Statistically consistent term structures have affine geometry

TL;DR

This paper demonstrates that finite-dimensional models for energy futures yield curves, which are arbitrage-free and modeled by diffusions, inherently possess an affine geometric structure.

Contribution

It establishes that the set of yield curves compatible with arbitrage-free diffusion models must have an affine geometry, linking geometric structure to financial modeling constraints.

Findings

Yield curve models must have affine geometry for arbitrage-free diffusion compatibility.

Finite-dimensional yield curve sets are constrained by arbitrage conditions.

Affine geometry ensures consistent estimation of yield curve dynamics.

Abstract

This paper is concerned with finite dimensional models for the entire term structure for energy futures. As soon as a finite dimensional set of possible yield curves is chosen, one likes to estimate the dynamic behaviour of the yield curve evolution from data. The estimated model should be free of arbitrage which is known to result in some drift condition. If the yield curve evolution is modelled by a diffusion, then this leaves the diffusion coefficient open for estimation. From a practical perspective, this requires that the chosen set of possible yield curves is compatible with any obtained diffusion coefficient. In this paper, we show that this compatibility enforces an affine geometry of the set of possible yield curves.