A preference free partial differential equation for the term structure of interest rates

The objectives of this paper are two-fold: the first is the reconciliation of the differences between the Vasicek and the Heath-Jarrow-Morton approaches to the modelling of term structure of interest rates. We demonstrate that under certain (not empirically unreasonable) assumptions prices of interest-rate sensitive claims within the Heath-Jarrow-Morton framework can be expressed as a partial differential equation which both is preference-free and matches the currently observed yield curve. This partial differential equation is shown to be equivalent to the extended Vasicek model of Hull and White. The second is the pricing of interest rate claims in this framework. The preference free partial differential equation that we obtain has the added advantage that it allows us to bring to bear on the problem of evaluating American style contingent claims in a stochastic interest rate environment the various numerical techniques for solving free boundary value problems which have been developed in recent years such as the method of lines.     

Modeling International Long-Term Interest Rates

This study investigates the relationship among interest rates on the long-term government bonds of five industrialized countries. Both standard and new unit root tests are applied, all of which confirm the presence of exactly one unit root. New cointegration tests are also applied to these data. In contrast to previous research on short-term bonds, stock prices, and exchange rates, these results find little evidence of cointegration among the five long-term interest rate series. Thus, when modeling or forecasting these central government long-term bond yields, one may assume separate sets of fundamentals and difference the data to achieve stationarity. An error correction model may not be appropriate.     

Pricing interest-rate-derivative securities

This article shows that the one-state-variable interest-ratemodels of Vasicek (1977) and Cox, Ingersoll, and Ross (1985b)can be extended so that they are consistent with both the currentterm structure of interest rates and either the current volatilitiesof all spot interest rates or the current volatilities of allforward interest rates. The extended Vasicek model is shownto be very tractable analytically. The article compares optionprices obtained using the extended Vasicek model with thoseobtained using a number of other models.     

Common Stochastic Trends in a System of Exchange Rates

Univariate tests reveal strong evidence for the presence of a unit root in the univariate time-series representation for seven daily spot and forward exchange rate series. Furthermore, all seven spot and forward rates appear to be cointegrated; that is, the forward premiums are stationary, and one common unit root, or stochastic trend, is detectable in the multivariate time-series models for the seven spot and forward rates, respectively. This is consistent with the hypothesis that the seven exchange rates possess one long-run relationship and that the disequilibrium error around that relationship partly accounts for subsequent movements in the exchange rates.     

Bond price representations and the volatility of spot interest rates

A common approach to modeling the term structure of interest rates in a single-factor economy is to assume that the evolution of all bond prices can be described by the current level of the spot interest rate. This article investigates the restrictions that this assumption imposes. Specifically, we show that this Markovian restriction, together with the no-arbitrage requirement, curtails the relationship of forward rates and their volatilities relative to spot-rate volatilities. Among such Markovian models, only a few provide simple analytical relationships between bond prices and the spot interest rate. This article identifies the class of spot-rate volatility specifications that permit simple analytical linkages to be derived between bond prices and interest rates. Included in the class are the volatility structures used by Vasicek and by Cox, Ingersoll, and Ross. Surprisingly, no other volatility structures permit simple analytical representations.     

Bivariate relative city price convergence in the United States: 1918-1997

As in international tests of purchasing power parity, panel unit root tests have been successful in rejecting a unit root process in U.S. city relative prices over the period 1918-1997. However, there is an empirical question of what the rejection of a ‘panel unit root’, particularly with respect to real exchange rates, means. This paper employs a variety of univariate unit root and cointegration tests which have recently come to the fore. These tests improve the power and reduce size distortion found in standard unit root and cointegration tests such as the Dickey-Fuller and Phillips-Perron tests. I find considerable evidence for rejecting a unit root process in the majority of U.S. city relative prices over the entire sample period and two subperiods. Less successful are stationarity tests conducted on regions of the U.S.     

Accounting Regulation,Financial Development,and Economic Growth

It is argued that the sustainability of external debts depends on the stationarity of the current account balance. This study tests for the stationarity of current account deficits for a sample of sixteen Latin American countries, employing a new test, advocated by Breuer et al. (2002), that allows one to test for unit roots in heterogeneous panel data sets. This version of the augmented Dickey-Fuller (ADF) test involves estimating ADF regressions within a seemingly unrelated regression (SURADF) framework. The benefits of creating a panel to overcome low test power are well known, but this particular test also offers key advantages over existing alternative panel data unit root tests. Unlike previous tests, this one identifies which members from within the panel are responsible for rejecting the null hypothesis of joint nonstationarity. In addition, the SURADF test does not presume disturbances that are independently and identically distributed. Using annual data covering the period 1979-2001, this study finds strong evidence in favor of current account mean-reversion for at least twelve Latin American countries.     

The behaviour of the real exchange rate: Evidence from regression quantiles

We test for mean reversion in real exchange rates using a recently developed unit root test for non-normal processes based on quantile autoregression inference in semi-parametric and non-parametric settings. The quantile regression approach allows us to directly capture the impact of different magnitudes of shocks that hit the real exchange rate, conditional on its past history, and can detect asymmetric, dynamic adjustment of the real exchange rate towards its long run equilibrium. It, therefore provides a detailed mapping of the real exchange rate behaviour, while being a robust alternative to previous unit root tests. The latter is confirmed by a simulation analysis comparing the power of the alternative tests. As concerns the real exchange rate, our results suggest that large shocks tend to induce strong mean reverting tendencies in the exchange rate, with half lives less than one year in the extreme quantiles. Mean reversion is faster when large shocks originate at points of large real exchange rate deviations from the long run equilibrium. However, in the absence of shocks no mean reversion is observed. Finally, we report asymmetries in the dynamic adjustment of the RER.     

Real interest parity: Evidence from trade partnerships

This study investigates real interest parity (RIP) in trade partnerships, and whether RIP depends on the type of trade partnership, using short term interest rates and the Consumer Price Index (CPI) obtained from the Organization for Economic Cooperation and Development (OECD) database between 1975 and 2016. The investigation employs unit root and stationarity tests on interest rate differentials to study RIP between countries using Germany, United States, and Japan as base countries for selected countries in the European Union (EU), member countries of the North American Free Trade Agreement (NAFTA) and selected Asian countries respectively. The results show evidence in favor of RIP in the selected EU countries. The interest rate differentials of Belgium, France, Italy, Spain and the UK with respect to Germany confirms a long‐run relationship and real interest rate parity. There is also evidence to support the RIP in the other trade partnerships. With the exception of Mexico, the interest rate differentials for all the countries are stationary, and each quickly reverts to its mean.     

Junp-Diffusion Interest Rate Process: An Empirical Examination

We investigate a jump-diffusion process, which is a mixture of an O-U process used by Vasicek (1977) and a compound Poisson jump process, for the term structure of interest rates. We develop a methodology for estimating the jump-diffusion model and complete an empirical study in comparing the model with the Vasicek model, for the US money market interest rates. The results show that when the short-term interest rate is low, both models predict an upward sloping term structure, with the jump-diffusion model fitting the actual term structure quite well and the Vasicek model overestimating significantly. When the short-term interest rate is high, both models predict a downward sloping term structure, with the jump-diffusion model underestimating the actual term structure more significantly than the Vasicek model.