. Levendorski?ilevendorski?levendorski?i, Generalizations of the Black-Scholes equation for truncated Lévy processes, 1999.

S. I. Boyarchenko and S. Z. Levendorski?ilevendorski?levendorski?i, OPTION PRICING FOR TRUNCATED L??VY PROCESSES, International Journal of Theoretical and Applied Finance, vol.03, issue.03, pp.549-552, 2000.
DOI : 10.1142/S0219024900000541

S. I. Boyarchenko and S. Z. Levendorski?ilevendorski?levendorski?i, Non-Gaussian Merton-Black-Scholes theory, World Scientific, vol.9, 2002.
DOI : 10.1142/4955

S. I. Boyarchenko and S. Z. Levendorski?ilevendorski?levendorski?i, American options: the EPV pricing model, Annals of Finance, vol.1, issue.3, pp.267-292, 2005.
DOI : 10.1007/s10436-004-0010-7

S. I. Boyarchenko and S. Z. Levendorski?ilevendorski?levendorski?i, Irreversible Decisions under Uncertainty (Optimal Stopping Made Easy) Series: Studies in Economic Theory, 2007.

A. Böttcer and B. Silbermann, Introduction to large truncated Toeplitz matrices, 1999.

P. Carr, Randomization and the American Put, Review of Financial Studies, vol.11, issue.3, pp.597-626, 1998.
DOI : 10.1093/rfs/11.3.597

P. Carr, H. Geman, D. B. Madan, and M. Yor, The Fine Structure of Asset Returns: An Empirical Investigation, The Journal of Business, vol.75, issue.2, pp.305-332, 2002.
DOI : 10.1086/338705

P. Carr and A. Hirsa, Why be backward?, Risk, vol.26, pp.103-107, 2003.

R. Cont and P. Tankov, Financial modelling with jump processes, 2004.
DOI : 10.1201/9780203485217
URL : https://hal.archives-ouvertes.fr/hal-00002693

R. Cont and E. Voltchkova, A Finite Difference Scheme for Option Pricing in Jump Diffusion and Exponential L??vy Models, SIAM Journal on Numerical Analysis, vol.43, issue.4, pp.1596-1626, 2005.
DOI : 10.1137/S0036142903436186

E. Eberlein and U. Keller, Hyperbolic Distributions in Finance, Bernoulli, vol.1, issue.3, pp.281-299, 1995.
DOI : 10.2307/3318481

E. Eberlein, U. Keller, and K. Prause, New Insights into Smile, Mispricing, and Value at Risk: The Hyperbolic Model, The Journal of Business, vol.71, issue.3, pp.371-406, 1998.
DOI : 10.1086/209749

G. Fusai, D. Marazzina, M. Marena, and M. Ng, -Transform and preconditioning techniques for option pricing, Quantitative Finance, vol.3, issue.4, p.15, 2011.
DOI : 10.1090/S0025-5718-03-01506-0
URL : https://hal.archives-ouvertes.fr/pasteur-00590982

A. Hirsa and D. B. Madan, Pricing American options under variance gamma, The Journal of Computational Finance, vol.7, issue.2, 2003.
DOI : 10.21314/JCF.2003.112

I. Koponen, Analytic approach to the problem of convergence of truncated L??vy flights towards the Gaussian stochastic process, Physical Review E, vol.52, issue.1, pp.1197-1199, 1995.
DOI : 10.1103/PhysRevE.52.1197

S. G. Kou, A Jump-Diffusion Model for Option Pricing, Management Science, vol.48, issue.8, pp.1086-1101, 2002.
DOI : 10.1287/mnsc.48.8.1086.166

S. G. Kou, Discrete barrier and lookback options, Financial Engineering. Handbooks in Operations Research and Management Science, pp.343-373, 2008.
DOI : 10.1016/s0927-0507(07)15008-8
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.601.9852

O. Kudryavtsev and S. Levendorski?ilevendorski?levendorski?i, Fast and accurate pricing of barrier options under L??vy processes, Finance and Stochastics, vol.10, issue.4, pp.531-562, 2009.
DOI : 10.1007/s00780-009-0103-2

S. Z. Levendorski?ilevendorski?levendorski?i, PRICING OF THE AMERICAN PUT UNDER L??VY PROCESSES, International Journal of Theoretical and Applied Finance, vol.07, issue.03, pp.303-335, 2004.
DOI : 10.1142/S0219024904002463

S. Levendorskii, O. Kudryavtsev, and V. Zherder, A Note on Relative Efficiency of Some Numerical Methods for Pricing of American Options Under Levy Processes, SSRN Electronic Journal, vol.9, issue.2, 2006.
DOI : 10.2139/ssrn.610542

A. Lipton, Assets with jumps, Risk, pp.149-153, 2002.

E. Lukacs, Characteristic functions, 1960.

R. Merton, Option pricing when underlying stock returns are discontinuous, Journal of Financial Economics, vol.3, issue.1-2, pp.125-144, 1976.
DOI : 10.1016/0304-405X(76)90022-2
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.139.5207

D. B. Madan, P. Carr, and E. C. Chang, The Variance Gamma Process and Option Pricing, Review of Finance, vol.2, issue.1, pp.79-105, 1998.
DOI : 10.1023/A:1009703431535

A. M. Matache, P. A. Nitsche, and C. Schwab, Wavelet Galerkin pricing of American options on L??vy driven assets, Quantitative Finance, vol.8, issue.4, pp.403-424, 2005.
DOI : 10.1142/9789812385192

W. Press, B. Flannery, S. Teukolsky, and W. Vetterling, Numerical recipes in C: The Art of Scientific Computing, 1992.

K. Sato, Lévy processes and infinitely divisible distributions, 1999.

W. Schoutens, Exotic options under L??vy models: An overview, Journal of Computational and Applied Mathematics, vol.189, issue.1-2, pp.526-538, 2006.
DOI : 10.1016/j.cam.2005.10.004
URL : http://doi.org/10.1016/j.cam.2005.10.004