Jens Christensen

We assess the impact of large-scale asset purchases, commonly known as quantitative easing (QE), conducted by Sveriges Riksbank and the European Central Bank (ECB) on bond risk premia in the Swedish government bond market. Using a novel arbitrage-free dynamic term structure model of nominal and real bond prices that accounts for bond-specific safety premia, we find that Sveriges Riksbank’s bond purchases raised inflation and short-rate expectations, lowered nominal and real term premia and inflation risk premia, and increased nominal bond safety premia, suggestive of signaling, portfolio rebalance, and safe asset scarcity effects. Furthermore, we document spillover effects of ECB’s QE programs on Swedish bond markets that are similar to the Swedish QE effects only after controlling for exchange rate fluctuations, highlighting the importance of exchange rate dynamics in the transmission of QE spillover effects.

Using a novel arbitrage-free dynamic term structure model of nominal and real yields, we account for liquidity premia and the deflation protection afforded by Japanese inflation-indexed bonds, known as JGBi’s. Adjusting for time-varying JGBi liquidity premia lowers the estimated value of JGBi deflation protection and raises inflation risk premium estimates, while long-term Japanese inflation expectations remain relatively stable at levels modestly exceeding one percent during the pandemic period. We then utilize our estimated liquidity measure to document statistically significant spillovers to JGBi market liquidity from global bond market illiquidity, as proxied by periods of low U.S. Treasury market depth.

The so-called equilibrium or natural rate of interest, widely known as r*t, is a key variable used to judge the stance of monetary policy. We offer a novel euro-area estimate based on a dynamic term structure model estimated directly on the prices of bonds with cash flows indexed to the euro-area harmonized index of consumer prices with adjustments for bond-specific risk and real term premia. Despite a recent increase, our estimate indicates that the natural rate in the euro area has fallen about 2 percentage points on net since 2002 and remains negative at the end of our sample. We also devise a related measure of the stance of monetary policy, which suggests that monetary policy in the euro area was not accommodative at the height of the COVID-19 pandemic.

Before the COVID-19 pandemic, researchers intensely debated the extent of the decline in the so-called equilibrium or natural rate of interest. Given the recent sharp increase in interest rates, we revisit this question in an emerging bond market context and offer a Chilean perspective using a dynamic term structure finance model estimated directly on the prices of individual Chilean inflation-indexed bonds with adjustments for bond-specific liquidity risk and real term premia. Beyond documenting the existence of large and time-varying liquidity risk premia in the bond prices, we estimate that the equilibrium real rate in Chile fell about 2 and a half percentage points in the 2003-2022 period and has remained low since then with model projections only suggesting a gradual reversal in coming years. Instead, recent increases in real interest rates in Chile are driven by spikes in the liquidity and term premia of inflation-indexed bond prices.

We provide market-based estimates of the natural real rate, that is, the steady-state short-term real interest rate, for Brazil, Chile, and Mexico. Our approach uses a dynamic term structure finance model estimated directly on the prices of individual inflation indexed bonds with adjustments for bond-specific liquidity and real term premia. First, we find that inflation-indexed bond liquidity premia in all three countries are sizable with significant variation. Second, we find large differences in their estimated equilibrium real rates: Brazil’s is large and volatile, Mexico’s is stable but elevated, while Chile’s is low and has fallen persistently. Although uncertain, our estimates could have important implications for the conduct of monetary policy in these three countries.

This article presents empirical evidence of a supply-induced transmission channel to long-term interest rates caused by a halt to government debt issuance. This is conceptually equivalent to a central bank-operated asset purchase program, commonly known as quantitative easing (QE). However, as it involves neither asset purchases nor associated creation of central bank reserves, we refer to it as passive QE. We introduce a general classification scheme of central bank balance sheet policies according to which passive QE is likely quite stimulative. For evidence, we analyze the response of Danish government bond risk premia to a temporary halt in government debt issuance announced by the Danish National Bank. The results suggest that declines in long-term yields during its enforcement reflected both reduced term premia, consistent with supply-induced portfolio balance effects, and increased safety premia, consistent with safe assets scarcity effects.

Through large-scale asset purchases, widely known as quantitative easing (QE), central banks around the world have affected the supply of safe assets by buying quasi-safe bonds in exchange for truly safe reserves. We examine the pricing effects of the European Central Bank’s bond purchases in the 2015-2021 period on an international panel of bond safety premia from four highly rated countries: Denmark, Germany, Sweden, and Switzerland. We find statistically significant negative effects for all four countries. This points to an important international spillover channel of QE programs to bond safety premia that operates by increasing the amount of truly safe assets.

Portfolio diversification is as important to debt management as it is to asset management. In this paper, we focus on diversification of sovereign debt issuance through greater reliance on inflation-indexed bonds for a representative emerging economy, Colombia. Using an arbitrage-free dynamic term structure model of fixed-coupon and inflation-indexed bond prices, we account for inflation and liquidity risk premia and calculate the net benefit of issuing inflation-indexed bonds over nominal bonds. Our results suggest that the Colombian government could lower its funding costs by as much as 0.68 percent through increased issuance of inflation-indexed debt.

