An Affine Term Structure Model with Auxiliary Stochastic Volatility-Covolatility

This paper proposes an affine term structure model in a stochastic volatility setting. It provides a useful modeling tool to bridge the two strands of macroeconomic and finance research: the DSGE-VAR with stochastic volatility and the macro-finance model of term structure. In the model, the state vector follows a VAR; its innovations are conditional normal with a time-varying variance-covariance following a Wishart Autoregression process, which directly drives the risk price in the stochastic discount factor. In this setting, the yield curve under no-arbitrage is determined both by the state vector and its stochastic volatility-covolatility matrix. A DSGE-VAR with stochastic volatility can readily be cast into the state of this term structure model. Simulation of the baseline model shows that: 1) two factors are sufficient to fully reproduce all typical shapes of the yield curve; 2) volatility and covolatility has sizable effect on medium to long maturity yields; 3) volatility is a curvature factor of the yield curve, and the net effect of a multivariate variance-covariance matrix is also a curvature factor; 4) expected excess returns are explicitly linked to the volatility-covolatility of state innovations; 5) the model can well explain the bond yield "conundrum" in 2004-2005, where the long term interest rate remains low while short term rate keeps rising continuously.(Note: Earlier versions of this paper circulated as "A Macro-Finance Term Structure Model with Stochastic Volatility".)