Laboratoire de Mathématiques Raphaël Salem

UMR 6085 CNRS - University of Rouen Normandy

This talk illustrates the application of stochastic stability methods - such as couplings,
optimal transport, irreducibility, and Lyapunov techniques - in establishing a rigorous
mathematical framework for the ergodicity of affine processes in the modelling of stochastic
interest rates, default intensities, and stochastic volatility. Such ergodicity results are
shown to be crucial for the estimation of parameters in the mean-reversion regime of affine
processes.
In the second part of this talk we address an extension towards the recently emerged
class of rough volatility models, but also possible applications to electricity spot-price
modelling. Such rough models are characterized by sample paths of very low regularity
combined with a path-dependent structure (memory). In particular, affine rough models
turn out to be neither semimartingales nor Markov processes, which makes their study a
challenging mathematical task.