In recent decades, long-term interest rates around the world have fallen to historic lows despite some recent reversal. We examine the source of this decline using a dynamic term structure model of Canadian nominal and real yields with adjustments for term, liquidity, and inflation risk premiums. Canada provides a novel perspective on this issue because of its established indexed debt market, negligible distortions from monetary quantitative easing or the zero lower bound, and absence of sovereign credit risk. We find that in the 2000-2019 period, the steady-state real interest rate fell by more than 2 percentage points, long-term inflation expectations edged down, and real bond and inflation risk premiums varied over time but showed little longer-run trend. Therefore, the drop in the equilibrium real rate appears largely to account for the lower new normal in interest rates.

Safe assets usually trade at a premium thanks to high credit quality and deep liquidity. To understand the role of credit quality for such premia, we examine Swiss government bonds, which are extremely safe but not particularly liquid. We therefore refer to their premia as safety premia and quantify them using an arbitrage-free term structure model that accounts for time-varying premia in individual bond prices. We find that Swiss safety premia are large with long-lasting trends. They shifted upwards persistently following the euro launch and have been depressed recently by asset purchases of the European Central Bank.

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.

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.

To study inflation expectations and associated risk premia in emerging bond markets, we provide estimates for Mexico based on an arbitrage-free dynamic term structure model of nominal and real bond prices that accounts for their liquidity risk. Beyond documenting the existence of large and weakly correlated liquidity premia in nominal and real bond prices, our results indicate that long-term inflation expectations in Mexico are well anchored close to the Bank of Mexico’s inflation target. Furthermore, Mexican inflation risk premia are larger and more volatile than those in Canada and the United States.

Portfolio diversification is as important to debt management as it is to asset management. In this paper, we focus on diversification of sovereign debt issuance by examining the extension of the maximum maturity of issued debt. In particular, we are interested in the potential costs to the U.S. Treasury of introducing 50-year bonds as a financing option. Therefore, we first examine international evidence from four developed foreign government bond markets with such long-term debt. The results show that 50-year bonds in these markets trade at an average yield that is at most 20 basis points above that of 30-year bonds. Results based on extrapolations from a dynamic yield curve model using just U.S. Treasury yields are similar.

Japanese realized and expected inflation has been below the Bank of Japan’s two percent target for many years. We examine the impact of announcements of expansionary monetary and fiscal policy under COVID-19 on inflation expectations from an arbitrage-free term structure model of nominal and real yields. We find that both types of policies failed to lift inflation expectations, which instead declined notably over the pandemic period and are projected to only slowly revert back to Bank of Japan target levels. Our results therefore illustrate the challenges faced in raising well-anchored low inflation expectations.

We assess the impact of news concerning recent Japanese monetary reforms on long-term inflation expectations using an arbitrage-free term structure model of nominal and real yields. Our model accounts for the value of deflation protection embedded in Japanese inflation-indexed bonds issued since 2013, which is sizable and time-varying. Our results suggest that Japanese long-term inflation expectations have remained positive despite extensive spells of deflation, leaving inflation risk premia mostly negative during this period. Moreover, adjusting for deflation protection demonstrates that market responses to policy changes were not as inflationary as they appear under standard modeling procedures. Consequently, the reforms were less “disappointing” than is widely perceived.

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 several countries. We find slight biases in extrapolated long bond yields of just 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.

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 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.

We introduce an 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 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 helps our model to match TIPS prices. Accounting for liquidity risk also improves the model’s ability to forecast inflation and match surveys of inflation expectations.

In their search for yield in the current low interest rate environment, many investors have turned to sovereign debt in emerging economies, which has raised concerns about risks to financial stability from these investment flows. To assess this risk, we study the effects of changes in the foreign-held share of Mexican sovereign bonds on their liquidity premiums. We find that a decade-long increase in foreign holdings of these securities have played a significant role in driving up their liquidity premiums. Provided the higher compensation for bearing liquidity risk is commensurate with the chance of a major foreign-led sell-off in the Mexican government bond market, this development may not pose a material risk to its financial stability.

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 both matching and nearly-matching maturities but of separate vintages are analyzed. Adjusting for differences in conventional liquidity premiums, values of embedded deflation options, and coupon rates, the results show a small, insignificant premium on recently issued TIPS, which leads us to conclude that there is no on-the-run premium in the TIPS 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.

Nearly all studies that analyze the term structure of interest rates take a two-step approach. First, actual bond prices are summarized by interpolated synthetic zero-coupon yields, and second, some 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 one-step 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.

This article presents empirical evidence of a reserve-induced transmission channel of quantitative easing to long-term interest rates. Reserve-induced effects are independent of the assets purchased and run through the impact of reserve expansions on bank balance sheets and the resulting bank portfolio rebalancing. For evidence, we analyse 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. The data suggest that declines in long-term yields following the announcements mainly reflected reduced term premiums, consistent with reserve-induced portfolio balance effects.

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.

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.

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.

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.