An Asset Pricing Approach to Testing General Term Structure Models including Heath-Jarrow-Morton Specifications and Affine Subclasses

We develop a new empirical approach to term structure analysis that allows testing for time-varying risk premia and for the absence of arbitrage opportunities based on the drift restriction within the Heath, Jarrow and Morton (1992) framework. As in the equity case, a zero intercept condition is tested, but in addition to the standard bilinear term in factor loadings and market prices of risk, the relevant mean restriction in the term structure case involves an additional nonlinear (quadratic) term in factor loadings. We estimate our general model using likelihood-based dynamic factor model techniques for a variety of volatility factors, and implement the relevant likelihood ratio tests. Our factor model estimates are similar across a general state space implementation and an alternative robust two-step principal components approach. The evidence favors time-varying market prices of risk. Most of the risk premium is associated with the slope factor, and individual risk prices depend on own past values, factor realizations, and past values of other risk prices, and are significantly related to the output gap, consumption, and the equity risk price. The absence of arbitrage opportunities is strongly rejected with one or two factors in the model, but not with three or more factors.