No-arbitrage Term Structure Model Research Articles

Modeling volatility in dynamic term structure models

We propose no-arbitrage term structure models with volatility factors that follow GARCH processes. The models’ tractability is similar to canonical affine term structure models, but they fit yield volatility much better, especially for long-maturity yields. This improvement does not come at the expense of a deterioration in yield fit. Because of the improved volatility fit, the model performs substantially better in pricing Treasury futures options. We conclude that the specification of the volatility factors is critical. Modeling volatility as a function of (lagged) squared innovations to factors improves on models where volatility is a linear function of the factors.

The relative pricing of WTI and Brent crude oil futures: Expectations or risk premia?

This paper studies the spread of Brent-WTI futures prices using a no-arbitrage term structure model with one common and two latent idiosyncratic risk factors. We document more negative risk premia for WTI than for Brent, and the differences are more pronounced at longer maturities. The expectation of future spot price dominates the risk premium in determining the term structure of Brent-WTI futures spread, especially at short maturities. The common risk premia in both markets are negative and similar, while their corresponding idiosyncratic risk premia have opposite signs. The common risk prices of WTI and Brent are generally related to the US crude commercial stock, inflation, economic uncertainty, and hedging pressure; however, idiosyncratic risk prices are more related to their corresponding local production, short rate, and the term structure factors. The variance decomposition indicates that the idiosyncratic factors account for a considerable part at longer forecast horizons in both markets.

International Yield Comovements

AbstractWe decompose long-term nominal bond yields into real and inflation components in an international context using inflation-linked and nominal bonds. In contrast to extant results, real rate variation dominates the variation in inflation-linked and nominal yields. Cross-country nominal and inflation-linked yield correlations have declined since the Great Recession. Real rates are the main source of the correlation between nominal yields. Our results are robust to various alternative measurements of inflation expectations and the liquidity premium. They continue to hold when a no-arbitrage term structure model with real, nominal, and inflation factors is used to effect the yield decomposition.

Macrofinancial information on the post-COVID-19 economic recovery: Will it be V, U or L-shaped?

We use standard macrofinancial no-arbitrage term structure models to forecast key macroeconomic variables such as GDP. Simple adaptations to the models are proposed in order to generate plausible forecasts in the context of the COVID-19 crisis. The financial market variables included in the models are shown to improve GDP forecasts. Forecasts of real GDP conditioned on macrofinancial information up to August 2020 suggest that the shape of the recovery will most likely be between a U and an L in most euro area countries considered, with substantial persistent losses.

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

Abstract We propose a general method for the Bayesian estimation of a very broad class of non-linear no-arbitrage term-structure models. The main innovation we introduce is a computationally efficient method, based on deep learning techniques, for approximating no-arbitrage model-implied bond yields to any desired degree of accuracy. Once the pricing function is approximated, the posterior distribution of model parameters and unobservable state variables can be estimated by standard Markov Chain Monte Carlo methods. As an illustrative example, we apply the proposed techniques to the estimation of a shadow-rate model with a time-varying lower bound and unspanned macroeconomic factors.

Oil and Inflation Compensation: Evidence from Treasury Inflation-Protected Security Prices

Why did the correlation between oil prices and 10-year TIPS Break-even Inflation, a measure of long-term inflation compensation, increase dramatically after the financial crisis? Using a shadow-rate no-arbitrage term structure model, we demonstrate that this is because when nominal interest rates bind at the zero lower bound (ZLB), investors doubt the effectiveness of monetary policy to control deflation. As a result, investors adjust their long-term inflation expectations more rapidly after negative oil price changes and pay higher premiums to hedge long-run deflation risks. We explain these findings by a stylized dynamic stochastic general equilibrium model including oil supply shocks, oil demand shocks, and a Taylor rule with the ZLB constraint.

No-arbitrage one-factor term structure models in zero- or negative-lower-bound environments

One-factor no-arbitrage term structure models where the instantaneous interest rate follows either the process proposed by Vasicek (1977) or by Cox, Ingersoll, and Ross (1985), commonly known as CIR, are parsimonious and analytically tractable. Models based on the original CIR process have the important characteristic of allowing for a time-varying conditional interest rate volatility but are undefined in negative interest rate environments. A Shifted-CIR no-arbitrage term structure model, where the instantaneous interest rate is given by the sum of a constant lower bound and a non-negative CIR-like process, allows for negative yields and benefits from similar tractability of the original CIR model. Based on the U.S. and German yield curve data, the Vasicek and Shifted-CIR specifications, both considering constant and time-varying risk premia, are compared in terms of information criteria and forecasting ability. Information criteria prefer the Shifted-CIR specification to models based on the Vasicek process. It also provides similar or better in-sample and out-of-sample forecasting ability of future yield curve movements. Introducing a time variation of the interest rate risk premium in no-arbitrage one-factor term structure models is instead not recommended, as it provides worse information criteria and forecasting performance.

