Some evidence on the international inequality of real interest rates

This paper undertakes econometric tests of the hypothesis that ex-ante real interest rates are equal across countries with highly integrated capital markets. The issue is of practical importance because the violation of real rate equality is a necessary condition for monetary policy to influence the open economy through the real interest rate channel. Although an empirical literature concerning real rate equality already exists, previous investigators have focused on pre-tax real rates. This paper contributes to the literature by attempting to incorporate the effects of taxation into the analysis.     

On the correlation of exchange rates and interest rates

This note shows that a negative correlation between the price of foreign currency and nominal interest rates in not necessarily an indication of movements in the real rate of interests. Such a correlation could be consistent with a monetarist model in which the real rate is constant.     

On a general class of one-factor models for the term structure of interest rates

We propose a general one-factor model for the term structure of interest rates which based upon a model for the short rate. The dynamics of the short rate is described by an appropriate function of a time-changed Wiener process. The model allows for perfect fitting of given term structure of interest rates and volatilities, as well as for mean reversion. Moreover, every type of distribution of the short rate can be achieved, in particular, the distribution can be concentrated on an interval. The model includes several popular models such as the generalized Vasicek (or Hull-White) model, the Black-Derman-Toy, Black-Karasinski model, and others. There is a unified numerical approach to the general model based on a simple lattice approximation which, in particular, can be chosen as a binomial or -nomial lattice with branching probabilities .     

The term structure of real interest rates: theory and evidence from UK index-linked bonds

This paper studies the behavior of the default-risk-free real term structure and term premia in two general equilibrium endowment economies with complete markets but without money. In the first economy there are no frictions as in Lucas (Econometrica 46 (1978) 1429) and in the second risk-sharing is limited by the risk of default as in Alvarez and Jermann (Econometrica 68 (2000) 775; Rev. Financial Studies 14 (2001) 1117). Both models are solved numerically, calibrated to UK aggregate and household data, and the predictions are compared to data on real interest rates constructed from the UK index-linked data. While both models produce time-varying risk or term premia, only the model with limited risk-sharing can generate enough variation in the term premia to account for the rejections of expectations hypothesis.     

Linear-quadratic term structure models – Toward the understanding of jumps in interest rates

We study linear-quadratic term structure models with random jumps in the short rate process where the jump arrival rate follows a stochastic process. Empirical results based on the US data show that incorporating stochastic jump intensity significantly improves model fit to the dynamics of both interest rate and volatility term structure. Our results also show that jump intensity is negatively correlated with interest rate changes and the average size is larger on the downside than upside. Examining the relation between jump intensity and macroeconomic shocks, we find that at monthly frequency, jumps are neither triggered by nor predictive of changes in macroeconomic variables. At daily frequency, however, we document interesting patterns for jumps associated with information shocks.     

Arbitrage bounds for the term structure of interest rates

This paper proposes a methodology for simultaneously computing a smooth estimator of the term structure of interest rates and economically justified bounds for it. It unifies existing estimation procedures that apply regression, smoothing and linear programming methods. Our methodology adjusts for possibly asymmetric transaction costs. Various regression and smoothing techniques have been suggested for estimating the term structure. They focus on what functional form to choose or which measure of smoothness to maximize, mostly neglecting the discussion of the appropriate measure of fit. Arbitrage theory provides insight into how small the pricing error will be and in which sense, depending on the structure of transaction costs. We prove a general result relating the minimal pricing error one incurs in pricing all bonds with one term structure to the maximal arbitrage profit one can achieve with restricted portfolios.     

Stock prices,inflation, and the term structure of interest rates

In this article, the quantitative form of capital market equilibrium is derived for a multi-period economy in which (a) there are many consumption goods whose future prices are uncertain, and (b) the investment opportunities available to consumers include both common stocks and default-free bills of many different maturities. Particular emphasis is placed on consumer reaction to uncertainty about shifts in commodity prices and the term structure of interest rates and on the way one should expect to observe this reaction reflected in portfolio choices and equilibrium stock prices.     

German dominance in the EMS: evidence from interest rates

The paper presents an empirical analysis of German dominance and asymmetries in the EMS based on a dynamic system of equations explaining national money market interest rates. The hypothesis of strict German dominance of the EMS is rejected. However, there are some noticeable asymmetries in the EMS. Germany is a relatively strong player and has been the least dependent country in the early phase of the system. Since 1983, German independence has diminished. In contrast, France throughout and Italy in the early phase of the EMS have been relatively weak players in the system.     

On the term structure of interest rates

The paper presents a valuation formula for default free bonds for a certain class of tastes when the instantaneously riskfree rate of interest follows a geometric Wiener process. Properties of the resulting term structure of interest rates are studied, and an application of the analysis to the pricing of Treasury Bills is proposed.     

