Yield-factor volatility models

The term structure of interest rates is often summarized using a handful of yield factors that capture shifts in the shape of the yield curve. In this paper, we develop a comprehensive model for volatility dynamics in the level, slope, and curvature of the yield curve that simultaneously includes level and GARCH effects along with regime shifts. We show that the level of the short rate is useful in modeling the volatility of the three yield factors and that there are significant GARCH effects present even after including a level effect. Further, we find that allowing for regime shifts in the factor volatilities dramatically improves the model’s fit and strengthens the level effect. We also show that a regime-switching model with level and GARCH effects provides the best out-of-sample forecasting performance of yield volatility. We argue that the auxiliary models often used to estimate term structure models with simulation-based estimation techniques should be consistent with the main features of the yield curve that are identified by our model.     

Monetary policy regimes: Implications for the yield curve and bond pricing

We develop a multivariate dynamic term structure model, which takes into account the nonlinear (time-varying) relation between interest rates and the state of the economy. In contrast to the classical term structure literature, in which nonlinearities are captured by increasing the number of latent state variables or by latent regime shifts, in our no-arbitrage framework the regimes are governed by thresholds and are directly linked to economic fundamentals. Specifically, starting from a simple monetary policy model for the short rate, we introduce a parsimonious and tractable model for the yield curve, which takes into account the possibility of regime shifts in the behavior of the Federal Reserve. In our empirical analysis, we show the merit of our approach three dimensions: interpretable bond dynamics, accurate short end yield curve pricing, and yield curve implications.     

Multi-Factor Cox-Ingersoll-Ross Models of the Term Structure: Estimates and Tests from a Kalman Filter Model

This paper presents a method for estimating multi-factor versions of the Cox-Ingersoll-Ross (1985b) model of the term structure of interest rates. The fixed parameters in one, two, and three factor models are estimated by applying an approximate maximum likelihood estimator in a state-space model using data for the U.S. treasury market. A nonlinear Kalman filter is used to estimate the unobservable factors. Multi-factor models are necessary to characterize the changing shape of the yield curve over time, and the statistical tests support the case for two and three factor models. A three factor model would be able to incorporate random variation in short term interest rates, long term rates, and interest rate volatility.     

The Empirical Implications of the Cox,Ingersoll, Ross Theory of the Term Structure of Interest Rates

The one-factor version of the Cox, Ingersoll, and Ross model of the term structure is estimated using monthly quotes on U.S. Treasury issues trading from 1952 through 1983. Using data from a single yield curve, it is possible to estimate implied short and long term zero coupon rates and the implied variance of changes in short rates. Analysis of residuals points to a probable neglected tax effect.     

Macroeconomic Sources of Risk in the Term Structure

We develop a new way of modeling time variation in term premia, based on the stochastic discount factor model of asset pricing. The joint distribution of excess U.S. bond returns of different maturity and the observable fundamental macroeconomic factors is modeled using multivariate GARCH with conditional covariances in the mean to capture the term premia. By testing the assumption of no arbitrage we derive a specification test of our model. We estimate the contribution made to the term premia at different maturities through real and nominal sources of risk. From the estimated term premia we recover the term structure of interest rates and examine how it varies through time. Finally, we examine whether the reported failures of the rational expectations hypothesis can be attributed to an omitted time-varying term premium.     

The Term Structure of Real Rates and Expected Inflation

Changes in nominal interest rates must be due to either movements in real interest rates, expected inflation, or the inflation risk premium. We develop a term structure model with regime switches, time‐varying prices of risk, and inflation to identify these components of the nominal yield curve. We find that the unconditional real rate curve in the United States is fairly flat around 1.3%. In one real rate regime, the real term structure is steeply downward sloping. An inflation risk premium that increases with maturity fully accounts for the generally upward sloping nominal term structure.     

Can interest rate volatility be extracted from the cross section of bond yields?

