Linearity-Inducing Processes: A Modelling Tool Yielding Closed Forms for Asset Prices

This methodological paper proposes a new class of stochastic processes with appealing properties for theoretical or empirical work in finance and macroeconomics, the “linearity-inducing” class. Its key property is that it yields simple exact closed-form expressions for stocks and bonds, with an arbitrary number of factors, feats that are not possible with the hitherto available modelling methods. It operates in discrete and continuous time. It has a number of economic modeling applications. These include macroeconomic situations with changing trend growth rates, or stochastic probability of disaster, asset pricing with stochastic risk premia or stochastic dividend growth rates, and yield curve analysis that allows flexibility and transparency. Many research questions may be addressed more simply and in closed form by using the linearity-inducing class. (JEL: G12, G13)