Dynamic Term Structure Models 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.

What is the Effect of Restrictions Imposed by Principal Components Analysis on the Empirical Performance of Dynamic Term Structure Models?

What is the Effect of Restrictions Imposed by Principal Components Analysis on the Empirical Performance of Dynamic Term Structure Models?

Inflation expectations and risk premia in emerging bond markets: Evidence from Mexico

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.

Inflation Expectations, Liquidity Premia and Global Spillovers in Japanese Bond Markets

We provide market-based estimates of Japanese inflation expectations using an arbitrage-free dynamic term structure model of nominal and real yields that accounts for liquidity premia and the deflation protection afforded by Japanese inflation-indexed bonds, known as JGBi’s. We find that JGBi liquidity premia exhibit significant variation, and even switch sign. Properly accounting for them significantly lowers the estimated value of the indexed bonds’ deflation protection and affects inflation risk premium estimates. After liquidity adjustment, long-term Japanese inflation expectations have remained relatively stable at levels modestly exceeding one percent during the pandemic period. We then utilize our estimated liquidity measure to confirm the existence of statistically significant and economically meaningful spillovers to the JGBi market from global bond market illiquidity, as proxied by periods of low U.S. Treasury market depth.

Quantitative Easing, Bond Risk Premia and the Exchange Rate in a Small Open Economy

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.

Sequential Learning and Economic Benefits from Dynamic Term Structure Models

We explore the statistical and economic importance of restrictions on the dynamics of risk compensation from the perspective of a real-time Bayesian learner who predicts bond excess returns using dynamic term structure models (DTSMs). The question on whether potential statistical predictability offered by such models can generate economically significant portfolio benefits out-of-sample is revisited while imposing restrictions on their risk premia parameters. To address this question, we propose a methodological framework that successfully handles sequential model search and parameter estimation over the restriction space in real time, allowing investors to revise their beliefs when new information arrives, thus informing their asset allocation and maximizing their expected utility. Empirical results reinforce the argument of sparsity in the market price of risk specification since we find strong evidence of out-of-sample predictability only for those models that allow for level risk to be priced and, additionally, only one or two of these risk premia parameters to be different than zero. Most importantly, such statistical evidence is turned into economically significant utility gains, across prediction horizons, different time periods and portfolio specifications. In addition to identifying successful DTSMs, the sequential version of the stochastic search variable selection scheme developed can be applied on its own and offer useful diagnostics monitoring key quantities over time. Connections with predictive regressions are also provided. This paper was accepted by Kay Giesecke, finance. Funding: T. Dubiel-Teleszynski acknowledges the support of the Economic and Social Research Council. Supplemental Material: The data files and online appendices are available at https://doi.org/10.1287/mnsc.2023.4801 .

Identification robust inference for the risk premium in term structure models

We propose identification robust statistics for testing hypotheses on the risk premia in dynamic affine term structure models. We do so using the moment equation specification proposed in Adrian et al. (2013). Statistical inference based on their three-stage estimator requires knowledge of the risk factors’ quality and can be misleading when the β’s are weak, which results when sampling errors are of comparable order of magnitude as the risk factor loadings. We extend the subset (factor) Anderson–Rubin test from Guggenberger et al. (2012) to models with multiple dynamic factors and time-varying risk prices. It provides a computationally tractable manner to conduct identification robust tests on a few risk premia when a larger number is present. We use it to analyze potential identification issues arising in the data from Adrian et al. (2013) for which we show that some factors, though potentially weak, may drive the time variation of risk prices, and weak identification issues are more prominent in multi-factor models.

The Natural Rate of Interest in the Euro Area: Evidence from Inflation-Indexed Bonds

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.

TERM STRUCTURE MODELING OF SOFR: EVALUATING THE IMPORTANCE OF SCHEDULED JUMPS

As interest rate benchmarks move from LIBOR to overnight risk-free rates (RFR), it has become increasingly important for models to accurately capture the interest rate dynamics at the overnight tenor. Overnight rates closely track central bank policy rate decisions resulting, in highly discontinuous dynamics around scheduled meeting dates. In this paper, we construct a dynamic term structure model, which accounts for the discontinuous short-rate dynamics. We show that the model is able to jointly fit the overnight US policy rate, secured overnight financing rate (SOFR) and SOFR futures rates through the recent Fed hiking cycle. Comparing our model with a standard continuous time-homogeneous short-rate model, we find several indications that our model avoids the clear misspecification of the continuous model, in particular with regard to the short-rate dynamics around meeting dates of the Federal Open Market Committee (FOMC). Thiseffect begins to disappear as the term of the rates under consideration is increased, suggesting that diffusive dynamics are a reasonably accurate reflection of the evolution of market expectations embodied in longer-term interest rates.

Supplementary Material for 'What is the Effect of Restrictions Imposed by Principal Components Analysis on the Empirical Performance of Dynamic Term Structure Models?'

Supplementary Material for 'What is the Effect of Restrictions Imposed by Principal Components Analysis on the Empirical Performance of Dynamic Term Structure Models?'

Forecasting the South African Real Spot-rate Curve During Covid-19 Stress

Purpose: The aim of this study is to investigate the performance of forecasting the South African real spot rate curve using different mathematical term-structure models during the Covid-19 period. This study follows previous studies by Reid (2009) and Mashoene et al., 2021) where dynamic term-structure models performed well compared to static term-structure models over normal market conditions. For high volatility, normality often breaks, which might result in a need for recalibration in the currently used methodology or a total change in the methodology.
 Methodology: This study explores the dynamism of both dynamic term-structure models, which follow the Nelson-Siegel framework, and static term-structure models with the option of recalibration of model parameters to account for a change in macro-economic dynamics brought by the effect of the Covid-19 pandemic. The forecasting exercise was applied to term-structure models following the Nelson-Siegel framework using AR(1) process.
 Findings: The incorporation of macroeconomic factors performed poorly in estimating future model parameters. This could be attributable to the effect of global stress, which resulted in poor linear relationships between macroeconomic and financial factors. Recalibration process on static Nelson-Siegel term-structure models improved the models' performance, especially during the high volatility/period of total economic shutdown due to the Covid-19 pandemic.
 Implications: The application of static Nelson-Siegel term-structure models with recalibrated parameters might improve bond pricing processes and risk management strategies in emerging markets, especially during market stress.

