A Note on the Relation Between Principal Components and Dynamic Factors in Affine Term Structure Models

Recent events have highlighted the potential importance of nonlinear efiects of flscal variables (notably debt and deflcits) on interest rates: While in times when government solvency is not a concern the standard crowding-out efiects are of moderate magnitude, in times when default risk becomes an issue the interest rate efiects can become very large. This paper provides new evidence on the magnitude of these efiects. For the case when default risk is not a concern, it uses an arbitrage-free term structure model to estimate the dynamic efiects of flscal policy shocks on interest rates along the entire maturity spectrum. For the case when default risk becomes a concern (thereby violating a central assumption of the term structure model), I present evidence based on EMU government bond spread regressions on time-varying efiects of national flscal policies on spreads as well as the time-varying sensitivity of yield spreads to international risk aversion as a function of the state of flscal policy. JEL classiflcation: E6, H6.

Dai and Singleton (2002) and Duffee (2002) show that there is a tension in affine term structure models between matching the mean and the volatility of interest rates. This article examines whether this tension can be solved by an alternative parametrization of the price of risk. The empirical evidence suggests that, first, the examined parametrization is not sufficient to solve the mean-volatility tension. Second, the usual result in the estimation of affine models, indicating that some of the state variables are extremely persistent, may have been caused by the lack of flexibility in the parametrization of the price of risk. Term structure models have several uses, including pricing fixed-income derivatives, managing the risk of fixed-income portfolios, and detecting relationships between the term structure of interest rates and macrovariables such as inflation and consumption. To perform well in these tasks, term structure models must be numerically and econometrically tractable while matching the empirical properties of the term structure movements. At least two empirical properties of the term structure of interest rates have been well established by financial economists over the years [see Dai and Singleton (2003) for a survey]. First, the term premium, or the expected excess return of Treasury bonds, has a high time variability. Second, the volatility of interest rates is time varying. These two properties are so prominent in the data that they will be referred to as stylized facts. While these two stylized facts are very well established in the empirical literature, affine term structure models are thoroughly discussed in the theoretical literature. Affine models are those in which the yield of zero coupon bonds are affine functions of the model state variables. Classic

With a Little Help from My Friends: Survey-Based Derivation of Euro Area Short Rate Expectations at the Effective Lower Bound

Existing results show that (i) lagged forward rates help predict bond returns and (ii) modern Markovian dynamic term structure models (DTSMs) cannot match the evidence [Cochrane JH, Piazzesi M (2005) Bond risk premia. Amer. Econom. Rev. 95(1):138–160]. We develop the family of conditional mean DTSMs where the dynamics depend on current yields and their history through a moving-average component. Our preferred conditional mean model combines one moving average with the usual three Gaussian risk factors, closely matches the bond risk premium measured from predictive regressions, and provides better forecasts of bond returns. Our framework nests Duffee’s models with a small “hidden” factor [Duffee G (2011) Information in (and not in) the term structure. Rev. Financial Stud. 24(9):2895–2934], and our results compare favorably with his five-factor model. Conditional mean models are easier to estimate than state-space term structure models based on Kalman estimates of latent factors. The online appendix is available at https://doi.org/10.1287/mnsc.2016.2602 . This paper was accepted by Lauren Cohen, finance.

Term Structure Estimation with Survey Data on Interest Rate Forecasts

The affine dynamic term structure model (DTSM) is the canonical empirical finance representation of the yield curve. However, the possibility that DTSM estimates may be distorted by small-sample bias has been largely ignored. We show that conventional estimates of DTSM coefficients are indeed severely biased, and this bias results in misleading estimates of expected future short-term interest rates and of long-maturity term premia. We provide a variety of bias-corrected estimates of affine DTSMs, both for maximally flexible and over-identified specifications. Our estimates imply short rate expectations and term premia that are more plausible from a macro-finance perspective.

Purpose: The aim of this study is to investigate the performance of forecasting the South African real spot rate curve using different mathematical term-structure models during the Covid-19 period. This study follows previous studies by Reid (2009) and Mashoene et al., 2021) where dynamic term-structure models performed well compared to static term-structure models over normal market conditions. For high volatility, normality often breaks, which might result in a need for recalibration in the currently used methodology or a total change in the methodology.
 Methodology: This study explores the dynamism of both dynamic term-structure models, which follow the Nelson-Siegel framework, and static term-structure models with the option of recalibration of model parameters to account for a change in macro-economic dynamics brought by the effect of the Covid-19 pandemic. The forecasting exercise was applied to term-structure models following the Nelson-Siegel framework using AR(1) process.
 Findings: The incorporation of macroeconomic factors performed poorly in estimating future model parameters. This could be attributable to the effect of global stress, which resulted in poor linear relationships between macroeconomic and financial factors. Recalibration process on static Nelson-Siegel term-structure models improved the models' performance, especially during the high volatility/period of total economic shutdown due to the Covid-19 pandemic.
 Implications: The application of static Nelson-Siegel term-structure models with recalibrated parameters might improve bond pricing processes and risk management strategies in emerging markets, especially during market stress.

