Jens Christensen
Research Advisor
Financial Research
Finance, Credit risk, Term structure
CV (pdf, 111.92 kb)
Working Papers
The Benefit of Inflation-Indexed Debt: Evidence from an Emerging Bond Market
2023-04 | with Cardozo | February 2023
abstract (+)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 0.69 percent by increasing its issuance of inflation-indexed debt, in particular at long maturities.
International Evidence on Extending Sovereign Debt Maturities
2021-19 | with Lopez and Mussche | July 2021
abstract (+)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 examine the potential costs to the U.S. Treasury of introducing 50-year bonds as a financing option. Based on evidence from foreign government bond markets with such long-term debt, our results suggest that a 50-year Treasury bond would likely trade at an average yield that is at most 20 basis points above that of a 30-year bond. Our results based on extrapolations from a dynamic yield curve model using just U.S. Treasury yields are similar.
Inflation Expectations and Risk Premia in Emerging Bond Markets: Evidence from Mexico
2021-08 | with Beauregard, Fischer, and Zhu | November 2021
abstract (+)To study inflation expectations and associated risk premia in emerging bond markets, this paper provides estimates for Mexico based on an arbitrage-free dynamic term structure model of nominal and real bond prices that accounts for their liquidity risk. In addition to documenting the existence of large and time-varying liquidity premia in nominal and real bond prices that are only weakly correlated, the results indicate that long-term inflation expectations in Mexico are well anchored close to the inflation target of the Bank of Mexico. Furthermore, Mexican inflation risk premia are larger and more volatile than those in Canada and the United States.
Accounting for Low Long-Term Interest Rates: Evidence from Canada
2020-35 | with Rudebusch and Shultz | July 2021
abstract (+)In recent decades, long-term interest rates around the world have fallen to historic lows.
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 since 2000, the steady-state real interest
rate has fallen by more than 2 percentage points, long-term inflation expectations have
edged down, and real bond and inflation risk premiums have varied over time but shown
little longer-run trend. Therefore, the drop in the equilibrium real rate appears largely to
account for the lower new normal in interest rates.
The Safety Premium of Safe Assets
2019-28 | with Mirkov | September 2022
abstract (+)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.
Can Spanned Term Structure Factors Drive Stochastic Yield Volatility?
2014-03 | with Lopez and Rudebusch | January 2014
abstract (+)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
A Regime-Switching Model of the Yield Curve at the Zero Bound
2013-34 | January 2016
abstract (+)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.
Could the U.S. Treasury Benefit from Issuing More TIPS?
2011-16 | with Gillan | June 2012
abstract (+)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)
Central Bank Credibility During COVID-19: Evidence from Japan
Journal of International Money and Finance 131, March 2023 | with Spiegel
abstract (+)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.
Monetary Reforms and Inflation Expectations in Japan: Evidence from Inflation-Indexed Bonds
Journal of Econometrics 231(2), December 2022, 410-431 | with Spiegel
abstract (+)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.
Extrapolating Long-Maturity Bond Yields for Financial Risk Measurement
Management Science 68(11), 2022, 8,286-8,300 | with Lopez and Mussche
abstract (+)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.
A Portfolio Model of Quantitative Easing
Quarterly Journal of Finance 12(4), 2022, 2250011-1-2250011-39 | with Krogstrup
abstract (+)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.
Does Quantitative Easing Affect Market Liquidity?
Journal of Banking and Finance 134, January 2022 | with Gillan
abstract (+)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.
The TIPS Liquidity Premium
Review of Finance 25(6), 2021, 1639–1675 | with Andreasen and Riddell
abstract (+)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.
Bond Flows and Liquidity: Do Foreigners Matter?
Journal of International Money and Finance 117-102397, 2021, 1-20 | with Fischer and Shultz | No
abstract (+)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.
Is There an On-the-Run Premium in TIPS?
Quarterly Journal of Finance 10(2), 2020 | with Lopez and Shultz
abstract (+)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.
A New Normal for Interest Rates? Evidence from Inflation-Indexed Debt
The Review of Economics and Statistics 101(5), December 2019, 933-949 | with Rudebusch
abstract (+)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.
Term Structure Analysis with Big Data: One-Step Estimation Using Bond Prices
Journal of Econometrics 212(1), September 2019, 26-46 | with Andreasen and Rudebusch
abstract (+)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.
Transmission of Quantitative Easing: The Role of Central Bank Reserves
Economic Journal 129, January 2019, 249-272 | with Krogstrup | No
abstract (+)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.
Pricing Deflation Risk with U.S. Treasury Yields
Review of Finance 20, 2016, 1107-1152 | with Lopez and Rudebusch
abstract (+)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.
Modeling Yields at the Zero Lower Bound: Are Shadow Rates the Solution?
In Dynamic Factor Models (Advances in Econometrics, Vol. 35), ed. by Eric Hillebrand and Siem Jan Koopman | Emerald Publishing Group, 2016. pp. 75-125 | with Rudebusch
abstract (+)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
Estimating Shadow-Rate Term Structure Models with Near-Zero Yields
Journal of Financial Econometrics 13 (2), Spring 2015, 226-259 | with Rudebusch
abstract (+)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.
