Insurance companies and pension funds have liabilities far into the future and typically well beyond the longest maturity bonds trading in fixed-income markets. Such long-lived liabilities still need to be discounted, and yield curve extrapolations based on the information in observed yields can be used. We use dynamic Nelson-Siegel (DNS) yield curve models for extrapolating risk-free yield curves for Switzerland, Canada, France, and the U.S. We find slight biases in extrapolated long bond yields of a few basis points. In addition, the DNS model allows the generation of useful financial risk metrics, such as ranges of possible yield outcomes over projection horizons commonly used for stress-testing purposes. Therefore, we recommend using DNS models as a simple tool for generating extrapolated yields for long-term interest rate risk management.
Analysis of the term structure of interest rates almost always takes a two-step approach.
First, actual bond prices are summarized by interpolated synthetic zero-coupon yields, and second, a small set of these yields are used as the source data for further empirical examination. In contrast, we consider the advantages of a one-step approach that directly analyzes the universe of bond prices. To illustrate the feasibility and desirability of the onestep approach, we compare arbitrage-free dynamic term structure models estimated using both approaches. We also provide a simulation study showing that a one-step approach can extract the information in large panels of bond prices and avoid any arbitrary noise introduced from a first-stage interpolation of yields.
We introduce a new arbitrage-free term structure model of nominal and real yields that accounts for liquidity risk in Treasury inflation-protected securities (TIPS). The novel feature of our model is to identify liquidity risk directly from individual TIPS prices by accounting for the tendency that TIPS, like most fixed-income securities, go into buy-and-hold investors’ portfolios as time passes. We find a sizable and countercyclical TIPS liquidity premium, which greatly helps our model in matching TIPS prices. Accounting for liquidity risk also improves the model’s ability to forecast inflation and match inflation surveys, although none of these series are included in the estimation.
In the U.S. Treasury market, the most recently issued, or so-called “on-the-run,” security typically trades at a price above those of more seasoned but otherwise comparable securities. This difference is known as the on-the-run premium. In this paper, yield spreads between pairs of Treasury Inflation-Protected Securities (TIPS) with identical maturities but of separate vintages are analyzed. Adjusting for differences in coupon rates and values of embedded deflation options, the results show a small, positive premium on recently issued TIPS – averaging between one and four basis points – that persists even after new similar TIPS are issued and hence is different from the on-the-run phenomenon observed in the nominal Treasury market.
Researchers have debated the extent of the decline in the steady-state short-term real interest rate—that is, in the so-called equilibrium or natural rate of interest. We examine this issue using a dynamic term structure finance model estimated directly on the prices of individual inflation-indexed bonds with adjustments for real term and liquidity risk premiums. Our methodology avoids two pitfalls of previous macroeconomic analyses: structural breaks at the zero lower bound and potential misspecification of output and inflation dynamics. We estimate that the equilibrium real rate has fallen about 2 percentage points and appears unlikely to rise quickly.
This paper presents a portfolio model of asset price effects arising from central bank large scale asset purchases, or quantitative easing (QE). Two financial frictions—segmentation of the market for central bank reserves and imperfect asset substitutability—give rise to two distinct portfolio effects. One is well known and derives from the reduced supply of the purchased assets. The other is new, runs through banks’ portfolio responses to reserves expansions, and is independent of the types of assets purchased. The results imply that central bank reserve expansions can affect long-term bond prices even in the absence of long-term bond purchases.
We argue that the issuance of central bank reserves per se can matter for the effect of central bank large-scale asset purchases—commonly known as quantitative easing—on long-term interest rates. This effect is independent of the assets purchased, and runs through a reserve-induced portfolio balance channel. For evidence we analyze the reaction of Swiss long-term government bond yields to announcements by the Swiss National Bank to expand central bank reserves without acquiring any long-lived securities. We find that declines in long-term yields following the announcements mainly reflected reduced term premiums suggestive of reserve-induced portfolio balance effects.
The ability of the usual factors from empirical arbitrage-free representations of the term structure — that is, spanned factors — to account for interest rate volatility dynamics has been much debated. We examine this issue with a comprehensive set of new arbitrage-free term structure specifications that allow for spanned stochastic volatility to be linked to one or more of the yield curve factors. Using U.S. Treasury yields, we find that much realized stochastic volatility cannot be associated with spanned term structure factors. However, a simulation study reveals that the usual realized volatility metric is misleading when yields contain plausible measurement noise. We argue that other metrics should be used to validate stochastic volatility models
This paper presents a regime-switching model of the yield curve with two states. One is a normal state, the other is a zero-bound state that represents the case when the monetary policy target rate is at its zero lower bound for a prolonged period. The model delivers estimates of the time-varying probability of exiting the zero-bound state, and it outperforms standard three- and four-factor term structure models as well as a shadow rate model at matching short-rate expectations and the compression in yield volatility near the zero lower bound.
