Term Structure Models Research Articles

APPROXIMATE SERIES SOLUTIONS OF A ONE-FACTOR TERM STRUCTURE MODEL FOR BOND PRICING

One-factor term structure model in finance and economic setups conveys the opinion that there exists only one Brownian process in the formulation of the short rate model as one source of randomness. To extend the theory, in this paper, we develop the approximate solution of a one-factor bond pricing model that can be used to obtain solutions of both nonlinear and multi-factor models and get applications of two proposed solution methods: Elzaki Adomian decomposition method (EADM) and Laplace Adomian decomposition solution method (LADM). We first obtain an efficient, reliable and approximate-analytical solution for a one-factor bond pricing model. We provide illustrative examples that are in good agreement when compared with those already in literature. The methods are very effective in the application being the modified version of the classical Elzaki, and Laplace transforms. Since our proposed methods are effective and efficient, we recommend academics and practitioners apply our proposed model to obtain solutions for some financial models, including both the multi-factor and nonlinear models.

Development of an Impairment Point in Time Probability of Default Model for Revolving Retail Credit Products: South African Case Study

A new methodology to derive IFRS 9 PiT PDs is proposed. The methodology first derives a PiT term structure with accompanying segmented term structures. Secondly, the calibration of credit scores using the Lorenz curve approach is used to create account-specific PD term structures. The PiT term structures are derived by using empirical information based on the most recent default information and account risk characteristics prior to default. Different PiT PD term structures are developed to capture the structurally different default risk patterns for different pools of accounts using segmentation. To quantify what a materially different term structure constitutes, three tests are proposed. Account specific PiT PDs are derived through the Lorenz curve calibration using the latest default experience and credit scores. The proposed methodology is illustrated on an actual dataset, using a revolving retail credit portfolio from a South African bank. The main advantages of the proposed methodology include the use of well-understood methods (e.g., Lorenz curve calibration, scorecards, term structure modelling) in the banking industry. Further, the inclusion of re-default events in the proposed IFRS 9 PD methodology will simplify the development of the accompanying IFRS 9 LGD model due to the reduced complexity for the modelling of cure cases. Moreover, attrition effects are naturally included in the PD term structures and no longer require a separate model. Lastly, the PD term structure is based on months since observation, and therefore the arrears cycle could be investigated as a possible segmentation.

Monetary reforms and inflation expectations in Japan: Evidence from inflation-indexed bonds

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.

Term structure modeling under volatility uncertainty

In this paper, we study term structure movements in the spirit of Heath et al. (Econometrica 60(1):77–105, 1992) under volatility uncertainty. We model the instantaneous forward rate as a diffusion process driven by a G-Brownian motion. The G-Brownian motion represents the uncertainty about the volatility. Within this framework, we derive a sufficient condition for the absence of arbitrage, known as the drift condition. In contrast to the traditional model, the drift condition consists of several equations and several market prices, termed market price of risk and market prices of uncertainty, respectively. The drift condition is still consistent with the classical one if there is no volatility uncertainty. Similar to the traditional model, the risk-neutral dynamics of the forward rate are completely determined by its diffusion term. The drift condition allows to construct arbitrage-free term structure models that are completely robust with respect to the volatility. In particular, we obtain robust versions of classical term structure models.

The TIPS Liquidity Premium

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 risk premia in emerging markets: evidence from Brazil, China, Mexico, and Russia

ABSTRACT We employ an affine term structure model with no-arbitrage restrictions and unspanned risk factors to analyse the global and domestic determinants of bond risk premia in four major emerging markets (Brazil, China, Mexico, and Russia). Among the risk factors, we select national inflation and economic growth, and the country-specific nominal exchange rate against the US dollar as the variables related to the domestic economy. We include a measure of worldwide economic activity, the Market Volatility Index (VIX), and an aggregate price index of commodities in the group of global factors. Our model captures (long-term) movements of realized risk premia and indicates that global economic and financial factors play a relevant role in explaining country-specific bond risk premia dynamics. In contrast, domestic variables carry little explanatory power to rationalize risk premia developments in these four economies. We also provide evidence of heterogeneous responses of country-specific risk premia to global and domestic shocks.

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.

Bayesian Estimation For Cox Ingersoll Ross Process

the model of term structure of interest rates are consider the most significant and computationally difficult portion of the modern finance due to a relative complexity of using techniques. This article concerns the Bayesian estimation of interest rate models. Assume the short term interest rate follows the Cox Ingersoll Ross (CIR) process , this process has several feature. In particular mean reverting and the other feature is remanis non- negative , so this is what distinguishes it from previous models. It is implement in the R programing.

Arbitrage-free Nelson\u2013Siegel model for multiple yield curves

We propose an affine term structure model that allows for tenor-dependence of yield curves and thus for different risk categories in interbank rates, an important feature of post-crisis interest rate markets. The model has a Nelson–Siegel factor loading structure and thus economically well interpretable parameters. We show that the model is tractable in terms of estimation and provides good in-sample fit and out-of-sample forecasting performance. The proposed model is arbitrage-free across maturities and tenors, and thus perfectly suited for risk management and pricing purposes. We apply our framework to the pricing of caplets in order to illustrate its practical applicability and its suitability for stress testing.

Long-term foreign exchange risk premia and inflation risk

As highlighted by recent literature, long-term foreign exchange risk premia (FRP) of a currency pair tend to covary negatively with short-term real interest rate differentials (RIRD) of the pair. We fit an affine term structure model for 9 major currencies against the US dollar and estimate two components of this covariance: the real risk premia (RRP) component and the inflation risk premia differential (IRPD) component. We find that the IRPD component is significantly negative for all currency pairs in our sample. We propose a macro-finance model to understand the types of shocks that generate such covariance.

