Long-Term Factorization of Affine Pricing Kernels

TL;DR

This paper develops a theoretical framework for decomposing affine pricing kernels into long-term discounting and martingale components, explicitly identifying key factors and providing illustrative examples from asset pricing.

Contribution

It introduces a novel long-term factorization method for affine pricing kernels, linking eigenfunctions to Riccati ODE fixed points and explicitly deriving volatilities.

Findings

Explicit formulas for long bond volatility and martingale component volatility.

Identification of the eigenfunction as an exponential-affine function.

Application of the theory to various asset pricing models.

Abstract

This paper constructs and studies the long-term factorization of affine pricing kernels into discounting at the rate of return on the long bond and the martingale component that accomplishes the change of probability measure to the long forward measure. The principal eigenfunction of the affine pricing kernel germane to the long-term factorization is an exponential-affine function of the state vector with the coefficient vector identified with the fixed point of the Riccati ODE. The long bond volatility and the volatility of the martingale component are explicitly identified in terms of this fixed point. A range of examples from the asset pricing literature is provided to illustrate the theory.