International linkages of term structures: US and Korea Treasury bond yields

This study analyzes the international linkages of term structures between the United States (US) and Korea using a Gaussian dynamic term structure model. The empirical analysis shows that the US level factor makes the most important contribution to the Korean term structure fluctuations. When two separate channels (i.e., policy and risk-compensation) are considered for propagating structural shocks into Korean bond yields, the policy channel dominates for the short-term rates, whereas for the long-term yield, the policy channel is dominant for the US level shock, but the risk channel is dominant for other shocks. These results are sensitive to whether or not small-sample bias is corrected. With a help of the bias correction, term premium estimates in the US and Korea exhibit substantial countercyclicality with respect to the US output gap. The US slope factor, which also has a significant impact on Korean long-term yields, is closely related to the global liquidity conditions for Korean bond returns.

Correcting estimation bias in regime switching dynamic term structure models

Correcting estimation bias in regime switching dynamic term structure models

Unspanned macro risks in VIX futures

AbstractThis study investigates hidden factors in the volatility index (VIX) futures market. Risk factors spanned by the futures curve have a limited ability to capture variations in the expected excess returns. The market's hidden factors provide additional predictive power for future returns in addition to that provided by the factors spanned by the futures curve. The use of a dynamic term structure model with these hidden factors indicates that the hidden factors as a proxy for macro risks materially impact the VIX futures returns and their yield term structure and are significantly helpful in depicting the dynamics of the risk premia.

Term Premia in Norwegian Interest Rate Swaps

Fundamentally, the term premium in long-term nominal yields is compensation to investors for bearing interest rate risk. There is substantial evidence of sizable and time-varying term premia. As opposed to yields, term premia are not directly observable. In this paper, we estimate term premia in Norwegian interest rate swaps from a set of dynamic term structure models, covering the period from 2001/04 until 2022/06. In line with international studies, we find evidence of declining term premia over the sample period. Furthermore, our estimates indicate that term premia have been close to zero, as well as negative in periods, during the last decade of global extraordinary monetary policy measures. We find that the recent rise in Norwegian interest rate swaps is partly caused by increases in term premia. From a practitioner’s perspective, our term premia estimates can be utilized as part of applied management of both investment and debt portfolios.

The Benefit of Inflation-Indexed Debt: Evidence from an Emerging Bond Market

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.

The Practicality of Vasicek Model in China’s Financial Market

In the changing financial market, the price of financial products fluctuates continuously over time. The study of the static term structure of the interest rate on the market can no longer satisfy the actual needs, and the dynamic model is imperative. Compared with the static term structure, the dynamic model introduces a stochastic differential term on the basis of the static term structure model of interest rate. This paper shows some relevant models including Vasicek Model, Single-Factor Dynamic Model, Multi-Factor Dynamic Model, and Kalman Filter method. To conclude, in the multi-factor dynamic interest rate term structure model, Kalman Filter has many benefits. However, it still has actual limitations. The multi-factor Vasicek model still needs some analysis to find the error and do the correction. In the research of bond pricing, risk management, and other aspects, the multi-factor model should be the main direction.

The time-varying bond risk premia in China

Unlike many developed countries in which zero interest rate policies are widely adopted, there is still room for interest rate fluctuations in China. Nevertheless, the dynamics of bond yields, forward rates and risk premia still differ from the traditional understanding. This paper focuses on the Chinese treasury bonds. By OLS regressions, we find movements in the current forward rate fully reflect future bond risk premia, while other variables do not improve its performances, regardless of in- and out-of-sample predictions. This result is confirmed by a group of no-arbitrage dynamic term structure models. Moreover, the theoretical models reveal three important findings: 1. there are about 20% predictable variations in annual excess returns; 2. only the level factor risk is priced; 3. the candidate macroeconomic variables cannot contribute to the term premia structure.

Special Repo Rates and the Cross-Section of Bond Prices: The Role of the Special Collateral Risk Premium

Abstract We price the risky component of specialness spreads—identified by their deviations from the expected auction cycle—within a dynamic term structure model estimated using daily prices of all outstanding Treasury securities and corresponding special collateral (SC) repo rates. This allows us to derive a time-varying SC risk premium that we quantitatively link to various price anomalies, such as the on-the-run premium. The SC risk premium explains about 80% of the on-the-run premium and a substantial share of other Treasury price anomalies, suggesting that unexpected fluctuations in the specialness spreads of recently issued nominal Treasury securities are a common risk factor.

Dynamic term structure models for SOFR futures

AbstractThe London InterBank Offered Rate is scheduled for discontinuation, and the replacement advocated by US regulators is the Secured Overnight Financing Rate (SOFR). The only SOFR‐linked derivative with significant liquidity and trading history is the SOFR futures contract, traded at the Chicago Mercantile Exchange. We use the historical record of futures prices to construct dynamic arbitrage‐free models for the SOFR term structure. We find that a Gaussian arbitrage‐free Nelson–Siegel model describes term structure well without accounting for jumps and seasonal effects observed in SOFR. However, a shadow‐rate extension is needed to describe volatility near the zero‐boundary impacting the futures convexity adjustment and option pricing.