Most affine models of the term structure with stochastic volatility predict that the variance of the short rate should play a ‘dual role’ in that it should also equal a linear combination of yields. However, we find that estimation of a standard affine three-factor model results in a variance state variable that, while instrumental in explaining the shape of the yield curve, is essentially unrelated to GARCH estimates of the quadratic variation of the spot rate process or to implied variances from options. We then investigate four-factor affine models. Of the models tested, only the model that exhibits ‘unspanned stochastic volatility’ (USV) generates both realistic short rate volatility estimates and a good cross-sectional fit. Our findings suggest that short rate volatility cannot be extracted from the cross-section of bond prices. In particular, short rate volatility and convexity are only weakly correlated.     

Nonlinear Drift And Stochastic Volatility: An Empirical Investigation Of Short-Term Interest Rate Models

In this article I provide new evidence on the role of nonlinear drift and stochastic volatility in interest rate modeling. I compare various model specifications for the short‐term interest rate using the data from five countries. I find that modeling the stochastic volatility in the short rate is far more important than specifying the shape of the drift function. The empirical support for nonlinear drift is weak with or without the stochastic volatility factor. Although a linear drift stochastic volatility model fits the international data well, I find that the level effect differs across countries.     

Uncertainty,Financial Frictions,and Nominal Rigidities: A Quantitative Investigation

Are uncertainty shocks a major source of business cycle fluctuations? This paper studies the effect of a mean preserving shock to the variance of aggregate total factor productivity (macro‐uncertainty) and to the dispersion of entrepreneurs' idiosyncratic productivity (micro‐uncertainty) in a financial accelerator dynamic stochastic general equilibrium model with sticky prices. It explores the different mechanisms through which uncertainty shocks are propagated and amplified. The time‐series properties of macro‐ and micro‐uncertainty are estimated using U.S. aggregate and firm‐level data, respectively. While surprise increases in micro‐uncertainty have a larger impact on total output than macro‐uncertainty, these can only account for a small (but nontrivial) share of output volatility.     

Multi-factor Affine Term Structure Model with Single Regime Shift: Real Term Structure under Zero Interest Rate

In this paper, we extend the one-factor, single regime shift, affine term structure model with time-dependent regime-shift probability to a multi-factor model. We model the nominal interest rate and the expected inflation rate, and estimate the term structure of the real interest rate in the Japanese government bond market using inflation-indexed bond data under zero interest rates. Incorporating the economic structure that the Bank of Japan terminates the zero interest rate when the expected inflation rate gets out of deflationary regime, we estimate the yield curve of the real interest rate for less than 10 years, consistent with the expectation of the market participants in the Japanese government bond market, where inflation-indexed bonds are traded for only around 10 years.     

Time‐Varying Asset Volatility and the Credit Spread Puzzle

Most extant structural credit risk models underestimate credit spreads—a shortcoming known as the credit spread puzzle. We consider a model with priced stochastic asset risk that is able to fit medium‐ to long‐term spreads. The model, augmented by jumps to help explain short‐term spreads, is estimated on firm‐level data and identifies significant asset variance risk premia. An important feature of the model is the significant time variation in risk premia induced by the uncertainty about asset risk. Various extensions are considered, among them optimal leverage and endogenous default.     

A Two-Factor Model for Low Interest Rate Regimes

This paper derives a two-factor model for the term structure of interest rates that segments the yield curve in a natural way. The first factor involves modelling a non-negative short rate process that primarily determines the early part of the yield curve and is obtained as a truncated Gaussian short rate. The second factor mainly influences the later part of the yield curve via the market index. The market index proxies the growth optimal portfolio (GOP) and is modelled as a squared Bessel process of dimension four. Although this setup can be applied to any interest rate environment, this study focuses on the difficult but important case where the short rate stays close to zero for a prolonged period of time. For the proposed model, an equivalent risk neutral martingale measure is neither possible nor required. Hence we use the benchmark approach where the GOP is chosen as numeraire. Fair derivative prices are then calculated via conditional expectations under the real world probability measure. Using this methodology we derive pricing functions for zero coupon bonds and options on zero coupon bonds. The proposed model naturally generates yield curve shapes commonly observed in the market. More importantly, the model replicates the key features of the interest rate cap market for economies with low interest rate regimes. In particular, the implied volatility term structure displays a consistent downward slope from extremely high levels of volatility together with a distinct negative skew. 1991 Mathematics Subject Classification: primary 90A12; secondary 60G30; 62P20 JEL Classification: G10, G13     