We argue that central bank large-scale asset purchases—commonly known as quantitative easing (QE)—can reduce priced frictions to trading through a liquidity channel that operates by temporarily increasing the bargaining power of sellers in the market for the targeted securities. For evidence we analyze how the Federal Reserve’s second QE program that included purchases of Treasury inflation-protected securities (TIPS) affected a measure of liquidity premiums in TIPS yields and inflation swap rates. We find that, for the duration of the program, the liquidity premium measure averaged about 10 basis points lower than expected. This suggests that QE can improve market liquidity.
Yes. We analyze the economic benefit of Treasury Inflation Protected Securities (TIPS) issuance by estimating the inflation risk premium that penalizes nominal Treasuries vis-a-vis TIPS and the cost derived from TIPS liquidity disadvantage. To account for the latter, we introduce a novel model-independent range for the liquidity premium in TIPS exploiting additional information from inflation swaps. We also adjust our model estimates for finite-sample bias. The resulting measure provides a lower bound to the benefit of TIPS, which is positive on average. Thus, our analysis suggests that the Treasury could save billions of dollars by significantly expanding its TIPS program.
Published Articles (Refereed Journals and Volumes)
We use an arbitrage-free term structure model with spanned stochastic volatility to determine the value of the deflation protection option embedded in Treasury inflation protected securities (TIPS). The model accurately prices the deflation protection option prior to the financial crisis when its value was near zero; at the peak of the crisis in late 2008 when deflationary concerns spiked sharply; and in the post-crisis period. During 2009, the average value of this option at the five-year maturity was 41 basis points on a par-yield basis. The option value is shown to be closely linked to overall market uncertainty as measured by the VIX, especially during and after the 2008 financial crisis.
Recent U.S. Treasury yields have been constrained to some extent by the zero lower bound (ZLB) on nominal interest rates. Therefore, we compare the performance of a standard affine Gaussian dynamic term structure model (DTSM), which ignores the ZLB, to a shadow-rate DTSM, which respects the ZLB. Near the ZLB, we find notable declines in the forecast accuracy of the standard model, while the shadow-rate model forecasts well. However, 10-year yield term premiums are broadly similar across the two models. Finally, in applying the shadow-rate model, we find no gain from estimating a slightly positive lower bound on U.S. yields
Standard Gaussian affine dynamic term structure models do not rule out negative nominal interest rates—a conspicuous defect with yields near zero in many countries. Alternative shadow-rate models, which respect the nonlinearity at the zero lower bound, have been rarely used because of the extreme computational burden of their estimation. However, by valuing the call option on negative shadow yields, we provide the first estimates of a three-factor shadow-rate model. We validate our option-based results by closely matching them using a simulation-based approach. We also show that the shadow short rate is sensitive to model fit and specification.
To support the economy, the Federal Reserve amassed a large portfolio of long-term bonds. We assess the Fed’s associated interest rate risk — including potential losses to its Treasury securities holdings and declines in remittances to the Treasury. Unlike past examinations of this interest rate risk, we attach probabilities to alternative interest rate scenarios. These probabilities are obtained from a dynamic term structure model that respects the zero lower bound on yields. The resulting probability-based stress test finds that the Fed’s losses are unlikely to be large and remittances are unlikely to exhibit more than a brief cessation.
In response to the global financial crisis that started in August 2007, central banks provided extraordinary amounts of liquidity to the financial system. To investigate the effect of central bank liquidity facilities on term interbank lending rates, we estimate a six-factor
arbitrage-free model of U.S. Treasury yields, financial corporate bond yields, and term interbank rates. This model can account for fluctuations in the term structure of credit risk and liquidity risk. A significant shift in model estimates after the announcement of
the liquidity facilities suggests that these central bank actions did help lower the liquidity premium in term interbank rates.
We construct probability forecasts for episodes of price deflation (i.e., a falling price level) using yields on nominal and real U.S. Treasury bonds. The deflation probability forecasts identify two “deflation scares” during the past decade: a mild one following the 2001 recession and a more serious one starting in late 2008 with the deepening of the financial crisis. The estimated deflation probabilities are generally consistent with those from macroeconomic models and surveys of professional forecasters, but they also provide high-frequency insight into the views of financial market participants. The probabilities can also be used to price the deflation protection option embedded in real Treasury bonds.
