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I present a novel term structure model of interest rates in which mean reversion is induced through level-dependent conditional volatility. The model reconciles unit roots and cointegration with global stationarity and thus captures the extremely persistent but mean-reverting behavior of interest rates.
The paper emphasizes that the combination of unit roots and mean reversion is important for estimating reliable term premia. In a nutshell, the proposed model provides a solution to the persistence problem of affine term structure models: by failing to accomodate unit roots, stationary affine models assign almost all variation in long-term yields to term premia, which is inconsistent with survey data suggesting that term premia are stable. On the other hand, unit-root affine models rule out mean-reversion implying that term premia are close to constant contradicting vast evidence that the expectations hypothesis fails.
The key feature of my model is that it exhibits volatility-induced stationarity. Intuitively, large realizations of the process are followed by periods with large conditional variance. Thus, the stochastic term eventually dominates the unit-root conditional mean, which generates mean reversion. I introduce an approximation that enables analytical computation of model-implied bond yields. In an empirical application with cointegrated macro-finance risk factors, I show that (i) the short rate exhibits volatility-induced stationarity, which (ii) affects the long-run dynamics; (iii) term premia implied by the volatility-induced stationary model are economically plausible and consistent with survey forecasts; and (iv) the model improves out-of-sample forecasting performance compared to a Gaussian affine term structure model.
