The Tractable 'Quadratic' Class of Growth and Interest Rate Processes

31 Pages Posted: 13 Jun 2006

See all articles by Xavier Gabaix

Xavier Gabaix

Harvard University - Department of Economics; National Bureau of Economic Research (NBER); Centre for Economic Policy Research (CEPR); European Corporate Governance Institute (ECGI)

Date Written: June 8, 2006

Abstract

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, Perpetuity, Modified Gordon growth model, Yield curve, Interest rate processes, Stochastic Discount Factor, Quadratic processes

JEL Classification: G12, G13

Suggested Citation

Gabaix, Xavier, The Tractable 'Quadratic' Class of Growth and Interest Rate Processes (June 8, 2006). MIT Department of Economics Working Paper No. 06-17. Available at SSRN: https://ssrn.com/abstract=907867 or http://dx.doi.org/10.2139/ssrn.907867

Xavier Gabaix (Contact Author)

Harvard University - Department of Economics ( email )

Littauer Center
Cambridge, MA 02138
United States

National Bureau of Economic Research (NBER)

1050 Massachusetts Avenue
Cambridge, MA 02138
United States

Centre for Economic Policy Research (CEPR)

London
United Kingdom

European Corporate Governance Institute (ECGI)

c/o ECARES ULB CP 114
B-1050 Brussels
Belgium

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