Interest Rate Volatility and No-Arbitrage Affine Term Structure Models

Within the affine framework, many have observed a tension between matching conditional first and second moments in dynamic term structure models (DTSMs). Although the existence of this tension is generally accepted, less understood is the mechanism that underlies it. We show that no arbitrage along with the rich information in the cross section of yields has strong implications for both the dynamics of volatility and the forecasts of yields. We show that this link implied by the absence of arbitrage—and not the factor structure per se—underlies the tension between first and second moments found in the literature. Adding to recent research that has suggested that no-arbitrage restrictions are nearly irrelevant in Gaussian DTSMs, our results show that no-arbitrage restrictions are potentially relevant when there is stochastic volatility. This paper was accepted by Gustavo Manso, finance.

Information in the Term Structure: A Forecasting Perspective

The existing literature finds that information not captured by traditional term structure factors helps predict excess bond returns. When estimating no-arbitrage affine term structure models, aligning in-sample and out-of-sample objective functions results in term structure factors that capture information that remains hidden from existing approaches. Specifically, the estimates of the third term structure factor radically differ and are related to the fourth principal component, which helps forecast bond returns. The new objective function leads to substantial improvements in forecasting performance. It also results in higher model term premiums and lower expected future short rates. This paper was accepted by David Simchi-Levi, finance.

Deep Arbitrage-Free Learning in a Generalized HJM Framework via Arbitrage-Regularization

A regularization approach to model selection, within a generalized HJM framework, is introduced, which learns the closest arbitrage-free model to a prespecified factor model. This optimization problem is represented as the limit of a one-parameter family of computationally tractable penalized model selection tasks. General theoretical results are derived and then specialized to affine term-structure models where new types of arbitrage-free machine learning models for the forward-rate curve are estimated numerically and compared to classical short-rate and the dynamic Nelson-Siegel factor models.

Deep Arbitrage-Free Learning in a Generalized HJM Framework via Arbitrage-Regularization

A regularization approach to model selection, within a generalized HJM framework, is introduced which learns the closest arbitrage-free model to a prespecified factor model. This optimization problem is represented as the limit of a one-parameter family of computationally tractable penalized model selection tasks. General theoretical results are derived and then specialized to affine term-structure models where new types of arbitrage-free machine learning models for the forward-rate curve are estimated numerically and compared to classical short-rate and the dynamic Nelson-Siegel factor models.

PRINCIPAL-COMPONENT-BASED GAUSSIAN AFFINE TERM STRUCTURE MODELS: CONSTRAINTS AND THEIR FINANCIAL IMPLICATIONS

This work builds on the work by Joslin et al. [(2011) A new perspective on Gaussian dynamic term structure Models, The Review of Financial Studies 24, 926–970] on the affine dynamics of portfolios of yields and addresses the unresolved issues of ‘internal consistency’ mentioned in the same paper. It shows the unexpected constraints that have to be satisfied by the [Formula: see text]-measure evolution of the yield curve if the portfolio of yields has to be interpreted as their principal components. This choice of state variables is common in the recent literature and so our findings are intrinsically interesting. However, we show that our results also extend to a wide class of choices for state variables, when these are chosen as linear combinations of yields. We show that these constraints have important financial consequences, which, to our knowledge, have not been appreciated. In particular, this paper highlights some puzzling issues of compatibility between the [Formula: see text]- and [Formula: see text]-measure dynamics of Gaussian dynamic term structure models when principal components are chosen as state variables, once the constraints we derive are taken into account.