Affine-Quadratic Jump-Diffusion Term Structure Models

Abstract

In this paper, we propose a unifying affine-quadratic jump-diffusion framework for the term structure dynamics. The model incorporates both stochastic volatility and random jumps in the short rate process. In particular, we extend the existing models by explicitly modeling the jump intensity as a stochastic process. Using information from the treasury futures market, a GMM estimation approach is proposed for the risk-neutral process. A distinguishing feature of the approach is that the latent state variables are obtained, together with the model parameter estimates. The estimated latent state variables, namely the stochastic volatility and stochastic jump intensity, allow us to investigate the premia of various risk factors as well as underlying economic variables driving the term structure dynamics. Our empirical results suggest that the stochastic jump intensity significantly improves the model fit to the term structure dynamics. We identify a jump intensity negatively correlated with interest rate changes, a higher probability of positive jump than negative jump, and an on average larger size of negative jump than positive jump. We document a significant time-varying risk premium that is positively correlated with volatility.

Keywords: Affine, Quadratic, Jump-Diffusions, Term Structure, GMM

JEL Classification: G12