Second Order Expansion for Implied Volatility in Two Factor Local Stochastic Volatility Models and Applications to the Dynamic \lambda -Sabr Model

[1]  P. Henry-Labordère A General Asymptotic Implied Volatility for Stochastic Volatility Models , 2005, cond-mat/0504317.

[2]  Jan Obloj,et al.  Fine-tune your smile: Correction to Hagan et al , 2007, 0708.0998.

[3]  Elton P. Hsu,et al.  ASYMPTOTICS OF IMPLIED VOLATILITY IN LOCAL VOLATILITY MODELS , 2009 .

[4]  Antoine Jacquier,et al.  The large-maturity smile for the Heston model , 2011, Finance Stochastics.

[5]  Andrew Lesniewski,et al.  Probability Distribution in the SABR Model of Stochastic Volatility , 2015 .

[6]  Robert A. Jarrow,et al.  The Stop-Loss Start-Gain Paradox and Option Valuation: A New Decomposition into Intrinsic and Time Value , 1990 .

[7]  Option pricing with quadratic volatility: a revisit , 2011, Finance Stochastics.

[8]  Antoine Jacquier,et al.  Asymptotic formulae for implied volatility in the Heston model , 2009, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[9]  Jin Feng,et al.  Short-Maturity Asymptotics for a Fast Mean-Reverting Heston Stochastic Volatility Model , 2010, SIAM J. Financial Math..

[10]  Antoine Jacquier,et al.  Large Deviations and Asymptotic Methods in Finance , 2015 .

[11]  A. Jacquier,et al.  SMALL-TIME ASYMPTOTICS FOR IMPLIED VOLATILITY UNDER THE HESTON MODEL , 2009 .

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

[13]  Marc Yor,et al.  From Local Volatility to Local Levy Models , 2004 .

[14]  tballest Séminaire de probabilités , 2013 .

[15]  Louis Paulot,et al.  Asymptotic Implied Volatility at the Second Order with Application to the SABR Model , 2009, 0906.0658.

[16]  S. Varadhan On the behavior of the fundamental solution of the heat equation with variable coefficients , 2010 .

[17]  S. Orszag,et al.  Advanced Mathematical Methods For Scientists And Engineers , 1979 .

[18]  K. Yosida On the fundamental solution of the parabolic equation in a Riemannian space , 1953 .

[19]  E. Stein,et al.  Stock Price Distributions with Stochastic Volatility: An Analytic Approach , 1991 .

[20]  I. Holopainen Riemannian Geometry , 1927, Nature.

[21]  Alan L. Lewis Option Valuation Under Stochastic Volatility: With Mathematica Code , 2000 .

[22]  N. Touzi,et al.  Option Hedging And Implied Volatilities In A Stochastic Volatility Model , 1996 .

[23]  S. Minakshisundaram,et al.  Some Properties of the Eigenfunctions of The Laplace-Operator on Riemannian Manifolds , 1949, Canadian Journal of Mathematics.

[24]  O. Scaillet,et al.  Approximation and Calibration of Short-Term Implied Volatilities Under Jump-Diffusion Stochastic Volatility , 2006 .

[25]  I. Chavel Eigenvalues in Riemannian geometry , 1984 .

[26]  Antoine Jacquier,et al.  The Small-Time Smile and Term Structure of Implied Volatility under the Heston Model , 2012, SIAM J. Financial Math..

[27]  David S. Bates Jumps and Stochastic Volatility: Exchange Rate Processes Implicit in Thephlx Deutschemark Options , 1993 .

[28]  Akihiko Takahashi,et al.  The Asymptotic Expansion Approach to the Valuation of Interest Rate Contingent Claims , 2001 .

[29]  P. Hagan,et al.  Equivalent Black volatilities , 1999 .

[30]  Pierre Henry-Labordere,et al.  Solvable local and stochastic volatility models: supersymmetric methods in option pricing , 2005, cond-mat/0511028.

[31]  M. Berger,et al.  Le Spectre d'une Variete Riemannienne , 1971 .

[32]  Srinivasa Varadhan,et al.  Diffusion processes in a small time interval , 1967 .

[33]  I. Avramidi Heat Kernel and Quantum Gravity , 2000 .

[34]  Rama Cont Encyclopedia of quantitative finance , 2010 .

[35]  Henri Berestycki,et al.  Asymptotics and calibration of local volatility models , 2002 .

[36]  P. Bourgade,et al.  Heat Kernel Expansion for a Family of Stochastic Volatility Models: Delta-Geometry , 2005 .

[37]  P. Carr,et al.  Stochastic Skew in Currency Options , 2004 .

[38]  Jesper Andreasen,et al.  Jump-Diffusion Processes: Volatility Smile Fitting and Numerical Methods for Pricing , 1999 .

[39]  Akihiko Takahashi,et al.  Computation in an Asymptotic Expansion Method , 2009 .

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

[41]  E. Benhamou,et al.  Local Time for the SABR Model: Connection with the 'Complex' Black Scholes and Application to CMS and Spread Options , 2007 .

[42]  Stanislav Molchanov,et al.  DIFFUSION PROCESSES AND RIEMANNIAN GEOMETRY , 1975 .

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