A. Ahdida and A. Alfonsi, Exact and high-order discretization schemes for wishart processes and their affine extensions, Annals of Applied Probabilities, vol.23, issue.3, pp.1025-1073, 2013.
URL : https://hal.archives-ouvertes.fr/hal-00491371

D. H. Ahn and B. Gao, A parametric nonlinear model of term structure dynamics, The Review of Financial Studies, vol.12, issue.4, pp.721-762, 1999.

A. Alfonsi, Affine Diffusions and Related Processes: Simulation, Theory and Applications, vol.6, 2015.

A. Alfonsi, A. Kebaier, R. , and C. , Maximum likelihood estimation for Wishart processes, Stochastic Processes and their Applications, vol.126, pp.3243-3282, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01184310

F. Antonelli and S. Scarlatti, Pricing options under stochastic volatility: a power series approach, Finance and Stochastics, vol.13, issue.2, pp.269-303, 2009.

R. Azencott, Densité des diffusions en temps petit: développements asymptotiques, Séminaire de Probabilités XVIII 1982/83, pp.402-498, 1984.

L. Bachelier, Théorie de la Spéculation, 1900.

O. E. Barndorff-nielsen, Processes of normal inverse Gaussian type, Finance and Stochastics, vol.2, issue.1, pp.41-68, 1997.

O. E. Barndorff-nielsen and N. Shephard, Non-Gaussian Ornstein-Uhlenbeck-based models and some of their uses in financial economics, Journal of the Royal Statistical Society: Series B (Statistical Methodology), vol.63, issue.2, pp.167-241, 2001.

D. S. Bates, Jumps and stochastic volatility: Exchange rate processes implicit in Deutsche mark options, The Review of Financial Studies, vol.9, issue.1, pp.69-107, 1996.

C. Bayer and P. Laurence, Asymptotics beats Monte-Carlo: The case of correlated local vol baskets, Communication on Pure and Applied Mathematics, vol.67, issue.10, pp.1618-1657, 2013.

C. Bayer and P. Laurence, Asymptotics for at the money local vol basket options, 2013.

D. Belomestny and J. Schoenmakers, A jump-diffusion Libor model and its robust calibration, Quantitative Finance, vol.11, issue.4, pp.529-546, 2011.

G. Ben-arous, Développement asymptotique du noyau de la chaleur hypoelliptique hors du cut-locus, Annales Scientifiques de l'École Normale Supérieure, vol.21, pp.307-331, 1988.

G. Ben-arous, Methode de Laplace et de la phase stationnaire sur l'espace de Wiener, Stochastics, vol.25, issue.3, pp.125-153, 1988.

A. Benabid, H. Bensusan, and N. Karoui, Wishart stochastic volatility: Asymptotic smile and numerical framework, 2008.
URL : https://hal.archives-ouvertes.fr/hal-00458014

E. Benhamou, E. Gobet, and M. Miri, Closed forms for european options in a local volatility model, 2008.

E. Benhamou, E. Gobet, and M. Miri, Smart expansion and fast calibration for jump diffusions, Finance and Stochastics, vol.13, issue.4, pp.563-589, 2009.

E. Benhamou, E. Gobet, and M. Miri, Time dependent Heston model, Society for Industrial and Applied Mathematics, vol.1, issue.1, pp.289-325, 2010.
URL : https://hal.archives-ouvertes.fr/hal-00370717

H. Berestycki, J. Busca, and I. Florent, Computing the implied volatility in stochastic volatility models, Communications on Pure and Applied Mathematics: A Journal Issued by the Courant Institute of Mathematical Sciences, vol.57, issue.10, pp.1352-1373, 2004.

J. Bismut, Large deviations and the Malliavin calculus. Progress in mathematics, 1984.

F. Black and M. Scholes, The pricing of options and corporate liabilities, Journal of Political Economy, vol.81, issue.3, pp.637-654, 1973.

N. Bleistein and R. A. Handelsman, Asymptotic Expansions of Integrals, 1975.

A. Brace, D. Gatarek, and M. Musiela, The market model of interest rate dynamics, Mathematical Finance, vol.7, issue.2, pp.127-155, 1997.

D. Brigo and F. Mercurio, Interest Rate Modelling -Theory and Practice, 2001.

M. F. Bru, Wishart processes, Journal of Theoretical Probability, vol.4, issue.4, pp.725-751, 1991.

P. Carr, H. Geman, D. B. Madan, Y. , and M. , The fine structure of asset returns: An empirical investigation, The Journal of Business, vol.75, issue.2, pp.305-332, 2002.

