27 citations · 44 across the 8 of their papers we have counts for
8 papers
Path-dependent PDEs for volatility derivatives
Alexandre Pannier
We regard options on VIX and Realised Variance as solutions to path-dependent partial differential equations (PDEs) in a continuous stochastic volatility model. The modeling assump…
Rough volatility, path-dependent PDEs and weak rates of convergence
Ofelia Bonesini, Antoine Jacquier, Alexandre Pannier
In the setting of stochastic Volterra equations, and in particular rough volatility models, we show that conditional expectations are the unique classical solutions to path-depende…
On the large-time behaviour of affine Volterra processes
Antoine Jacquier, Alexandre Pannier, Konstantinos Spiliopoulos
We show the existence of a stationary measure for a class of multidimensional stochastic Volterra systems of affine type. These processes are in general not Markovian, a shortcomin…
Rough multifactor volatility for SPX and VIX options
Antoine Jacquier, Aitor Muguruza, Alexandre Pannier
We provide explicit small-time formulae for the at-the-money implied volatility, skew and curvature in a large class of models, including rough volatility models and their multi-fa…
Pathwise large deviations for white noise chaos expansions
Alexandre Pannier
We consider a family of continuous processes which are measurable with respect to a white noise measure, take values in the space of continuous…
Large and moderate deviations for stochastic Volterra systems
Antoine Jacquier, Alexandre Pannier
We provide a unified treatment of pathwise Large and Moderate deviations principles for a general class of multidimensional stochastic Volterra equations with singular kernels, not…
On the uniqueness of solutions of stochastic Volterra equations
Alexandre Pannier, Antoine Jacquier
We prove strong existence and uniqueness, and Hölder regularity, of a large class of stochastic Volterra equations, with singular kernels and non-Lipschitz diffusion coefficient. E…
Analytical approximation to the multidimensional Fokker--Planck equation with steady state
R. J. Martin, R. V. Craster, A. Pannier +1
The Fokker--Planck equation is a key ingredient of many models in physics, and related subjects, and arises in a diverse array of settings. Analytical solutions are limited to spec…