Modeling Volatility in Dynamic Term Structure Models

We propose no-arbitrage term structure models in which the volatility factors follow GARCH processes. The models’ tractability is similar to that of canonical affine term structure models, but they capture the conditional variances of yields much more accurately. We estimate a model with one volatility factor using Treasury yield data for 1971-2019. Relative to standard affine term structure models with stochastic volatility, the model improves the fit of yield volatility substantially, especially for long-maturity yields. This improvement does not come at the expense of a deterioration in yield fit. We conclude that the ability of no-arbitrage term structure models to extract and model conditional volatility critically depends on the specification of the volatility factors. Modeling volatility as a function of (lagged) squared innovations to factors improves on models where volatility is a linear function of the factors.

No-Arbitrage Pricing of GDP-Linked Bonds

We use a no-arbitrage term structure model of equity yields computed from the prices of dividend swaps to estimate the yields on hypothetical bonds with cash-flows indexed to the level of US GDP. This provides a novel approach for estimating the possible relative cost of conventional and GDP-linked bonds, which is likely to be of interest to sovereigns considering the case for issuing GDP-linked debt. Our model predicts that US GDP-linked bonds would typically have yields lower than those on conventional Treasury bonds with the same maturity in our sample from 2010 to 2017. Positive expected future GDP growth lowers the yield on GDP-linked bonds relative to conventional bonds, which typically more than offsets the estimated GDP risk premium demanded by investors for holding GDP risk. These risk premia decrease with maturity,with unconditional averages falling in absolute value from 7 percentage points at the short-end of the curve to 1 percentage points at the 10-year horizon.

Inflation-Linked versus Nominal Bond Yields: On Liquidity and Inflation Risk Premiums Around the World

We decompose long-term nominal bond yields into real and inflation components in an international context using inflation-linked and nominal bonds. In contrast to extant results, real rate variation dominates the variation in inflation-linked and nominal yields. Cross-country nominal and inflation-linked yield correlations have declined since the Great Recession. Real rates are the main source of the correlation between nominal yields. Our results are robust to various alternative measurements of inflation expectations and the liquidity premium. They continue to hold when a no-arbitrage term structure model with real, nominal, and inflation factors is used to effect the yield decomposition.

The Information in the Joint Term Structures of Bond Yields

While standard no-arbitrage term structure models are estimated using nominal yields from a single country, a growing literature estimates joint models of yields in multiple countries or nominal and real yields from a single country. However, this paper argues that, in two of the most common applications joint modelling does not bring any material benefits in capturing the dynamics of bond yields. Joint models of US and German nominal yields do not offer economically significant advantages in fitting the cross section of yields or predicting future yields. We obtain similar results for joint models of US nominal and real yields.

Macroeconomic determinants of the term structure: Long-run and short-run dynamics

Abstract We propose a no-arbitrage term structure model with a Taylor rule and two macroeconomic variables, real activity growth and inflation, that each contain long-run and short-run components. Variance decompositions indicate that the impact of macroeconomic variables on the term structure differs from existing models. For short maturities, inflation is relatively more important than real activity growth at short forecast horizons. For longer maturity yields, the long-run component of inflation explains most of the long-horizon forecast variance, but real activity growth matters for short forecast horizons. Unlike existing macro models, the model implies plausible term premia and expectations of short rates. The long-run components also improve the prediction of bond excess returns relative to information in the yield curve and macro variables. Measures of in-sample and out-of-sample fit confirm the benefits of allowing for long- and short-run components.

A term structure model of interest rates with quadratic volatility

This study proposes a no-arbitrage term structure model that can capture the volatility of interest rates without sacrificing the goodness-of-fit to the cross-section and predictive ability about the level of interest rates. The key feature of the model is the covariance matrix of changes in factors, which is specified as quadratic functions of factors. The quadratic specification can capture intense volatility even with spanned factors, which is not the case for the affine specification. Furthermore, since the quadratic specification guarantees the positive definiteness of the covariance matrix without restricting the sign of factors, it allows for a flexible specification of the physical drift as does the Gaussian term structure model, contributing also to accurate level prediction.

Tips from TIPS: The Informational Content of Treasury Inflation-Protected Security Prices

Treasury Inflation-Protected Securities (TIPS) are frequently thought of as risk-free real bonds. Using no-arbitrage term structure models, we show that TIPS yields exceeded risk-free real yields by as much as 100 basis points when TIPS were first issued and up to 300 basis points during the 2007–2008 financial crisis. This spread predominantly reflects the poorer liquidity of TIPS relative to nominal Treasury securities. Other factors, including the indexation lag and the embedded deflation protection in TIPS, play a much smaller role. Ignoring this spread also significantly distorts the informational content of TIPS break-even inflation, a widely used proxy for expected inflation.