P. Carr, H. Geman, D. B. Madan, Y. , and M. , Pricing options on realized variance, Finance and Stochastics, vol.9, issue.4, pp.453-475, 2005.
URL : https://hal.archives-ouvertes.fr/hal-00101942

P. Carr, H. Geman, D. B. Madan, Y. , and M. , Self decomposability and option pricing, Mathematical Finance, vol.17, issue.1, pp.31-57, 2007.
URL : https://hal.archives-ouvertes.fr/hal-00128018

P. Carr and R. Lee, Robust replication of volatility derivatives, PRMIA award for best paper in derivatives, MFA Annual Meeting, 2008.

P. Carr and R. Lee, Volatility derivatives, Annual Review of Financial Economics, vol.1, issue.1, pp.319-339, 2009.

P. Carr and D. Madan, Option valuation using the fast Fourier transform, Journal of Computational Finance, vol.2, issue.4, pp.61-73, 1999.

P. Carr and J. Sun, A new approach for option pricing under stochastic volatility, Review of Derivatives Research, vol.10, issue.2, pp.87-150, 2007.

P. Carr and L. Wu, What type of process underlies options? a simple robust test, The Journal of Finance, vol.58, issue.6, pp.2581-2610, 2003.

A. Cern?, S. Denkl, and J. Kallsen, Hedging in Lévy models and the time step equivalent of jumps, 2013.

, Vix white paper, CBOE, 2018.

R. Cont and P. Tankov, Financial Modelling with Jump Processes, vol.2, 2004.
URL : https://hal.archives-ouvertes.fr/hal-00002693

J. C. Cox, The constant elasticity of variance option pricing model, The Journal of Portfolio Management, vol.23, issue.5, pp.15-17, 1996.

J. C. Cox, J. E. Ingersoll, and S. A. Ross, An intertemporal general equilibrium model of asset prices, Econometrica, pp.363-384, 1985.

C. Cuchiero, D. Filipovi?, E. Mayerhofer, and J. Teichmann, Affine processes on positive semidefinite matrices, The Annals of Applied Probability, vol.21, pp.397-463, 2011.

J. Da-fonseca, M. Grasselli, and C. Tebaldi, Option pricing when correlations are stochastic: An analytical framework, Review of Derivatives Research, vol.10, issue.2, pp.151-180, 2007.

J. Da-fonseca, M. Grasselli, and C. Tebaldi, A multifactor volatility Heston model, Quantitative Finance, vol.8, issue.6, pp.591-604, 2008.

R. C. Dalang, A. Morton, and W. Willinger, Equivalent martingale measures and no-arbitrage in stochastic securities market models, Stochastics: An International Journal of Probability and Stochastic Processes, vol.29, issue.2, pp.185-201, 1990.

C. De-franco, Two Studies in Risk Management: Portfolio Insurance under Risk Measure Constraint and Quadratic Hedge for Jump Processes, 2012.
URL : https://hal.archives-ouvertes.fr/tel-00708397

A. Dembo and O. Zeitouni, Large Deviations Techniques and Applications, Application of Mathematics, 1998.

J. D. Deuschel, P. K. Friz, A. Jacquier, V. , and S. , Marginal density expansions for diffusions and stochastic volatility I: Theoretical foundations, Communications on Pure and Applied Mathematics, vol.67, issue.1, pp.40-82, 2014.

J. D. Deuschel, P. K. Friz, A. Jacquier, V. , and S. , Marginal density expansions for diffusions and stochastic volatility II: Applications, Communications on Pure and Applied Mathematics, vol.67, issue.2, pp.321-350, 2014.

G. G. Drimus, Options on realized variance by transform methods: a non-affine stochastic volatility model, Quantitative Finance, vol.12, issue.11, pp.1679-1694, 2012.

D. Duffie, D. Filipovic, and W. Schachermayer, Affine processes and applications in finance, The Annals of Applied Probability, vol.13, issue.3, pp.984-1053, 2003.

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.

B. Dupire, Pricing with a smile, Risk, vol.7, issue.1, 1994.

P. Dupuis and H. Wang, Importance sampling, large deviations, and differential games, Stochastics: An International Journal of Probability and Stochastic Processes, vol.76, pp.481-508, 2004.

