Asymptotic behaviour of randomised fractional volatility models

[1]  Antoine Jacquier,et al.  Marginal Density Expansions for Diffusions and Stochastic Volatility II: Applications , 2014 .

[2]  Antoine Jacquier,et al.  Marginal Density Expansions for Diffusions and Stochastic Volatility I: Theoretical Foundations , 2011, 1111.2462.

[3]  M. Schilder,et al.  Some asymptotic formulas for Wiener integrals , 1966 .

[4]  D. Nualart,et al.  Large Deviations for a Class of Anticipating Stochastic Differential Equations , 1992 .

[5]  Scott Robertson Sample Path Large Deviations and Optimal Importance Sampling for Stochastic Volatility Models , 2010 .

[6]  The asymptotic smile of a multiscaling stochastic volatility model , 2015, 1501.03387.

[7]  Claude Martini,et al.  On VIX futures in the rough Bergomi model , 2017, 1701.04260.

[8]  F. Comte,et al.  Affine fractional stochastic volatility models , 2012 .

[9]  Hongzhong Zhang,et al.  Asymptotics for Rough Stochastic Volatility Models , 2017, SIAM J. Financial Math..

[10]  F. Comte,et al.  Long memory in continuous‐time stochastic volatility models , 1998 .

[11]  M. Mellouk A Large-Deviation Principle for Random Evolution Equations , 2000 .

[12]  Gérard Ben Arous,et al.  Methods de laplace et de la phase stationnaire sur l'espace de wiener , 1988 .

[13]  'Hot-Start' Initialization of the Heston Model , 2015 .

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

[15]  Kun Gao,et al.  Asymptotics of implied volatility to arbitrary order , 2011, Finance Stochastics.

[16]  R. Azencott,et al.  Grandes deviations et applications , 1980 .

[17]  I. Norros,et al.  An elementary approach to a Girsanov formula and other analytical results on fractional Brownian motions , 1999 .

[18]  Small-time kernel expansion for solutions of stochastic differential equations driven by fractional Brownian motions , 2010, 1005.3483.

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

[20]  Jim Gatheral,et al.  Pricing under rough volatility , 2015 .

[21]  D. Nualart,et al.  Large deviations for multiple Wiener-Itô integral processes , 1992 .

[22]  Antoine Jacquier,et al.  Asymptotics of Forward Implied Volatility , 2012, SIAM J. Financial Math..

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

[24]  Antoine Jacquier,et al.  The Randomized Heston Model , 2019, SIAM J. Financial Math..

[25]  Carol Bezuidenhout A Large Deviations Principle for Small Perturbations of Random Evolution Equations , 1987 .

[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]  Antoine Jacquier,et al.  Pathwise large deviations for the rough Bergomi model , 2017, Journal of Applied Probability.

[28]  Mathieu Rosenbaum,et al.  The microstructural foundations of leverage effect and rough volatility , 2018, Finance Stochastics.

[29]  A Large Deviation Principle for Stochastic Integrals , 2008 .

[30]  M. Fukasawa Short-time at-the-money skew and rough fractional volatility , 2015, 1501.06980.

[31]  Paolo Guasoni,et al.  Optimal importance sampling with explicit formulas in continuous time , 2007, Finance Stochastics.

[32]  Fabrice Baudoin,et al.  On Small Time Asymptotics for Rough Differential Equations Driven by Fractional Brownian Motions , 2014, 1403.0872.

[33]  Litan Yan,et al.  Some properties of the fractional Ornstein–Uhlenbeck process , 2008 .