A Probability-Based Stress Test of Federal Reserve Assets and Income
Journal of Monetary Economics 73, 2015, 26-43 | with Lopez and Rudebusch
abstract (+)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.
Do Central Bank Liquidity Facilities Affect Interbank Lending Rates?
Journal of Business and Economic Statistics 32(1), January 2014, 136-151 | with Lopez and Rudebusch
abstract (+)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.
Extracting Deflation Probability Forecasts from Treasury Yields
International Journal of Central Banking 8(4), December 2012, 21-60 | with Lopez and Rudebusch
abstract (+)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.
The Response of Interest Rates to U.S. and U.K. Quantitative Easing
Economic Journal 122(564), November 2012, F385-F414 | with Rudebusch
abstract (+)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(1), September 2011, 4-20 | with Diebold and Rudebusch
abstract (+)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
abstract (+)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.
An Arbitrage-Free Generalized Nelson-Siegel Term Structure Model
Econometrics Journal 12(3), November 2009, 33-64 | with Diebold and Rudebusch
abstract (+)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
abstract (+)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.
FRBSF Publications
Are Inflation Expectations Well Anchored in Mexico?
Economic Letter 2023-01 | January 17, 2023 | with Beauregard, Fischer, and Zhu
COVID-19 Fiscal Expansion and Inflation Expectations in Japan
Economic Letter 2022-20 | August 3, 2022 | with Spiegel
The Increase in Inflation Compensation: What’s Up?
Economic Letter 2022-18 | July 5, 2022
What Would It Cost to Issue 50-year Treasury Bonds?
Economic Letter 2021-29 | November 8, 2021 | with Lopez and Mussche
Exploring the Safety Premium of Safe Assets
Economic Letter 2021-13 | May 10, 2021 | with Mirkov
Emerging Bond Markets and COVID-19: Evidence from Mexico
Economic Letter 2020-23 | August 17, 2020 | with Fischer and Shultz
Coronavirus and the Risk of Deflation
Economic Letter 2020-11 | May 11, 2020 | with Gamble and Zhu
Yield Curve Responses to Introducing Negative Policy Rates
Economic Letter 2019-27 | October 15, 2019
Negative Interest Rates and Inflation Expectations in Japan
Economic Letter 2019-22 | August 26, 2019 | with Spiegel
The Risk of Returning to the Zero Lower Bound
Economic Letter 2019-14 | May 13, 2019
The Slope of the Yield Curve and the Near-Term Outlook
Economic Letter 2018-23 | October 15, 2018
Do Foreign Funds Matter for Emerging Market Bond Liquidity?
Economic Letter 2018-16 | June 18, 2018 | with Fischer and Shultz
Do Adjustment Lags Matter for Inflation-Indexed Bonds?
Economic Letter 2018-08 | March 26, 2018
New Evidence for a Lower New Normal in Interest Rates
Economic Letter 2017-17 | June 19, 2017 | with Rudebusch
Measuring Interest Rate Risk in the Very Long Term
Economic Letter 2017-12 | April 24, 2017 | with Lopez and Mussche
Do All New Treasuries Trade at a Premium?
Economic Letter 2017-03 | February 6, 2017 | with Lopez and Shultz
TIPS Liquidity and the Outlook for Inflation
Economic Letter 2016-35 | November 21, 2016 | with Andreasen
Differing Views on Long-Term Inflation Expectations
Economic Letter 2016-11 | April 4, 2016 | with Lopez
Assessing Supervisory Scenarios for Interest Rate Risk
Economic Letter 2015-29 | September 8, 2015 | with Lopez
Transmission of Asset Purchases: The Role of Reserves
Economic Letter 2015-20 | June 22, 2015 | with Krogstrup
Assessing Expectations of Monetary Policy
Economic Letter 2014-27 | September 8, 2014 | with Kwan
Financial Market Outlook for Inflation
Economic Letter 2014-14 | May 12, 2014 | with Bauer
Stress Testing the Fed
Economic Letter 2014-08 | March 24, 2014 | with Lopez and Rudebusch
When Will the Fed End Its Zero Rate Policy?
Economic Letter 2014-04 | February 10, 2014
Do Fed TIPS Purchases Affect Market Liquidity?
Economic Letter 2012-07 | March 5, 2012 | with Gillan
TIPS Liquidity, Breakeven Inflation, and Inflation Expectations
Economic Letter 2011-19 | June 20, 2011 | with Gillan
Has the Treasury Benefited from Issuing TIPS?
Economic Letter 2011-12 | April 18, 2011 | with Gillan
TIPS and the Risk of Deflation
Economic Letter 2010-32 | October 25, 2010
Inflation Expectations and the Risk of Deflation
Economic Letter 2009-34 | November 2, 2009
Have the Fed Liquidity Facilities Had an Effect on Libor?
Economic Letter 2009-25 | August 10, 2009
Treasury Bond Yields and Long-Run Inflation Expectations
Economic Letter 2008-25 | August 15, 2008
The Corporate Bond Credit Spread Puzzle
Economic Letter 2008-10 | March 14, 2008
Internal Risk Models and the Estimation of Default Probabilities
Economic Letter 2007-29 | September 28, 2007
