Y. Aît-sahalia and A. Lo, Nonparametric Estimation of State-Price Densities Implicit in Financial Asset Prices, The Journal of Finance, vol.51, issue.2, pp.499-547, 1998.
DOI : 10.1111/0022-1082.215228

Y. Aît-sahalia and A. Lo, Nonparametric risk management and implied risk aversion, Journal of Econometrics, vol.94, pp.9-51, 2000.
DOI : 10.3386/w6130

A. Badescu and R. Kulperger, GARCH option pricing: A semiparametric approach, Insurance: Mathematics and Economics, vol.43, issue.1, pp.69-84, 2007.
DOI : 10.1016/j.insmatheco.2007.09.011

G. Bakshi and N. Kapadia, Delta-Hedged Gains and the Negative Market Volatility Risk Premium, Review of Financial Studies, vol.16, issue.2, pp.527-566, 2003.
DOI : 10.1093/rfs/hhg002

G. Barone-adesi, R. Engle, and L. Mancini, A GARCH Option Pricing Model with Filtered Historical Simulation, Review of Financial Studies, vol.21, issue.3, pp.1223-1258, 2008.
DOI : 10.1093/rfs/hhn031

D. Bates, Jumps and Stochastic Volatility: Exchange Rate Processes Implicit in Deutsche Mark Options, Review of Financial Studies, vol.9, issue.1, pp.69-107, 1996.
DOI : 10.1093/rfs/9.1.69

F. Black and M. Scholes, The Pricing of Options and Corporate Liabilities, Journal of Political Economy, vol.81, issue.3, pp.637-659, 1973.
DOI : 10.1086/260062

N. Bollen and R. Whaley, What Determines the Shape of Implied Volatility Functions, Journal of Finance, 2003.

J. P. Bouchaud and M. Potters, Theory of Financial Risk and Derivative Pricing, 2003.
DOI : 10.1017/CBO9780511753893
URL : https://hal.archives-ouvertes.fr/hal-00121107

D. P. Brown and J. Jackwerth, The Pricing Kernel Puzzle: Reconciling Index Option Data and Economic Theory, 2001.
DOI : 10.1108/S1569-3759(2012)0000094009

G. Chacko, V. Luis, and M. , Spectral GMM estimation of continuous-time processes, Journal of Econometrics, vol.116, issue.1-2, pp.259-292, 2003.
DOI : 10.1016/S0304-4076(03)00109-X

J. Chevallier, F. Ielpo, and L. Mercier, Risk aversion and institutional information disclosure on the European carbon market: A case-study of the 2006 compliance event, Energy Policy, vol.37, issue.1, pp.15-28, 2006.
DOI : 10.1016/j.enpol.2008.07.030
URL : https://hal.archives-ouvertes.fr/hal-00992085

P. Christoffersen, S. Heston, and K. Jacobs, Option valuation with conditional skewness, Journal of Econometrics, vol.131, issue.1-2, pp.253-284, 2006.
DOI : 10.1016/j.jeconom.2005.01.010

P. Christoffersen, S. Heston, and K. Jacobs, A GARCH Option Model with Variance-Dependent Pricing Kernel, 2011.
DOI : 10.2139/ssrn.1538394

C. Chorro, D. Guégan, and F. Ielpo, Martingalized historical approach for option pricing, Finance Research Letters, vol.7, issue.1, pp.24-28, 2010.
DOI : 10.1016/j.frl.2009.11.002
URL : https://hal.archives-ouvertes.fr/halshs-00437927

C. Chorro, D. Guégan, and F. Ielpo, Option pricing for GARCH-type models with generalized hyperbolic innovations, Quantitative Finance, vol.8, issue.9, 2012.
DOI : 10.2307/2326626
URL : https://hal.archives-ouvertes.fr/hal-00511965

J. Coval and T. Shumway, Expected Option Returns, The Journal of Finance, vol.49, issue.3, pp.983-1009, 2001.
DOI : 10.1111/0022-1082.00352

Z. Ding, C. W. Granger, and R. F. Engle, A long memory property of stock market returns and a new model, Journal of Empirical Finance, vol.1, issue.1, pp.83-106, 1993.
DOI : 10.1016/0927-5398(93)90006-D

J. C. Duan, P. Ritchken, and Z. Sun, Jump Starting GARCH: Pricing Options with Jumps in Returns and Volatilities. Risk Management Institute WP 07-35, 2007.