We analyze declines in government bond yields following announcements by the Federal Reserve and the Bank of England of plans to buy longer term debt. Using dynamic term structure models, we decompose US and UK yields into expectations about future short-term interest rates and term premiums. We find that declines in US yields mainly reflected lower expectations of future short-term interest rates, while declines in UK yields appeared to reflect reduced term premiums. Thus, the relative importance of the signalling and portfolio balance channels of quantitative easing may depend on market institutional structures and central bank communication policies.
The Affine Arbitrage-Free Class of Nelson-Siegel Term Structure Models
Journal of Econometrics 164, September 2011, 4-20 | With Diebold and Rudebusch
We derive the class of affine arbitrage-free dynamic term structure models that approximate the widely-used Nelson-Siegel yield curve specification. These arbitrage-free Nelson-Siegel (AFNS) models can be expressed as slightly restricted versions of the canonical
representation of the three-factor affine arbitrage-free model. Imposing the Nelson-Siegel structure on the canonical model greatly facilitates estimation and can improve predictive performance. In the future, AFNS models appear likely to be a useful workhorse
representation for term structure research.
Inflation Expectations and Risk Premiums in an Arbitrage-Free Model of Nominal and Real Bond Yields
Journal of Money, Credit, and Banking 42, September 2010, 143-178 | With Lopez and Rudebusch
Differences between yields on comparable-maturity U.S. Treasury nominal and real debt, the so-called breakeven inflation (BEI) rates, are widely used indicators of inflation expectations. However, better measures of inflation expectations could be obtained by subtracting inflation risk premiums from the BEI rates. We provide such decompositions using an estimated affine arbitrage-free model of the term structure that captures the pricing of both nominal and real Treasury securities. Our empirical results suggest that long-term inflation expectations have been well anchored over the past few years, and inflation risk premiums, although volatile, have been close to zero on average.
The Svensson generalization of the popular Nelson-Siegel term structure model is widely used by practitioners and central banks. Unfortunately, like the original Nelson-Siegel specification, this generalization, in its dynamic form, does not enforce arbitrage-free consistency over time. Indeed, we show that the factor loadings of the Svensson generalization cannot be obtained in a standard finance arbitrage-free affine term structure representation. Therefore, we introduce a closely related generalized Nelson-Siegel model on which the no-arbitrage condition can be imposed. We estimate this new arbitrage-free generalized Nelson-Siegel model and demonstrate its tractability and good in-sample fit.
Confidence Sets for Continuous-Time Rating Transition Probabilities
Journal of Banking and Finance 28, August 2004, 2575-2602 | With Lando and Hansen
This paper addresses the estimation of default probabilities and associated confidence sets with special focus on rare events. Research on rating transition data has documented a tendency for recently downgraded issuers to be at an increased risk of experiencing further downgrades
compared to issuers that have held the same rating for a longer period of time. To capture this non-Markov effect we introduce a continuous-time hidden Markov chain model in which downgrades firms enter into a hidden, “excited” state. Using data from Moody’s we estimate the parameters of the model, and conclude that both default probabilities and confidence sets are strongly influenced by the introduction of hidden excited states.
The vast majority of the term structure literature has focused on modeling the risk-free term structure as implied by Treasury bond yields. As fixed-income markets should be interconnected, we combine the modeling of Treasury yields with a modeling of the common factors present in representative risky credit spread term structures derived from Bloomberg corporate bond data. The question we address is whether we can improve our understanding of, and our ability to forecast, Treasury yields by incorporating information from corporate bond market. We use the arbitrage-free dynamic version of the Nelson-Siegel yield-curve model derived Christensen, Diebold and Rudebusch (2007) to model Treasury yields and corporate bond spreads across rating and industry categories. In addition to the three-factor Nelson-Siegel factors for Treasury yields, we find two common factors—a level and a slope factor—are required to capture the time series dynamics of aggregated credit spreads. We find that the preferred specifications of the joint dynamics of all five factors have feedback effects from the Treasury factors to the credit risk factors, but we also find feedback effects from the credit risk factors to the Treasury factors. To determine the significance of these feedback effects, we perform an out-of-sample forecast exercise. The results so far suggest that the preferred Treasury yield model can easily beat the random walk and that adding the information from the credit markets allows us to improve forecast performance even further for forecast horizons up to 26-weeks.
Default and Recovery Risk Modeling and Estimation
Ph.D. Dissertation, Copenhagen Business School, February 2007
Joint Estimation of Default and Recovery Risk: A Simulation Study
Presentation, 16th Annual Derivative Securities & Risk Measurement Conference, FDIC Center for Financial Research and Cornell University, April 2006
Recovery Risk Modeling: An Application of the Quadratic Class
Presentation, International Conference on Finance, University of Copenhagen, September 2005