Taylor rules, McCallum rules and the term structure of interest rates

Recent empirical research shows that a reasonable characterization of federal-funds-rate targeting behavior is that the change in the target rate depends on the maturity structure of interest rates and exhibits little dependence on lagged target rates. See, for example, Cochrane and Piazzesi [2002. The Fed and interest rates—a high-frequency identification. American Economic Review 92, 90-95.]. The result echoes the policy rule used by McCallum [1994a. Monetary policy and the term structure of interest rates. NBER Working Paper No. 4938.] to rationalize the empirical failure of the ‘expectations hypothesis’ applied to the term structure of interest rates. That is, rather than forward rates acting as unbiased predictors of future short rates, the historical evidence suggests that the correlation between forward rates and future short rates is surprisingly low. McCallum showed that a desire by the monetary authority to adjust short rates in response to exogenous shocks to the term premiums imbedded in long rates (i.e. “yield-curve smoothing”), along with a desire for smoothing interest rates across time, can generate term structures that account for the puzzling regression results of Fama and Bliss [1987. The information in long-maturity forward rates. The American Economic Review 77, 680-392.]. McCallum also clearly pointed out that this reduced-form approach to the policy rule, although naturally forward looking, needed to be studied further in the context of other response functions such as the now standard Taylor [1993. Discretion versus policy rules in practice. Carnegie-Rochester Conference Series on Public Policy 39, 195-214.] Rule. We explore both the robustness of McCallum's result to endogenous models of the term premium and also its connections to the Taylor Rule. We model the term premium endogenously using two different models in the class of affine term-structure models studied in Duffie and Kan [1996. A yield-factor model of interest rates. Mathematical Finance 57, 405-443.]: a stochastic volatility model and a stochastic price-of-risk model. We then solve for equilibrium term structures in environments in which interest rate targeting follows a rule such as the one suggested by McCallum (i.e., the “McCallum Rule”). We demonstrate that McCallum's original result generalizes in a natural way to this broader class of models. To understand the connection to the Taylor Rule, we then consider two structural macroeconomic models which have reduced forms that correspond to the two affine models and provide a macroeconomic interpretation of abstract state variables (as in Ang and Piazzessi [2003. A no-arbitrage vector autoregression of term structure dynamics with macroeconomic and latent variables. Journal of Monetary Economics 50, 745-787.]). Moreover, such structural models allow us to interpret the parameters of the term-structure model in terms of the parameters governing preferences, technologies, and policy rules. We show how a monetary policy rule will manifest itself in the equilibrium asset-pricing kernel and, hence, the equilibrium term structure. We then show how this policy can be implemented with an interest-rate targeting rule. This provides us with a set of restrictions under which the Taylor and McCallum Rules are equivalent in the sense if implementing the same monetary policy. We conclude with some numerical examples that explore the quantitative link between these two models of monetary policy.     

Differential taxation and the equilibrium structure of interest rates

Equilibrium coupon bond pricing relationships given differential taxation are derived under uncertainty assuming that both corporate and municipal bonds were originally issued at par but are currently selling at a discount. The impact of differential taxation upon the term structure and coupon structure of interest rates is investigated, while the tax structure of interest rates is uniquely characterized. Differential taxation substantially alters the prevailing equilibrium structure of interest rates.     

Estimation for factor models of term structure of interest rates with jumps: the case of the Taiwanese government bond market

This paper examines the Ornstein–Uhlenbeck (O–U) process used by Vasicek, J. Financial Econ. 5 (1977) 177, and a jump-diffusion process used by Baz and Das, J. Fixed Income (Jnue, 1996) 78, for the Taiwanese Government Bond (TGB) term structure of interest rates. We first obtain the TGB term structures by applying the B-spline approximation, and then use the estimated interest rates to estimate parameters for the one-factor and two-factor Vasicek and jump-diffusion models. The results show that both the one-factor and two-factor Vasicek and jump-diffusion models are statistically significant, with the two-factor models fitting better. For two-factor models, compared with the second factor, the first factor exhibits characteristics of stronger mean reversion, higher volatility, and more frequent and significant jumps in the case of the jump-diffusion process. This is because the first factor is more associated with short-term interest rates, and the second factor is associated with both short-term and long-term interest rates. The jump-diffusion model, which can incorporate jump risks, provides more insight in explaining the term structure as well as the pricing of interest rate derivatives.     

Fitting the term structure of interest rates for Taiwanese government bonds

The term structure of interest rates provides a basis for pricing fixed-income securities and interest rate derivative securities as well as other capital assets. Unfortunately, the term structure is not always directly observable because most of the substitutes for default-free bonds are not pure discount bonds. We use curve fitting techniques with the observed government coupon bond prices to estimate the term structure. In this paper, the B-spline approximation is used to estimate the Taiwanese Government Bond (TGB) term structure. We apply the B-spline functions to approximate the discount function, spot yield curve, and forward yield curve respectively. Among the three approaches, the discount fitting approach and the spot fitting approach are reasonable and reliable, but the spot fitting approach achieves the most suitable fit. Using this methodology, we can investigate term structure fitting problems, identify coupon effects, and analyze factors which drive term structure fluctuations in the TGB market.     

Surprises,sentiments, and the expectations hypothesis of the term structure of interest rates

Between 2005 and 2009, we document evident time-varying credit risk price discovery between the equity and credit default swap (CDS) markets for 174 US non-financial investment-grade firms. We test the economic significance of a simple portfolio strategy that utilizes fluctuation in CDS spreads as a trading signal to set stock positions, conditional on the CDS price discovery status of the reference entities. We show that a conditional portfolio strategy which updates the list of CDS-influenced firms over time, yields a substantively larger realized return net of transaction cost over the unconditional strategy. Furthermore, the conditional strategy’s Sharpe ratio outperforms a series of benchmark portfolios over the same trading period, including buy-and-hold, momentum and dividend yield strategies.     

Euler equations and money market interest rates: A challenge for monetary policy models

Standard macroeconomic models equate the money market rate targeted by the central bank with the interest rate implied by a consumption Euler equation. We use U.S. data to calculate the interest rates implied by Euler equations derived from a number of specifications of household preferences. Correlations between these Euler equation rates and the Federal Funds rate are generally negative. Regression results and impulse response functions imply that the spreads between the Euler equation rates and the Federal Funds rate are systematically linked to the stance of monetary policy. Our findings pose a fundamental challenge for models that equate the two.