# Existence of affine realizations for L\'evy term structure models

## TL;DR

This paper explores conditions under which affine realizations exist for Le9vy-driven term structure models, highlighting stricter volatility restrictions compared to diffusion models and examining special cases like constant direction volatilities.

## Contribution

It provides new insights into the existence of affine realizations in Le9vy models, extending classical results to jump processes with specific focus on volatility restrictions.

## Key findings

- Stricter volatility restrictions for Le9vy models compared to diffusion models
- Existence of affine realizations depends on specific volatility structures
- Analysis of short rate realizations in the context of Le9vy processes

## Abstract

We investigate the existence of affine realizations for term structure models driven by L\'evy processes. It turns out that we obtain more severe restrictions on the volatility than in the classical diffusion case without jumps. As special cases, we study constant direction volatilities and the existence of short rate realizations.