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The paper is devoted to the study of the short rate equation of the form $$dR(t)=F(R(t))dt+\sum_{i=1}^{d}G_i(R(t-))dZ_i(t), \quad R(0)=x\geq 0, \quad t>0,$$ with deterministic functions $F,G_1,...,G_d$ and independent L\'evyprocesses of infinite variation $Z_1,...,Z_d$ with regularly varying Laplaceexponents. The equation is supposed to have a nonnegative solution whichgenerates an affine term structure model. A precise form of the generator of$R$ is characterized and a related classification of equations which generateaffine models introduced in the spirit of Dai and Singleton\cite{DaiSingleton}. Each class is shown to have its own canonicalrepresentation which is an equation with the same drift and the jump diffusionpart based on a L\'evy process taking values in $\mathbb{R}^{g}, 1\leq g\leqd$, with independent coordinates being stable processes with stability indicesin the range $(1,2]$. Numerical calibration results of canonicalrepresentations to the market term structure of interest rates are presentedand compared with the classical CIR model. The paper generalizes the classicalresults on the CIR model from \cite{CIR}, as well as on its extended versionfrom \cite{BarskiZabczykCIR} and \cite{BarskiZabczyk} where $Z$ was aone-dimensional L\'evy process.

Classification and calibration of affine models driven by independent L\'evy processes