Reduced-form Models with Regime Switching: An Empirical Analysis for Corporate Bonds

Empirical evidence shows that there is a close link between regime shifts and business cycle fluctuations. A standard term structure of interest rates, such as the Cox et al. (1985 Econometrica, 53, 385–407; CIR) model, is sharply rejected in the Treasury bond data. Only Markov regime-switching models on the entire yield curve of the Treasury bond data can account for the observed behavior of the yield curve. In this paper, we examine the impact of regime shifts on AAA-rated and BBB-rated corporate bonds through the use of a reduced-form model. The model is estimated by the Efficient Method of Moments (EMM). Our empirical results suggest that regime-switching risk has significant implications for corporate bond prices and hence has a material impact on the entire corporate bond yield curve, providing evidence for the approach of rating through the cycle employed by rating agencies.     

MODELING THE TERM STRUCTURE FROM THE ON‐THE‐RUN TREASURY YIELD CURVE

We propose a new model to estimate the term structure of interest rates using observed on‐the‐run Treasury yields. The new model is an improvement over models that require a priori knowledge of the shape of the yield curve to estimate the term structure. The general form of the model is an exponential function that depends on the estimation of four parameters fit by nonlinear least squares and has straightforward interpretations. In comparing the proposed model with current yield‐curve‐smoothing models, we find that, for the data used, the proposed model does best overall in terms of pricing accuracy both in sample and out of sample. JEL classification: E43, G12     

Estimating Trend Inflation Based on Unobserved Components Model: Is It Correlated with the Inflation Gap?

Building on the work of Stock and Watson (2007), this paper empirically shows that a negative correlation between innovations to trend inflation and the inflation gap plays an important role in the dynamics of postwar U.S. inflation. Additional features that we incorporate in our model include regime‐switching inflation gap persistence and association between inflation and inflation uncertainty. The resulting estimate of trend inflation is smooth, and our model provides superior out‐of‐sample forecasts than Stock and Watson's (2007) unobserved components model with stochastic volatility or than Atkeson and Ohanian's (2001) random walk model does.     

Price‐Level Targeting and Stabilization Policy

We construct a dynamic stochastic general equilibrium model to study optimal monetary stabilization policy. Prices are fully flexible and money is essential for trade. Our main result is that if the central bank pursues a price‐level target, it can control inflation expectations and improve welfare by stabilizing short‐run shocks to the economy. The optimal policy involves smoothing nominal interest rates that effectively smooths consumption across states.     

Yield curve modeling and forecasting using semiparametric factor dynamics

Using a dynamic semiparametric factor model (DSFM) we investigate the term structure of interest rates. The proposed methodology is applied to monthly interest rates for four southern European countries: Greece, Italy, Portugal and Spain from the introduction of the Euro to the recent European sovereign-debt crisis. Analyzing this extraordinary period, we compare our approach with the standard market method – dynamic Nelson–Siegel model. Our findings show that two nonparametric factors capture the spatial structure of the yield curve for each of the bond markets separately. We attributed both factors to the slope of the yield curve. For panel term structure data, three nonparametric factors are necessary to explain 95% variation. The estimated factor loadings are unit root processes and reveal high persistency. In comparison with the benchmark model, the DSFM technique shows superior short-term forecasting in times of financial distress.     

Are there nonlinearities in short‐term interest rates?

The present paper investigates the characteristics of short‐term interest rates in several countries. We examine the importance of nonlinearities in the mean reversion and volatility of short‐term interest rates. We examine various models that allow the conditional mean (drift) and conditional variance (diffusion) to be functions of the current short rate. We find that different markets require different models. In particular, we find evidence of nonlinear mean reversion in some of the countries that we examine, linear mean reversion in others and no mean reversion in some countries. For all countries we examine, there is strong evidence of the need for the volatility of interest rate changes to be highly sensitive to the level of the short‐term interest rate. Out‐of‐sample forecasting performance of one‐factor short rate models is poor, stemming from the inability of the models to accommodate jumps and discontinuities in the time series data.