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M. Bibliographie, R. Avellaneda, C. Buff, N. Friedman, L. Grandchamp et al., Weighted Monte Carlo: a new technique for calibrating asset-pricing models, Int. J. Theor. Appl. Finance, vol.4, pp.91-119, 2001.

O. E. Barndorff-nielsen and N. Shephard, Econometric analysis of realized volatility and its use in estimating stochastic volatility models, Journal of the Royal Statistical Society: Series B (Statistical Methodology), vol.4, issue.2, pp.253-280, 2002.
DOI : 10.1111/1467-9868.00336

D. Bates, Jumps and stochastic volatility: the exchange rate processes implicit in Deutschemark options, Rev. Fin. Studies, vol.9, pp.69-107, 1996.
DOI : 10.3386/w4596

D. S. Bates, Testing option pricing models, in Statistical Methods in Finance, of Handbook of Statistics, pp.567-611, 1996.

A. Ben-haj-yedder, Calibration of stochastic volatility model with jumps. A computer program, part of Premia software, 2004.

H. Berestycki, J. Busca, and I. Florent, Asymptotics and calibration of local volatility models, Quantitative Finance, vol.4, issue.1, pp.61-69, 2002.
DOI : 10.1002/cpa.3160450103

T. Bollerslev, Generalized autoregressive conditional heteroskedasticity, Journal of Econometrics, vol.31, issue.3, pp.31-307, 1986.
DOI : 10.1016/0304-4076(86)90063-1

D. Breeden and R. Litzenberger, Prices of State-Contingent Claims Implicit in Option Prices, The Journal of Business, vol.51, issue.4, pp.621-651, 1978.
DOI : 10.1086/296025

M. Broadie and O. Kaya, Exact simulation of stochastic volatility and other affine jump diffusion processes. Discussion paper

R. Byrd, P. Lu, and J. Nocedal, A Limited Memory Algorithm for Bound Constrained Optimization, SIAM Journal on Scientific Computing, vol.16, issue.5, pp.1190-1208, 1995.
DOI : 10.1137/0916069

P. Carr and D. Madan, Towards a Theory of Volatility Trading, 1998.
DOI : 10.1017/CBO9780511569708.013

T. F. Coleman, Y. Lee, and A. Verna, Reconstructing the unknown local volatility function, The Journal of Computational Finance, vol.2, issue.3, pp.77-102, 1999.
DOI : 10.21314/JCF.1999.027

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 P. Tankov, Non-parametric calibration of jump???diffusion option pricing models, The Journal of Computational Finance, vol.7, issue.3, pp.1-49, 2004.
DOI : 10.21314/JCF.2004.123

R. Cont and P. Tankov, Retrieving L??vy Processes from Option Prices: Regularization of an Ill-posed Inverse Problem, SIAM Journal on Control and Optimization, vol.45, issue.1, pp.1-25, 2006.
DOI : 10.1137/040616267

R. Cont and E. Voltchkova, Integro-differential equations for option prices in exponential L??vy models, Finance and Stochastics, vol.9, issue.3, pp.299-325, 2005.
DOI : 10.1007/s00780-005-0153-z

J. W. Cooley and J. W. Tukey, An algorithm for the machine calculation of complex Fourier series, Mathematics of Computation, vol.19, issue.90, pp.297-301, 1965.
DOI : 10.1090/S0025-5718-1965-0178586-1

J. C. Cox, The Constant Elasticity of Variance Option Pricing Model, The Journal of Portfolio Management, vol.23, issue.5, pp.15-17, 1996.
DOI : 10.3905/jpm.1996.015

J. C. Cox, J. E. Ingersoll, J. , and S. A. Ross, An Intertemporal General Equilibrium Model of Asset Prices, Econometrica, vol.53, issue.2, pp.53-363, 1985.
DOI : 10.2307/1911241

S. Crépey, Calibration of the local volatility in a trinomial tree using Tikhonov regularization, Inverse Problems, vol.19, issue.1, pp.91-127, 2003.
DOI : 10.1088/0266-5611/19/1/306

F. Delbaen and W. Schachermayer, The fundamental theorem of asset pricing for unbounded stochastic processes, Mathematische Annalen, vol.312, issue.2, pp.215-250, 1998.
DOI : 10.1007/s002080050220

E. Derman, Regimes of volatility, RISK, 1999.

E. Derman and I. Kani, Riding on a Smile, RISK, vol.7, pp.32-39, 1994.

E. Derman, I. Kani, and N. Chriss, Implied trinomial trees of the volatility smile, The Journal of Derivatives, 1996.

D. Duffie, D. Filipovic, and W. Schachermayer, Affine processes and applications in finance, Ann. Appl. Probab, vol.13, pp.984-1053, 2003.
DOI : 10.3386/t0281

D. Duffie, J. Pan, and K. Singleton, Transform analysis and asset pricing for affine jump-diffusions, Econometrica, pp.68-1343, 2000.
DOI : 10.2139/ssrn.157733
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.139.6955