E. Eberlein and W. Kluge, Calibration of Lévy term structure models, Advances in Mathematical Finance, pp.147-172, 2007.

E. Eberlein and F. Andözkan, The Lévy Libor model, Finance and Stochastics, vol.9, issue.3, pp.327-348, 2005.

M. Forde and A. Jacquier, Small-time asymptotics for implied volatility under the Heston model, International Journal of Theoretical and Applied Finance, vol.12, issue.06, pp.861-876, 2009.

M. Forde and A. Jacquier, The large-maturity smile for the Heston model, Finance and Stochastics, vol.15, issue.4, pp.755-780, 2011.

M. Forde and A. Jacquier, Small-time asymptotics for an uncorrelated local-stochastic volatility model, Applied Mathematical Finance, vol.18, issue.6, pp.517-535, 2011.

J. P. Fouque, G. Papanicolaou, and R. Sircar, Derivatives in Financial Markets with Stochastic Volatility, 2000.

J. P. Fouque, G. Papanicolaou, R. Sircar, and K. Solna, Multiscale stochastic volatility asymptotics. Multiscale Modeling & Simulation, vol.2, pp.22-42, 2003.

M. I. Freidlin and A. D. Wentzell, Random Perturbations of Dynamical Systems, 2012.

N. Frikha and A. Kohatsu-higa, A parametrix approach for asymptotic expansion of markov semigroups with applications to multidimensional diffusion processes, 2016.

D. Gatarek, Libor market model with stochastic volatility, 2003.

J. Gatheral, E. P. Hsu, P. Laurence, C. Ouyang, and T. H. Wang, Asymptotics of implied volatility in local volatility models, Mathematical Finance, vol.22, issue.4, pp.591-620, 2012.

A. Genin and P. Tankov, Optimal importance sampling for Lévy processes, 2016.

P. Glasserman, P. Heidelberger, and P. Shahabuddin, Asymptotically optimal importance sampling and stratification for pricing pathdependent options, Mathematical Finance, vol.9, issue.2, pp.117-152, 1999.

P. Glasserman and S. G. Kou, The term structure of simple forward rates with jump risk, Mathematical Finance, vol.13, issue.3, pp.383-410, 2003.

A. Gombani and W. J. Runggaldier, A filtering approach to pricing in multifactor term structure models, International Journal of Theoretical and Applied Finance, vol.4, issue.2, pp.303-320, 2001.

C. Gourieroux and R. Sufana, Derivative pricing with multivariate stochastic volatility: Application to credit risk, Les Cahiers du CREF of HEC Montréal, 2004.

Z. Grbac, D. Krief, and P. Tankov, Long-time trajectorial large deviations for affine stochastic volatility models and application to variance reduction for option pricing, 2018.

Z. Grbac and W. J. Runggaldier, Interest Rate Modeling: Post-Crisis Challenges and Approaches, 2015.
URL : https://hal.archives-ouvertes.fr/hal-01485724

P. Guasoni and S. Robertson, Optimal importance sampling with explicit formulas in continuous time, Finance and Stochastics, vol.12, issue.1, pp.1-19, 2008.

A. Gulisashvili and E. M. Stein, Asymptotic behavior of the stock price distribution density and implied volatility in stochastic volatility models, Applied Mathematics and Optimization, vol.61, issue.3, pp.287-315, 2010.

P. Hagan and A. Lesniewski, Libor market model with SABR style stochastic volatility, p.32, 2008.

P. S. Hagan, D. Kumar, A. S. Lesniewski, and D. E. Woodward, Managing smile risk, The Best of Wilmott, vol.1, pp.249-296, 2002.

P. S. Hagan and D. E. Woodward, Equivalent Black volatilities, Applied Mathematical Finance, vol.6, issue.3, pp.147-157, 1999.

D. Heath, R. Jarrow, M. , and A. , Bond pricing and the term structure of interest rates: A new methodology for contingent claims valuation, Econometrica, vol.60, issue.1, pp.77-105, 1992.

P. Henry-labordère, Analysis, Geometry and Modeling in Finance: Advanced Methods in Option Pricing, 2008.

P. Henry-labordere, Model-free Hedging: A Martingale Optimal Transport Viewpoint, 2017.

S. L. Heston, A closed-form solutions for options with stochastic volatility with applications to bond and currency options, Review of Financial Studies, vol.6, issue.2, pp.327-343, 1993.

