Empirical evidence suggests that fixed income markets exhibit unspanned stochastic volatility (USV), that is, that one cannot fully hedge volatility risk solely using a portfolio of bonds. While Collin-Dufresne and Goldstein (2002) showed that no two-factor Cox-Ingersoll-Ross (CIR) model can...

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...

We develop a comprehensive mathematical framework for polynomial jump-diffusions in a semimartingale context, which nest affine jump-diffusions and have broad applications in finance. We show that the polynomial property is preserved under polynomial transformations and Lévy time change. We...

Polynomial processes have the property that expectations of polynomial functions (of degree n, say) of the future state of the process conditional on the current state are given by polynomials (of degree n) of the current state. Here we explore the application of polynomial processes in the...

We introduce the class of linear-rational term structure models in which the state price density is modeled such that bond prices become linear-rational functions of the factors. This class is highly tractable with several distinct advantages: i) ensures nonnegative interest rates, ii) easily...

Aggregation is an often used tool in finance and macroeconomics, whereby economic equilibrium in a heterogeneous trader economy is characterized by means of the first order optimality conditions of a representative agent. In this paper we study the conditions under which a representative agent...