THE AFFINE RATIONAL POTENTIAL MODEL

We develop a class of rational term structure models in the framework of the potential approach based upon a family of positive supermartingales that are driven by an affine Markov process. These models generally feature nonnegative interest rates and analytic pricing formulae for zero bonds, caps, swaptions, and European currency options, even in the presence of multiple factors. Moreover, in a model specification, the short rate stays near the zero lower bound for an extended period.

Monetary Policy Risk: Rules versus Discretion

AbstractLong-run asset pricing restrictions in a macro term structure model identify discretionary monetary policy separately from a policy rule. We find that policy discretion is an important contributor to aggregate risk. In addition, discretionary easing coincides with good news about the macroeconomy in the form of lower inflation, higher output growth, and lower risk premiums on short-term nominal bonds. However, it also coincides with bad news about long-term financial conditions in the form of higher risk premiums on long-term nominal bonds. Shocks to the rule correlate with changes in the yield curve’s level. Shocks to discretion correlate with changes in its slope.

The application of different term-structure models to estimate South African real spot rate curve

The purpose of this study is to investigate the suitable arbitrage-free term-structure model that might be able to fit the South African inflation-indexed spot-rate curve. The instrument has relatively less tradability in the market, which then translates into a lack of adequate data for bond valuation/pricing. Pricing deviations might give inflated/deflated projections on the value of government debt; consequently, higher estimated interest cost to be paid. A proper valuation of these instruments is mandatory as they form part of government funding/borrowing and the country’s budgeting processes in the medium term. The performance of newly developed non-linear multifactor models that follows the Nelson-Siegel (1987) framework was compared to the arbitrage-free Vasicek (1977) model and linear parametric models to assess any significant deviations in forecasting the real spot-rate curve over a short period. Models with constant parameters (i.e. linear parametric, cubic splines, Nelson-Siegel (1987) and Svensson (1994)) gave a perfect fit, they proved to marginally lose fitting capabilities during periods of higher volatility. Therefore, it could be concluded that the application of either Nelson-Siegel (1987) model or Svensson (1994) model on forecasting South African real spot-rate curve gave a perfect fit. However, for a solid conclusion to be derived, it is imperative to explore the performance of these models over a period of stressed market and economic conditions.

Monetary policy surprises and their transmission through term premia and expected interest rates

Monetary policy moves the yield curve. What is the economic interpretation of such moves and what are their macroeconomic consequences? Applying an affine term structure model to high-frequency yield curve movements around FOMC announcements, we shed new light on these questions. Estimation is subject to restrictions addressing estimation bias in previous studies. By imposing additional structure, expectations and term premia are decomposed into three components interpreted as monetary policy action, expected path and its uncertainty. In a local projections model, the shocks identified by the three components provide insights into monetary policy transmission in the context of existing theories.

A Computational Analysis of the Tradeoff in the Estimation of Different State Space Specifications of Continuous Time Affine Term Structure Models

A Computational Analysis of the Tradeoff in the Estimation of Different State Space Specifications of Continuous Time Affine Term Structure Models

Estimating the Interest Rate Term Structures of Treasury and Corporate Debt with Bayesian Penalized Splines

This paper provides a Bayesian approach to estimating the interest rate term structures of Treasury and corporate debt with a penalized spline model. Although the literature on term structure modeling is vast, to the best of our knowledge, all methods developed so far belong to the frequentist school. In this paper, we develop a two-step estimation procedure from a Bayesian perspective. The Treasury term structure is first estimated with a Bayesian penalized spline model. The smoothing parameter is naturally embedded in the model as a ratio of posterior variances and does not need to be selected as in the frequentist approach. The corporate term structure is then estimated by adding a credit spread to the estimated Treasury term structure, incorporating knowledge of the positive credit spread into the Bayesian model as an informative prior. In contrast to the frequentist method, the small sample size of the corporate debt poses no particular difficulty to the proposed Bayesian approach.

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.

No‐arbitrage priors, drifting volatilities, and the term structure of interest rates

AbstractWe use a Bayesian vector autoregression with stochastic volatility to forecast government bond yields. We form the conjugate prior from a no‐arbitrage affine term structure model. The model improves on the accuracy of point and density forecasts from a no‐change random walk and an affine term structure model with stochastic volatility. Our proposed approach may succeed by relaxing the no‐arbitrage affine term structure model's requirements that yields obey a factor structure and that the factors follow a Markov process. In the term structure model, its cross‐equation no‐arbitrage restrictions on the factor loadings appear to play a marginal role in forecasting gains.

Yield Curve Momentum

I analyze time series momentum along the Treasury term structure. Past bond returns predict future returns because of autocorrelation in both bond carry and yield changes. Yield curve momentum can largely be captured using a single bond return or yield change factor. Because yield changes are partly induced by changes in the federal funds rate, yield curve momentum is related to FOMC post announcement drift. The momentum factor is unspanned by the information in the term structure today and is hence inconsistent with standard term structure, macrofinance and behavioural models, including models designed to explain momentum. I propose a potential resolution.

A Segmented and Observable Yield Curve for Colombia

Abstract Following (Almeida, Ardison, Kubudi, Simonsen, & Vicente, 2018) we implement a segmented three factor Nelson-Siegel model for the yield curve using daily observable bond prices and short term interbank rates for Colombia. The flexible estimation for each segment (short, medium, and long) provides an improvement over the classical Nelson-Siegel approach in particular in terms of in-sample and out-of-sample forecasting performance. A segmented term structure model based on observable bond prices provides a tool closer to the needs of practitioners in terms of reproducing the market quotes and allowing for independent local shocks in the different segments of the curve.