J. C. Duan and J. G. Simonato, Empirical Martingale Simulation for Asset Prices, Management Science, vol.44, issue.9, pp.1218-1233, 1998.
DOI : 10.1287/mnsc.44.9.1218
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.196.1541

D. Duffie, J. Pan, and K. Singleton, Transform Analysis and Asset Pricing for Affine Jump-diffusions, Econometrica, vol.68, issue.6, pp.1343-1376, 2000.
DOI : 10.1111/1468-0262.00164
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.139.6955

E. Eberlein and K. Prause, The Generalized Hyperbolic Model: Financial Derivatives and Risk Measures, Mathematical Finance-Bachelier Congress, pp.245-267, 2000.
DOI : 10.1007/978-3-662-12429-1_12

R. Elliott and D. Madan, A Discrete Time Equivalent Martingale Measure, Mathematical Finance, vol.8, issue.2, pp.127-152, 1998.
DOI : 10.1111/1467-9965.00048
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.53.4656

T. Fujiwara and Y. Miyahara, The minimal entropy martingale measures for geometric L???vy processes, Finance and Stochastics, vol.7, issue.4, pp.509-531, 2003.
DOI : 10.1007/s007800200097

H. U. Gerber and S. W. Shiu, Abstract, Proceedings of the 4th AFIR International Colloqium, pp.659-689, 1994.
DOI : 10.1111/j.1540-6261.1987.tb02569.x

H. U. Gerber and S. W. Shiu, Option Pricing by Esscher Transforms, pp.99-191, 1994.

L. R. Glosten, R. Jagannathan, and D. E. Runkle, On the Relation between the Expected Value and the Volatility of the Nominal Excess Return on Stocks, The Journal of Finance, vol.25, issue.5, pp.1791-1801, 1993.
DOI : 10.1111/j.1540-6261.1993.tb05128.x

C. Gourieroux, A. Monfort, and A. Trognon, Pseudo Maximum Likelihood Methods: Applications to Poisson Models, Econometrica, vol.52, issue.3, pp.701-720, 1984.
DOI : 10.2307/1913472

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

J. Jackwerth, Recovering Risk Aversion from Option Prices and Realized Returns, Review of Financial Studies, vol.13, issue.2, pp.433-451, 2000.
DOI : 10.1093/rfs/13.2.433
URL : http://rfs.oxfordjournals.org/cgi/content/short/13/2/433

R. C. Merton, Theory of Rational Option Pricing, The Bell Journal of Economics and Management Science, vol.4, issue.1, pp.141-183, 1973.
DOI : 10.2307/3003143

R. C. 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

R. Michael and . Maria, Estimation of Jump-Diffusion Process vis Empirical Characteristic Function, FAME Research Paper Series 150, International Center for Financial Asset Management and Engineering, 2005.

Y. Miyahara and N. Moriwaki, Option Pricing Based on Geometric Stable Processes and Minimal Entropy Martingale Measures Recent Advances in Financial Engineering, World Sci. Publ, pp.119-133, 2009.
DOI : 10.1142/9789814273473_0007

D. B. Nelson, Conditional Heteroskedasticity in Asset Returns: A New Approach, Econometrica, vol.59, issue.2, pp.347-370, 1991.
DOI : 10.2307/2938260

J. V. Rosenberg and R. F. Engle, Empirical pricing kernels, Journal of Financial Economics, vol.64, issue.3, pp.341-372, 2002.
DOI : 10.1016/S0304-405X(02)00128-9
URL : http://archive.nyu.edu/bitstream/2451/26919/2/wpa99014.pdf

W. Schoutens, Lévy Processes in Finance: Pricing Financial Derivatives, 2003.
DOI : 10.1002/0470870230

N. Nig-gjr and . Nig-aparch, APARCH, Model (3)-EGARCH, Model (3)-GJR and Model (3)-APARCH under an exponential affine stochastic discount factor (also known as Esscher transform ESS) or under a minimal entropy martingal measure (MEMM) For example, NIG-EGARCH ESS means we use the model (1) with NIG innovation and EGARCH volatility model associated with an exponential affine stochastic discount factor. We put the minimal errors in bold face, These tables present the AARPE using the

N. Nig-gjr and . Nig-aparch, These tables present the AARPE using theAPARCH, Model (3)-EGARCH, Model (3)-GJR and Model (3)-APARCH under an exponential affine stochastic discount factor (also known as Esscher transform ESS) or under a minimal entropy martingal measure (MEMM) For example, NIG-EGARCH ESS means we use the model (1) with NIG innovation and EGARCH volatility model associated with an exponential affine stochastic discount factor, Table 11: Absolute Average Relative Pricing Errors (AARPE) for the S&P 500 index)-EGARCH, Model We put the minimal errors in bold face