P. Jäckel and R. Rebonato, The link between caplet and swaption volatilities in a Brace-Gatarek-Musiela/Jamshidian framework: approximate solutions and empirical evidence, Journal of Computational Finance, vol.6, issue.4, pp.41-60, 2003.

J. Jacod and A. Shiryaev, Limit Theorems for Stochastic Processes, vol.288, 2003.

A. Jacquier and M. Keller-ressel, Implied volatility in strict local martingale models, SIAM Journal on Financial Mathematics, vol.9, issue.1, pp.171-189, 2018.

A. Jacquier, M. Keller-ressel, and A. Mijatovi?, Large deviations and stochastic volatility with jumps: asymptotic implied volatility for affine models, Stochastics: An International Journal of Probability and Stochastic Processes, vol.85, issue.2, pp.321-345, 2013.

A. Jacquier and M. Lorig, From characteristic functions to implied volatility expansions, Advances in Applied Probability, vol.47, issue.3, pp.837-857, 2015.

A. Jacquier and A. Mijatovi?, Large deviations for the extended Heston model: the large-time case, Asia-Pacific Financial Markets, vol.21, issue.3, pp.263-280, 2014.

B. Jourdain and J. Lelong, Robust adaptive importance sampling for normal random vectors, The Annals of Applied Probability, vol.19, issue.5, pp.1687-1718, 2009.
URL : https://hal.archives-ouvertes.fr/hal-00334697

V. Jurdjevic, Geometric Control Theory, vol.52, 1997.

J. Kallsen, A didactic note on affine stochastic volatility models, pp.343-368, 2006.

J. Kallsen, J. Muhle-karbe, and M. Voß, Pricing options on variance in affine stochastic volatility models, Mathematical Finance, vol.21, issue.4, pp.627-641, 2011.

M. Keller-ressel, Moment explosions and long-term behavior of affine stochastic volatility models, Mathematical Finance, vol.21, issue.1, pp.73-98, 2011.

M. Keller-ressel and J. Muhle-karbe, Asymptotic and exact pricing of options on variance, Finance and Stochastics, vol.17, issue.1, pp.107-133, 2013.

W. Kluge, Time-Inhomogeneous Lévy Processes in Interest Rate and Credit Risk Models, 2005.

A. Kohatsu-higa and P. Tankov, Jump-adapted discretization schemes for Lévy-driven SDEs, Stochastic Processes and their Applications, vol.120, pp.2258-2285, 2010.

S. G. Kou, A jump-diffusion model for option pricing, Management Science, vol.48, issue.8, pp.1086-1101, 2002.

N. Kunitomo and A. Takahashi, The asymptotic expansion approach to the valuation of interest rate contingent claims, 1995.

N. Kunitomo and A. Takahashi, The asymptotic expansion approach to the valuation of interest rate contingent claims, Mathematical Finance, vol.11, issue.1, pp.117-151, 2001.

N. Kunitomo and A. Takahashi, On validity of the asymptotic expansion approach in contingent claim analysis, The Annals of Applied Probability, vol.13, issue.3, pp.914-952, 2003.

R. Léandre, Minoration en temps petit de la densité d'une diffusion dégénérée, Journal of Functional Analysis, vol.74, issue.2, pp.399-414, 1987.

R. W. Lee, Implied and local volatilities under stochastic volatility, International Journal of Theoretical and Applied Finance, vol.4, issue.1, pp.45-89, 2001.

C. Léonard, Large deviations for Poisson random measures and processes with independent increments. Stochastic Processes and their Applications, vol.85, pp.93-121, 2000.

B. Mandelbrot, The variation of certain speculative prices, The Journal of Business, vol.36, issue.4, pp.394-419, 1963.

C. Ménassé and P. Tankov, Asymptotic indifference pricing in exponential Lévy models, 2015.

R. C. Merton, Theory of rational option pricing. The Bell Journal of economics and management science, pp.141-183, 1973.

R. C. Merton, Option pricing when underlying stock returns are discontinuous, Journal of financial economics, vol.3, issue.1-2, pp.125-144, 1976.

K. R. Miltersen, K. Sandmann, and D. Sondermann, Closed form term structure derivatives in a Heath-Jarrow-Morton model with lognormal annually compounded interest rates, Proceedings of the Seventh Annual European Futures Research Symposium, 1994.

