The tractable "quadratic" class of growth and interest rate processes

Xavier Gabaix

We propose a new class of growth and interest rate processes with appealing properties for the paper-and-pencil theorist. It yields simple closed-form solutions for stocks, bonds, and perpetuities, and can accommodate an arbitrary number of factors. Expressions are linear in the state variables, such as the interest rate, the equity premium and the stock's growth rate. Surprisingly, one can change the volatility of the process, or force the interest rate to be positive, without changing bond prices. The process generalizes to discrete-time settings, and has a number of economic modeling applications. These include (i) macroeconomic situations with changing trend growth rates, (ii) asset pricing with time-varying risk premia or time-varying dividend growth rates, and (iii) yield curve analysis that allows flexibility and transparency. Keywords: Long term risk, Growth rate risk,...