Y. Achdou, B. Franchi, and N. Tchou, A partial differential equation connected to option pricing with stochastic volatility: Regularity results and discretization, Mathematics of Computation, vol.74, issue.251, pp.1291-1322, 2005.
DOI : 10.1090/S0025-5718-04-01714-4

URL : https://hal.archives-ouvertes.fr/hal-00019756

Y. Achdou and N. Tchou, Variational Analysis for the Black and Scholes Equation with Stochastic Volatility, ESAIM: Mathematical Modelling and Numerical Analysis, vol.36, issue.3, pp.373-395, 2002.
DOI : 10.1051/m2an:2002018

T. Aubin, A course in differential geometry, Graduate Studies in Mathematics, vol.27, 2001.
DOI : 10.1090/gsm/027

G. Barles, Convergence of numerical schemes for degenerate parabolic equations arising in finance theory, Numerical methods in finance, Publ. Newton Inst, vol.13, pp.1-21, 1997.

H. Brézis, Inéquations variationnelles paraboliques, Séminaire Jean Leray. 6. ,Probì emes unilatéraux, Journal de Mathématiques pures et appliquées, vol.51, pp.1-168, 1972.

S. Marco, C. Hillairet, and A. Jacquier, Shapes of implied volatility with positive mass at zero, ArXiv e-prints, 2013.

P. Gauthier and D. Possama¨?possama¨?, Efficient simulation of the double Heston model, Tech. report, SSRN working paper series, 2009.

Y. Haugazeau, Sur des inéquations variationnelles, C. R. Acad. Sci. Paris Sér. A-B, vol.265, pp.95-98, 1967.

S. L. 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, p.327343, 1993.
DOI : 10.1093/rfs/6.2.327

J. Lions and E. Magenes, Non-homogeneous boundary value problems and applications, 1972.
DOI : 10.1007/978-3-642-65161-8

P. Lions and M. Musiela, Correlations and bounds for stochastic volatility models, Annales de l'Institut Henri Poincare (C) Non Linear Analysis, vol.24, issue.1, pp.1-16, 2007.
DOI : 10.1016/j.anihpc.2005.05.007

URL : https://hal.archives-ouvertes.fr/hal-00667359

K. Jacobs, P. Christoffersen, and S. Heston, The shape and term structure of the index option smirk: Why multifactor stochastic volatility models work so well, Management Science, vol.55, issue.12, pp.1914-1932, 2009.