B. Dupire, Pricing with a smile, pp.18-20, 1994.

N. Karoui, Couverture des risques dans les marchés financiers. Lecture notes for master 'Probability and Finance

R. F. Engle, Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation, Econometrica, vol.50, issue.4, pp.50-987, 1982.
DOI : 10.2307/1912773

P. Friz and S. Benhaim, Regular variation and smile asymptotics, Mathematical Finance

M. B. Garman and S. W. Kohlhagen, Foreign currency option values, Journal of International Money and Finance, vol.2, issue.3, pp.231-237, 1983.
DOI : 10.1016/S0261-5606(83)80001-1

J. Gatheral, The Volatility Surface: a Practitioner's Guide, 2006.
DOI : 10.1002/9781119202073

H. Geman, D. Madan, and M. Yor, Asset prices are Brownian motion: Only in business time, in Quantitative Analysis in Financial Markets, World Scientific, pp.103-146, 2001.

P. Glasserman, Monte Carlo Methods in Financial Engineering, 2003.
DOI : 10.1007/978-0-387-21617-1

T. Goll and J. Kallsen, Optimal portfolios for logarithmic utility, Stochastic Process, Appl, vol.89, pp.31-48, 2000.

P. S. Hagan and D. E. Woodward, Equivalent Black volatilities, Applied Mathematical Finance, vol.7, issue.3, 1998.
DOI : 10.1007/978-1-4757-4213-8

J. Harrison and D. Kreps, Martingales and arbitrage in multiperiod securities markets, Journal of Economic Theory, vol.20, issue.3, pp.381-408, 1979.
DOI : 10.1016/0022-0531(79)90043-7

T. Hayashi and P. A. Mykland, EVALUATING HEDGING ERRORS: AN ASYMPTOTIC APPROACH, Mathematical Finance, vol.80, issue.2, pp.309-343, 2005.
DOI : 10.1007/s004400050134

S. Heston, A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options, Review of Financial Studies, vol.6, issue.2, pp.327-343, 1993.
DOI : 10.1093/rfs/6.2.327

N. Jackson, E. Süli, and S. Howison, Computation of deterministic volatility surfaces, The Journal of Computational Finance, vol.2, issue.2, pp.5-32, 1999.
DOI : 10.21314/JCF.1998.022

M. Keller, Moment explosions and long-term behavior of affine stochastic volatility models, Forthcoming in Mathematical Finance, 2008.

H. J. Kushner and P. Dupuis, Numerical Methods for Stochastic Control Problems in Continuous Time, 2001.

R. Lagnado and S. Osher, A technique for calibrating derivative security pricing models: numerical solution of an inverse problem, The Journal of Computational Finance, vol.1, issue.1, p.1, 1997.
DOI : 10.21314/JCF.1997.002

R. Lee, THE MOMENT FORMULA FOR IMPLIED VOLATILITY AT EXTREME STRIKES, Mathematical Finance, vol.32, issue.4, pp.469-480, 2004.
DOI : 10.1287/mnsc.48.8.1086.166

R. Lord and C. Kahl, Complex logarithms in heston-like models Available at SSRN: http://ssrn, 2008.

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

D. Madan and M. Konikov, Option pricing using variance gamma Markov chains, Rev. Derivatives Research, vol.5, pp.81-115, 2002.

D. Madan and F. Milne, Option Pricing With V. G. Martingale Components, Mathematical Finance, vol.49, issue.4, pp.39-55, 1991.
DOI : 10.1016/0304-405X(87)90009-2

A. Medvedev and O. Scaillet, A Simple Calibration Procedure of Stochastic Volatility Models with Jumps by Short Term Asymptotics, SSRN Electronic Journal, 2004.
DOI : 10.2139/ssrn.477441

D. Nualart, The Malliavin Calculus and Related Topics, 1995.
DOI : 10.1007/978-1-4757-2437-0

P. Protter, Stochastic integration and differential equations, 1990.

M. Romano and N. Touzi, Contingent Claims and Market Completeness in a Stochastic Volatility Model, Mathematical Finance, vol.7, issue.4, pp.399-410, 1997.
DOI : 10.1111/1467-9965.00038

M. Rubinstein, Implied Binomial Trees, The Journal of Finance, vol.6, issue.3, pp.771-819, 1994.
DOI : 10.1111/j.1540-6261.1994.tb00079.x

K. Sato, Lévy Processes and Infinitely Divisible Distributions, 1999.

M. Stutzer, A Simple Nonparametric Approach to Derivative Security Valuation, The Journal of Finance, vol.27, issue.5, pp.1633-1652, 1996.
DOI : 10.1111/j.1540-6261.1996.tb05220.x

P. Tankov, Lévy Processes in Finance: Inverse Problems and Dependence Modelling, 2004.

R. Zhang, Couverture approchée des options Européennes, Ecole Nationale des Ponts et Chaussées, 1999.