Term Structure Models Research Articles

Consistent time‐homogeneous modeling of SPX and VIX derivatives

AbstractThis paper shows how to recover a stochastic volatility model (SVM) from a market model of the VIX futures term structure. Market models have more flexibility for fitting of curves than do SVMs, and therefore are better suited for pricing VIX futures and VIX derivatives. But the VIX itself is a derivative of the S&P500 (SPX) and it is common practice to price SPX derivatives using an SVM. Therefore, consistent modeling for both SPX and VIX should involve an SVM that can be obtained by inverting the market model. This paper's main result is a method for the recovery of a stochastic volatility function by solving an inverse problem where the input is the VIX function given by a market model. Analysis will show conditions necessary for there to be a unique solution to this inverse problem. The models are consistent if the recovered volatility function is non‐negative. Examples are presented to illustrate the theory, to highlight the issue of negativity in solutions, and to show the potential for inconsistency in non‐Markov settings.

Volatility Level Dependence and Linear-Rational Term Structure Models

ABSTRACT We outline a subclass of linear-rational term structure models, based on CEV dynamics. A tractable and arbitrage-free term structure results from the linear-rational aspect of the model, independently of the term-structure volatility dynamics that follow from the CEV specification. This specification is devised to capture a flexible degree of volatility-level dependence, i.e., the degree to which yield-curve volatility depends on yield levels. We estimate the model based on a panel of South African swap rates, and extract the degree of volatility-level dependence inherent in the time series of rates, without interference from the shape of the swap curve. The CEV exponent parameters are found to be essential for matching the low degree of volatility-level dependence that tends to be observed in the high interest-rate environments of emerging markets.

International Yield Comovements

AbstractWe decompose long-term nominal bond yields into real and inflation components in an international context using inflation-linked and nominal bonds. In contrast to extant results, real rate variation dominates the variation in inflation-linked and nominal yields. Cross-country nominal and inflation-linked yield correlations have declined since the Great Recession. Real rates are the main source of the correlation between nominal yields. Our results are robust to various alternative measurements of inflation expectations and the liquidity premium. They continue to hold when a no-arbitrage term structure model with real, nominal, and inflation factors is used to effect the yield decomposition.

The yen–dollar risk premium: A story of regime shifts in bond markets

We document a new risk premium in the yen–dollar currency pair that compensates for the uncertainty over regime shifts in the bond market. We estimate a no-arbitrage regime-switching term structure model, where the transition of volatility regimes is driven by the level of yields and is associated with a regime risk premium. We find that the currency excess return is explained by the regime risk premium in Japan in the second half of 1990s and in the US at the height of the Great Recession. The regime risk premium contains information beyond the affine model, the forward premium, and the carry and dollar factors.

Berry–Esseen inequalities for the fractional Black–Karasinski model of term structure of interest rates

Abstract The Black–Karasinski model is a one-factor non-affine interest rate model as it describes interest rate movements driven by a single source of randomness and the drift function is a nonlinear function of the interest rate. The drift parameters represent the level and the speed of mean reversion of the interest rate. It belongs to the class of no-arbitrage models. The paper introduces some new approximate minimum contrast estimators of the mean reversion speed parameter in the model based on discretely sampled data which are efficient and studies their asymptotic distributional properties with precise rates of convergence.

Long-term sovereign interest rates in Czechia, Hungary and Poland: a comparative assessment with an affine term structure model

Abstract This paper provides a comparative evaluation of the behaviour of long-term sovereign yields in Czechia, Hungary and Poland from 2001 to 2019. An affine term structure model developed by Adrian, Crump and Moench (2013) is used as an empirical framework for the decomposition of the bond yields into term premium and risk-neutral components. We document a substantial compression in term premia which started in Central European economies around 2013 and played a decisive role in the changes that occurred in 10-year sovereign yields. This pattern, however, was more prevalent in Czechia and Poland than in Hungary. We show that long-term rates in all three economies remained higher than in Germany due to relatively large risk-neutral components. Nevertheless, cross-country correlations became increasingly dependent on term premium dynamics, both among Central European economies and between each of them and Germany. These results are robust to bias-correction in the baseline models and interpreted in the light of the general interest rates decline in the global economy. Potential policy implications are also discussed.

