On the Relation between Linearity-Generating Processes and Linear-Rational Models

Mathematical Finance, Forthcoming

Swiss Finance Institute Research Paper No. 16-23

32 Pages Posted: 24 Mar 2016 Last revised: 13 Jun 2018

See all articles by Damir Filipović

Damir Filipović

Ecole Polytechnique Fédérale de Lausanne; Swiss Finance Institute

Martin Larsson

ETH Zurich - Department of Mathematics

Anders B. Trolle

HEC Paris - Finance Department

Date Written: June 5, 2018

Abstract

We review the notion of a linearity-generating (LG) process introduced by Gabaix (2007) and relate LG processes to linear-rational (LR) models studied by Filipovic, Larsson, and Trolle (2017). We show that every LR model can be represented as an LG process and vice versa. We find that LR models have two basic properties which make them an important representation of LG processes. First, LR models can be easily specified and made consistent with nonnegative interest rates. Second, LR models go naturally with the long-term risk factorization due to Alvarez and Jermann (2005), Hansen and Scheinkman (2009), and Qin and Linetsky (2017). Every LG process under the long forward measure can be represented as a lower dimensional LR model.

Keywords: Linearity-Generating Process, Linear-Rational Model, Long-Term Risk, State Price Density

JEL Classification: C32, G12, G13

Suggested Citation

Filipovic, Damir and Larsson, Martin and Trolle, Anders B., On the Relation between Linearity-Generating Processes and Linear-Rational Models (June 5, 2018). Mathematical Finance, Forthcoming; Swiss Finance Institute Research Paper No. 16-23. Available at SSRN: https://ssrn.com/abstract=2753484 or http://dx.doi.org/10.2139/ssrn.2753484

Damir Filipovic (Contact Author)

Ecole Polytechnique Fédérale de Lausanne ( email )

Odyssea
Station 5
Lausanne, 1015
Switzerland

HOME PAGE: http://people.epfl.ch/damir.filipovic

Swiss Finance Institute

c/o University of Geneva
40, Bd du Pont-d'Arve
CH-1211 Geneva 4
Switzerland

Martin Larsson

ETH Zurich - Department of Mathematics ( email )

Ramistrasse 101
Zurich, 8092
Switzerland

HOME PAGE: http://math.ethz.ch/~larssonm

Anders B. Trolle

HEC Paris - Finance Department ( email )

France
+33 (0)1 39 67 98 70 (Phone)

HOME PAGE: http://sites.google.com/view/anderstrolle

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