Jens Christensen

Senior Economist

Financial Research

Finance, Credit risk, Term structure

Jens.Christensen (at)


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Show less Current Unpublished Working Papers

Transmission of Quantitative Easing: The Role of Central Bank Reserves
2014-18 | With Krogstrup | March 2015

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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.

Can Spanned Term Structure Factors Drive Stochastic Yield Volatility?
2014-03 | With Lopez and Rudebusch | January 2014

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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

Modeling Yields at the Zero Lower Bound: Are Shadow Rates the Solution?
2013-39 | With Rudebusch | December 2013

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Recent U.S. Treasury yields have been constrained to some extent by the zero lower bound (ZLB) on nominal interest rates. In modeling these yields, we compare the performance of a standard affine Gaussian dynamic term structure model (DTSM), which ignores the ZLB, and a shadow-rate DTSM, which respects the ZLB. We find that the standard affine model is likely to exhibit declines in fit and forecast performance with very low interest rates. In contrast, the shadow-rate model mitigates ZLB problems significantly and we document superior performance for this model class in the most recent period.

A Probability-Based Stress Test of Federal Reserve Assets and Income
2013-38 | With Lopez and Rudebusch | December 2013

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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.

A Regime-Switching Model of the Yield Curve at the Zero Bound
2013-34 | January 2015

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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, as the U.S. economy has been since December 2008. 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.

Does Quantitative Easing Affect Market Liquidity?
2013-26 | With Gillan | July 2014

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The Federal Reserve’s second program of large-scale asset purchases, or quantitative easing – frequently referred to as QE2 – included repeated purchases of Treasury inflation protected securities (TIPS). Using a counterfactual analysis, we quantify the effect QE2 had on a model-free measure of combined liquidity premiums in TIPS yields and inflation swap rates. We find that, for the duration of the QE2 program, the liquidity premium measure averaged 12 to 14 basis points lower than expected, a reduction of about 50 percent. This suggests that one benefit of quantitative easing is to improve market liquidity.

Pricing Deflation Risk with U.S. Treasury Yields
2012-07 | With Lopez and Rudebusch | July 2014

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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.

Could the U.S. Treasury Benefit from Issuing More TIPS?
2011-16 | With Gillan | June 2012

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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.

Show less Published Articles (Refereed Journals and Volumes)

Estimating Shadow-Rate Term Structure Models with Near-Zero Yields
Journal of Financial Econometrics, April 2014 | With Rudebusch

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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.

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

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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

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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

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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

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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

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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

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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

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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.

Show less FRBSF Publications

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

Show more Other Works

Common Risk Factors in the U.S. Treasury and Corporate Bond Markets: An Arbitrage-free Dynamic Nelson-Siegel Modeling Approach
Work in Progress, October 2012 | With Lopez

+ abstract
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