A Joint Model for the Term Structure of Interest Rates and Realized Volatility

Abstract This paper presents a term structure model for no-arbitrage bond yields and realized bond market volatility. Based on well-known results, realized yield curve covariation is linked to generalized autoregressive conditional heteroskedasticity (GARCH)-type conditional covariation. The model is tractable and its latent state variables can be filtered using an exact algorithm. In an empirical study of U.S. Treasury bond data, the model shows that conditional yield curve covariation is priced in long-term yields. Moreover, the model proves useful for multi-step ahead forecasting of realized covariation. Finally, I use the model to quantify interest-rate risk and risk compensation.

Tractable Term Structure Models

We introduce a new framework that facilitates term structure modeling with both positive interest rates and flexible time series dynamics but that is also tractable, meaning amenable to quick and robust estimation. Using both simulations and U.S. historical data, we compare our approach with benchmark Gaussian and stochastic volatility models as well as a shadow rate model that enforces positive interest rates. Our approach, which remains arbitrarily close to arbitrage free, offers a more accurate characterization of bond Sharpe ratios because of a better fit of the volatility dynamics and a more efficient estimation of the return dynamics. Further, the shadow rate and stochastic volatility models exhibit important restrictions that are largely absent in our approach. This paper was accepted by Agostino Capponi, finance. Supplemental Material: The data files and online appendix are available at https://doi.org/10.1287/mnsc.2021.4214 .

Break-even inflation rates: the Italian case

PurposeThis work aims to study the break-even inflation rates (BEIRs), a widely used market-based measure of expected inflation. The authors focus on Italian Government bonds, one of the most liquid debt markets in the euro area.Design/methodology/approachThe authors set up an auto-regressive distributed lag model and regress the BEIR on a set of variables that proxy inflation, market risk aversion, protection against deflation, credit as well as liquidity risk to get some insights into the importance of these factors. Subsequently, to disentangle market participants’ inflation expectations from their associated risk premia, the authors estimate a term structure model for the joint pricing of the Italian Government’s nominal and real yield curves, considering also a credit and a liquidity pricing factor.FindingsThe results show that BEIRs could be a misleading measure of the expected inflation due to the importance of the inflation risk premium and the credit risk effect. According to the estimates, the decrease of market-based measures of inflation observed in the last part of the sample period seems to reflect a lowering of both inflation expectations and risk premia. Inflation premia co-move with a measure of the tail risk of the long-term inflation distribution, signalling that investors become more concerned with downside risks.Originality/valueThis study complements the existing literature primarily based on the USA and euro area data focusing on the Italian market. To this end, the authors modify and adapt a well-known term structure model developed for nominal and real curves.

Affine term structure models: A time‐change approach with perfect fit to market curves

AbstractWe address the so‐called calibration problem, which consists of fitting in a tractable way a given model to a specified term structure such as yield, prepayment or default probability curves. Time‐homogeneous affine jump diffusions (HAJD) are tractable processes but have limited flexibility; they fail to perfectly replicate actual market curves. Applying a deterministic shift to the latter is a simple but efficient solution that is widely used by both academics and practitioners. However, the shift approach may not be appropriate when positivity is required, a common constraint when dealing with credit spreads or default intensities. In this paper, we address this problem by adopting a time‐change technique. Specific attention is paid to the Cox–Ingersoll–Ross model with compound Poisson jumps (JCIR), which remains standard for modeling intensities. Our time‐changed JCIR (TC‐JCIR) is compared to the shifted JCIR (JCIR++) in various credit applications such as credit default swap (CDS), credit default swaption, and credit valuation adjustment (CVA) under wrong‐way risk (WWR). The TC‐JCIR model is able to generate much larger implied volatilities and covariance effects than JCIR++ under positivity constraints and represents an appealing alternative to the latter.

Term Structure Model for Sri Lankan Bond Market

Term Structure Model for Sri Lankan Bond Market

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.

