Nearly Exact Bayesian Estimation of Non-Linear No-Arbitrage Term Structure Models

We propose a general method for the Bayesian estimation of nonlinear no-arbitrage term structure models. The main innovations we introduce are: 1) a computationally efficient method, based on deep learning techniques, for approximating no-arbitrage model-implied bond yields to any desired degree of accuracy; and 2) computational graph optimizations for accelerating the MCMC sampling of the model parameters and of the unobservable state variables that drive the short-term interest rate. We apply the proposed techniques for estimating a shadow rate model with a time-varying lower bound, in which the shadow rate can be driven by both spanned unobservable factors and unspanned macroeconomic factors