Affine processes are regular

TL;DR

This paper proves that all stochastically continuous, time-homogeneous affine processes on certain state spaces are inherently regular, removing the need for this assumption in their analysis.

Contribution

It demonstrates that regularity automatically follows from stochastic continuity and affine properties, simplifying the theoretical framework for affine processes.

Findings

Regularity is guaranteed by stochastic continuity and affine structure.

The proof combines transformation semigroup differentiability with the moving frame method.

This result removes the regularity assumption from prior affine process theory.

Abstract

We show that stochastically continuous, time-homogeneous affine processes on the canonical state space $\Rplus^m \times \RR^n$ are always regular. In the paper of \citet{Duffie2003} regularity was used as a crucial basic assumption. It was left open whether this regularity condition is automatically satisfied, for stochastically continuous affine processes. We now show that the regularity assumption is indeed superfluous, since regularity follows from stochastic continuity and the exponentially affine behavior of the characteristic function. For the proof we combine classic results on the differentiability of transformation semigroups with the method of the moving frame which has been recently found to be useful in the theory of SPDEs.