Dimension-Invariant Dynamic Term Structures

Abstract

We model term structure dynamics using a recursive cascade of heterogeneously persistent factors. The cascade naturally orders the factors by their adjustment speeds, and generates smooth zero-coupon bond prices and forward curves in closed form. For a class of specifications, the number of parameters is invariant to the size of the state space, and the term structure converges to a stochastic limit as the number of factors goes to infinity. The cascade construction thereby defeats the curse of dimensionality associated with general affine models. Using a panel of interest rates, we estimate specifications with from one to 15 factors and only five parameters. High-dimensional versions of the model fit empirical yield curves almost perfectly in sample, with root mean squared errors of less than one basis point, while maintaining reasonable maximal Sharpe ratios. Out-of-sample interest rate forecasts significantly outperform prior benchmarks.