K. R. Miltersen, K. Sandmann, and D. Sondermann, Closed form solutions for term structure derivatives with log-normal interest rates, The Journal of Finance, vol.52, issue.1, pp.409-430, 1997.

S. A. Mol?anov, Diffusion processes and riemannian geometry. Russian Mathematical Surveys, vol.30, pp.1-63, 1975.

D. Nualart, The Malliavin Calculus and Related Topics, 1995.

L. S. Ornstein and G. E. Uhlenbeck, On the theory of the brownian motion, Physical review, vol.36, issue.5, pp.823-841, 1930.

G. Papanicolaou, J. P. Fouque, K. Solna, and R. Sircar, Singular perturbations in option pricing, SIAM Journal on Applied Mathematics, vol.63, issue.5, pp.1648-1665, 2003.

A. Papapantoleon, J. Schoenmakers, and D. Skovmand, Efficient and accurate log-Lévy approximations to Lévy driven Libor models, Journal of Computational Finance, pp.1460-1559, 2011.

L. Paulot, Asymptotic implied volatility at the second order with application to the SABR model, pp.37-69, 2015.

V. Piterbarg, A stochastic volatility forward Libor model with a term structure of volatility smiles, 2003.

S. Robertson, Sample path large deviations and optimal importance sampling for stochastic volatility models, Stochastic Processes and their Applications, vol.120, pp.66-83, 2010.

R. T. Rockafellar, Convex Analysis, 1970.

R. T. Rockafellar, Integrals which are convex functionals, II. Pacific Journal of Mathematics, vol.39, issue.2, pp.439-469, 1971.

J. Schoenmakers, Robust Libor Modelling and Pricing of Derivative Products, Financial Mathematics Series, 2005.

A. Sepp, Pricing options on realized variance in the Heston model with jumps in returns and volatility, Journal of Computational Finance, vol.11, issue.4, pp.33-70, 2008.

K. Shiraya and A. Takahashi, Pricing average options on commodities, Journal of Futures Markets, vol.31, issue.5, pp.407-439, 2011.

K. Shiraya and A. Takahashi, Pricing multiasset cross-currency options, Journal of Futures Markets, vol.34, issue.1, pp.1-19, 2014.

K. Shiraya and A. Takahashi, An approximation formula for basket option prices under local stochastic volatility with jumps: An application to commodity markets, J. Computational Applied Mathematics, vol.292, pp.230-256, 2016.

K. Shiraya and A. Takahashi, An asymptotic expansion for localstochastic volatility with jump models, Stochastics, vol.89, issue.1, pp.65-88, 2017.

K. Shiraya and A. Takahashi, Pricing average and spread options under local-stochastic volatility jump-diffusion models online appendix, 2017.

D. Siegmund, Importance sampling in the Monte Carlo study of sequential tests, The Annals of Statistics, vol.4, issue.4, pp.673-684, 1976.

R. Sircar and G. C. Papanicolaou, Stochastic volatility, smile & asymptotics, Applied Mathematical Finance, vol.6, pp.107-145, 1999.

E. M. Stein and J. C. Stein, Stock price distributions with stochastic volatility: an analytic approach. The review of financial studies, vol.4, pp.727-752, 1991.

A. Takahashi, An asymptotic expansion approach to pricing financial contingent claims, Asia-Pacific Financial Markets, vol.6, issue.2, pp.115-151, 1999.

M. R. Tehranchi, Asymptotics of implied volatility far from maturity, Journal of Applied Probability, vol.46, issue.3, pp.629-650, 2009.

S. R. Varadhan, Diffusion processes in a small time interval, Communications on Pure and Applied Mathematics, vol.20, issue.4, pp.659-685, 1967.

S. R. Varadhan, On the behavior of the fundamental solution of the heat equation with variable coefficients, Communications on Pure and Applied Mathematics, vol.20, issue.2, pp.431-455, 1967.

O. Vasicek, An equilibrium characterization of the term structure, Journal of Financial Economics, vol.5, pp.177-188, 1977.

S. Watanabe, Analysis of Wiener functionals (Malliavin calculus) and its applications to heat kernels, The Annals of Probability, pp.1-39, 1987.

M. Widdicks, P. W. Duck, A. D. Andricopoulos, and D. P. Newton, The Black-Scholes equation revisited: Asymptotic expansions and singular perturbations, Mathematical Finance, vol.15, issue.2, pp.373-391, 2005.