What do the prices of UK inflation-linked securities say on inflation expectations, risk premia and liquidity risks?

Abstract The difference between yields on nominal and inflation-linked government bonds or inflation swap rates are important indicators of the outlook for inflation and are monitored regularly by central banks, including the United Kingdom's Monetary Policy Committee (MPC). However, in the United Kingdom, inflation-linked instruments reference RPI inflation, whereas the MPC's target is CPI inflation of 2%. In this paper we extract market expectations for UK CPI inflation with the help of UK RPI-linked gilt prices, which is a novelty in the literature. To better extract useful information about expectations for CPI inflation, we develop a no-arbitrage term structure model and decompose the forward inflation curve into: measures of CPI inflation expectations; the expected wedge between RPI and CPI inflation; estimates of inflation risk premia and estimates of liquidity risk premia. We show that long-horizon expectations of CPI inflation fell in the 1990 s, after the introduction of inflation targeting and the creation of the MPC, and have since remained fairly stable at around 2%.

A Gaussian Affine Term Structure Model of Interest Rates and Credit Spreads

We estimate a no-arbitrage term structure model of U.S. Treasury yields and corporate bond spreads with both economic factors and latent factors as drivers of term structure dynamics. We consider two sets of economic factors: macro factors consisting of inflation and real activity, and financial market factors consisting of funding liquidity and market volatility. We show that financial market factors have limited effects on the Treasury yield curve but substantial impacts on the credit spread term structure. In particular, negative liquidity shocks widen credit spreads, and this effect is more pronounced for short-term corporate bonds. We also find that out-of-sample forecasts for credit spreads improve when financial market factors are incorporated and when no-arbitrage restrictions are imposed. We also propose a minimum-chi-square method for estimating the term structure models of interest rate and credit spreads, which is more efficient and accurate than the widespread maximum-likelihood estimation.

Jumps in Bond Yields at Known Times

We construct a no-arbitrage term structure model with jumps in the entire state vector at deterministic times but of random magnitudes. Jump risk premia are allowed for. We show that the model implies a closed-form representation of yields as a time-inhomogenous ane function of the state vector. We apply the model to the term structure of US Treasury rates, estimated at the daily frequency, allowing for jumps on days of employment report announcements. Our model can match the empirical fact that the term structure of interest rate volatility has a hump-shaped pattern on employment report days (but not on other days). The model also produces patterns in bond risk premia that are consistent with the empirical nding that much of the time-variation in excess bond returns accrues at times of important macroeconomic data releases.

Jumps in Bond Yields at Known Times

We construct a no-arbitrage term structure model with jumps in the entire state vector at deterministic times but of random magnitudes. Jump risk premia are allowed for. We show that the model implies a closed-form representation of yields as a time-inhomogenous ane function of the state vector. We apply the model to the term structure of US Treasury rates, estimated at the daily frequency, allowing for jumps on days of employment report announcements. Our model can match the empirical fact that the term structure of interest rate volatility has a hump-shaped pattern on employment report days (but not on other days). The model also produces patterns in bond risk premia that are consistent with the empirical nding that much of the time-variation in excess bond returns accrues at times of important macroeconomic data releases.

Jumps in Bond Yields at Known Times

We construct a no-arbitrage term structure model with jumps in the entire state vector at deterministic times but of random magnitudes. Jump risk premia are allowed for. We show that the model implies a closed-form representation of yields as a time-inhomogeneous affine function of the state vector, and derive other theoretical implications. We apply the model to the term structure of US Treasury rates, estimated at the daily frequency, allowing for jumps on days of employment report announcements. Our model can match the empirical fact that the term structure of interest rate volatility has a hump-shaped pattern on employment report days (but not on other days). The model also produces patterns in bond risk premia that are consistent with the empirical finding that much of the time-variation in excess bond returns accrues at times of important macroeconomic data releases.

Long-Run Priors for Term Structure Models

Dynamic no-arbitrage term structure models are popular tools for decomposing bond yields into expectations of future short-term interest rates and term premia. But there is insufficient information in the time series of observed yields to estimate the unconditional mean of yields in maximally flexible models. This can result in implausibly low estimates of long-term expected future short-term interest rates, as well as considerable uncertainty around those estimates. This paper proposes a tractable Bayesian approach for incorporating prior information about the unconditional means of yields. We apply it to UK data and find that with reasonable priors it results in more plausible estimates of the long-run average of yields, lower estimates of term premia in long-term bonds and substantially reduced uncertainty around these decompositions in both affine and shadow rate term structure models.