On the Relation between Linearity-Generating Processes and Linear-Rational Models
Mathematical Finance, Forthcoming
32 Pages Posted: 24 Mar 2016 Last revised: 13 Jun 2018
Date Written: June 5, 2018
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: Suggested Citation