Dissecting the yield curve: The international evidence

We develop a term structure model that decomposes nominal yields into the sum of an expectation, term premium, and convexity term and in turn of their real and inflation counterparts. The model explicitly captures the interrelation between yield-only and macroeconomic factors while allowing for aggregate stochastic volatility. We extract the components from the nominal and real yield curve of the United States, the Euro Area, the United Kingdom, and Japan. We find that short-rate expectations have steadily declined over the last two decades and account for the bulk of yield dynamics. Term premia increase with maturity but explain a smaller fraction of yield forecast error variance than previously documented. With regard to yield comovement, the United States generates the strongest spillovers at the long end of the yield curve, whereas the Japanese market is the top importer of shocks.

A Consumption-Based Term Structure Model of Bond and Equity

A Consumption-Based Term Structure Model of Bond and Equity

A Linear-Rational Multi-Curve Term Structure Model with Stochastic Spread

A Linear-Rational Multi-Curve Term Structure Model with Stochastic Spread

A Quantum Mechanics for interest rate derivatives markets

We present a model-free axiomatic formulation of Option Pricing Theory for interest rate derivatives. In this setting, completely analogous to axiomatic Quantum Mechanics, the role of the wave function is played by the discounted zero-coupon bond price. The theory is linked to term structure models through the Hamiltonian operator, and we show that its associated Schrödinger equation is consistent with the [25] model. We also find the quantum-mechanical equivalent of the standard risk-neutral option pricing formula.In order to take advantage of this quantum framework, we develop a time-dependent perturbation theory and we apply it to obtain an approximate closed-form expression for the price of a call option under the [26] model with a small local volatility perturbation.

Central Bank Credibility During COVID-19: Evidence from Japan

Japanese realized and expected inflation has been below the Bank of Japan’s two percent target for many years. We use the exogenous COVID-19 pandemic shock to examine the efficacy of monetary and fiscal policy responses for elevating inflation expectations from an arbitrage-free term structure model of nominal and real yields. We find that monetary and fiscal policy announcements during this period failed to lift inflation expectations, which instead declined notably and are projected to only slowly revert back to levels far below the announced target. Hence, our results illustrate the challenges faced in raising well-anchored low inflation expectations.

Lower Bound Uncertainty and Long‐Term Interest Rates

AbstractNominal interest rates are constrained by an effective lower bound, but the level of the lower bound is uncertain. This paper uses a simple shadow rate term structure model to study how lower bound uncertainty affects long‐term interest rates. A decline in lower bound uncertainty, in the sense of a mean‐preserving contraction, is associated with a drop in expected short rates. The effect on the variance of short rates, and hence the term premium, is ambiguous. A calibration to Canadian data suggests that a decline in lower bound uncertainty is associated with a modest drop in interest rates.

Predicting future exchange rate changes based on interest rates and holding-period returns differentials net of the forward risk premium effects

One of the well-known puzzles in the empirical exchange rate literature is the forward premium anomaly; the interest rates differential between two countries predicts the opposite direction of their future exchange rate changes compared to the predictions of the uncovered interest rate parity (UIRP) under the rational expectations hypothesis (REH). In this paper, we show that the above puzzle can be attributed to the time-variation of the exchange rate risk premium (known as forward risk premium). This premium can also explain the failure of the holding-period returns differential to provide unbiased predictions of the future exchange rate changes. To control for the risk premium effects, in this paper we suggest a new forward premium regression framework adjusting the interest rates differential for these effects which are estimated by a two-country term structure model. We provide evidence that the suggested framework can predict the correct direction of the future exchange rate changes for a number of developed countries with liquid currencies. However, its predictive power is small due to excess volatility of the exchange rate changes.

Modeling persistent interest rates with double-autoregressive processes

We propose a term structure model featuring double-autoregressive dynamics, which can accommodate unit roots and cointegrating relations while maintaining stationarity. In an empirical application, the model reduces in-sample misspecification and significantly improves out-of-sample yield forecasts compared with term structure models based on linear VAR dynamics. The double-autoregressive process implies term premia that resemble the term spread. We test whether these premia help in overcoming the persistence problem of stationary VAR models with mixed results. Finally, we discuss alternative interpretations of the mechanism inducing stationarity in our model.