Non-parametric model calibration in finance

[1]  A. D. Sneyd,et al.  An alternating-direction implicit scheme for parabolic equations with mixed derivatives , 1988 .

[2]  Daoud S. Daoud,et al.  Overlapping Schwarz waveform relaxation method for the solution of the forward-backward heat equation , 2007 .

[3]  R. C. Merton,et al.  Theory of Rational Option Pricing , 2015, World Scientific Reference on Contingent Claims Analysis in Corporate Finance.

[4]  Nguyen Van Duc,et al.  Stability results for the heat equation backward in time , 2009 .

[5]  Houde Han,et al.  A non-overlap domain decomposition method for the forward-backward heat equation , 2003 .

[6]  S. Heston.  A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options , 1993 .

[7]  Carl Graham,et al.  McKean-Vlasov Ito-Skorohod equations, and nonlinear diffusions with discrete jump sets , 1992 .

[8]  Denis Talay,et al.  A STOCHASTIC PARTICLE METHOD WITH RANDOM WEIGHTS FOR THE COMPUTATION OF STATISTICAL SOLUTIONS OF MCKEAN-VLASOV EQUATIONS , 2001 .

[9]  J. Saut,et al.  Short-wave instabilities and ill-posed initial-value problems , 1990 .

[10]  J. Smoller.  Shock Waves and Reaction-Diffusion Equations , 1983 .

[11]  J. Douglas,et al.  A general formulation of alternating direction methods , 1964 .

[12]  Tadahisa Funaki,et al.  A certain class of diffusion processes associated with nonlinear parabolic equations , 1984 .

[13]  P. Lions,et al.  User’s guide to viscosity solutions of second order partial differential equations , 1992, math/9207212.

[14]  M. Schweizer,et al.  TERM STRUCTURES OF IMPLIED VOLATILITIES: ABSENCE OF ARBITRAGE AND EXISTENCE RESULTS , 2007 .

[15]  X. Mao,et al.  Stochastic Differential Equations and Applications , 1998 .

[16]  R. D. Richtmyer,et al.  Difference methods for initial-value problems , 1959 .

[17]  I. Gyöngy.  Mimicking the one-dimensional marginal distributions of processes having an ito differential , 1986 .

[18]  M. Kac.  Foundations of Kinetic Theory , 1956 .

[19]  A. Friedman.  Partial Differential Equations of Parabolic Type , 1983 .

[20]  Raphael Roux,et al.  Existence, uniqueness and convergence of a particle approximation for the Adaptive Biasing Force process , 2009 .

[21]  Nathael Alibaud,et al.  Existence, uniqueness and regularity for nonlinear parabolic equations with nonlocal terms , 2007 .

[22]  J. J. Douglas.  Alternating direction methods for three space variables , 1962 .

[23]  D. Lamberton,et al.  Introduction au calcul stochastique appliqué à la finance , 1997 .

[24]  G. Papanicolaou,et al.  Derivatives in Financial Markets with Stochastic Volatility , 2000 .

[25]  H. Berestycki,et al.  Computing the implied volatility in stochastic volatility models , 2004 .

[26]  Alan G. White,et al.  The Pricing of Options on Assets with Stochastic Volatilities , 1987 .

[27]  Olivier Alvarez,et al.  Viscosity solutions of nonlinear integro-differential equations , 1996 .

[28]  H. H. Rachford,et al.  On the numerical solution of heat conduction problems in two and three space variables , 1956 .

[29]  M. Hp.  A class of markov processes associated with nonlinear parabolic equations. , 1966 .

[30]  E. M. Lifshitz,et al.  Course in Theoretical Physics , 2013 .

[31]  A. Veretennikov,et al.  On Ergodic Measures for McKean-Vlasov Stochastic Equations , 2006 .

[32]  Amnon Pazy,et al.  Semigroups of Linear Operators and Applications to Partial Differential Equations , 1992, Applied Mathematical Sciences.

[33]  D. Gilbarg,et al.  Elliptic Partial Differential Equa-tions of Second Order , 1977 .

[34]  B. Jourdain,et al.  Nonlinear SDEs driven by L\'evy processes and related PDEs , 2007, 0707.2723.

[35]  D. Brigo,et al.  Parameterizing correlations: a geometric interpretation , 2007 .

[36]  R. D. Richtmyer,et al.  Survey of the stability of linear finite difference equations , 1956 .

[37]  F. Black,et al.  The Pricing of Options and Corporate Liabilities , 1973, Journal of Political Economy.

[38]  O. Ladyženskaja.  Linear and Quasilinear Equations of Parabolic Type , 1968 .

[39]  D. Heath,et al.  Bond Pricing and the Term Structure of Interest Rates: A Discrete Time Approximation , 1990, Journal of Financial and Quantitative Analysis.

[40]  W. Feller.  TWO SINGULAR DIFFUSION PROBLEMS , 1951 .

[41]  From Implied to Spot Volatilities , 2008 .

[42]  B. Jourdain,et al.  Coupling index and stocks , 2008, 0911.2834.

[43]  J. Hull.  Options, Futures, and Other Derivatives , 1989 .

[44]  F. Delbaen,et al.  A general version of the fundamental theorem of asset pricing , 1994 .

[45]  Benjamin Jourdain,et al.  Propagation of chaos and fluctuations for a moderate model with smooth initial data , 1998 .

[46]  Douglas T. Breeden,et al.  Prices of State-Contingent Claims Implicit in Option Prices , 1978 .

[47]  Frédéric Abergel,et al.  A nonlinear partial integro-differential equation from mathematical finance , 2010 .

[48]  Aurélien Alfonsi,et al.  Credit default swap calibration and derivatives pricing with the SSRD stochastic intensity model , 2005, Finance Stochastics.