This paper investigates the implications of mixtures of affine, quadratic, and nonlinear models for the term structure of volatility. The dynamics of the term structure of interest rates appear to exhibit pronounced time-varying or stochastic volatility. Ahn, Dittmar, and Gallant (2000) provide evidence suggesting that term structure models incorporating a set of quadratic state variables are better able to reproduce yield dynamics than affine models, though none of the models is able to fully capture the term structure of volatility. In this study, we combine affine, quadratic and nonlinear factors in order to maximize the strengths of a term structure model in generating heteroskedastic volatility. We show that this combination entails a tradeoff between specification of heteroskedastic volatility and correlations among the state variables. By combining these factors, we are able to gauge the cost of this tradeoff. Using the Efficient Method of Moments [Gallant and Tauchen (1996)], we find that augmenting a quadratic model with a nonlinear factor results in improvement in fit over a model characterized only by quadratic factors. Since the nonlinear factor is characterized by stronger dependence of volatility on the level of the factor, we conclude that flexibility in the specification of both level dependence and correlation structure are important for describing term structure dynamics.

An Arbitrage-Free Nelson-Siegel Term Structure Model with Stochastic Volatility for the Determination of Currency Risk Premia

The role of macroeconomic variables in sovereign risk

The downtrend in U.S. interest rates over the past two decades may partly reflect a decline in the longer-run equilibrium real rate of interest. We examine this issue using dynamic term structure models that account for time-varying term and liquidity risk premiums and are estimated directly from prices of individual inflation-indexed bonds. Our finance-based approach avoids two potential pitfalls of previous macroeconomic analyses: structural breaks at the zero lower bound and misspecification of output and inflation dynamics. We estimate that the longer-run equilibrium real rate has fallen about 2 percentage points and appears unlikely to rise quickly.

Global Evidence on Unspanned Macro Risks in Dynamic Term Structure Models

Survey-Based Daily Estimates of Inflation Expectations and Risk Premia in the Euro Area

Adaptive dynamic Nelson–Siegel term structure model with applications

Recent empirical research shows that a reasonable characterization of federal-funds-rate targeting behavior is that the change in the target rate depends on the maturity structure of interest rates and exhibits little dependence on lagged target rates. See, for example, Cochrane and Piazzesi (2002). The result echoes the policy rule used by (1994) to rationalize the empirical failure of the `expectations hypothesis' applied to the term- structure of interest rates. That is, rather than forward rates acting as unbiased predictors of future short rates, the historical evidence suggests that the correlation between forward rates and future short rates is surprisingly low. showed that a desire by the monetary authority to adjust short rates in response to exogenous shocks to the term premiums imbedded in long rates (i.e. yield-curve smoothing), along with a desire for smoothing interest rates across time, can generate term structures that account for the puzzling regression results of Fama and Bliss (1987). also clearly pointed out that this reduced-form approach to the policy rule, although naturally forward looking, needed to be studied further in the context of other response functions such as the now standard Taylor (1993) rule. We explore both the robustness of McCallum's result to endogenous models of the term premium and also its connections to the Taylor Rule. We model the term premium endogenously using two different models in the class of affine term structure models studied in Duffie and Kan (1996): a stochastic volatility model and a stochastic price-of- risk model. We then solve for equilibrium term structures in environments in which interest rate targeting follows a rule such as the one suggested by (i.e., the McCallum Rule). We demonstrate that McCallum's original result generalizes in a natural way to this broader class of models. To understand the connection to the Taylor Rule, we then consider two structural macroeconomic models which have reduced forms that correspond to the two affine models and provide a macroeconomic interpretation of abstract state variables (as in Ang and Piazzesi (2003)). Moreover, such structural models allow us to interpret the parameters of the term-structure model in terms of the parameters governing preferences, technologies, and policy rules. We show how a monetary policy rule will manifest itself in the equilibrium asset-pricing kernel and, hence, the equilibrium term structure. We then show how this policy can be implemented with an interest-rate targeting rule. This provides us with a set of restrictions under which the Taylor and Rules are equivalent in the sense if implementing the same monetary policy. We conclude with some numerical examples that explore the quantitative link between these two models of monetary policy.