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.     

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.     

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.     

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.     

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.     

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.     

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.     

The Behavior of Interest Rates

The evidence in Fama and Bliss (1987) that forward interestrates forecast future spot interest rates for horizons beyonda year repeats in the out-of-sample 1986–2004 period.But the inference that this forecast power is due to mean reversionof the spot rate toward a constant expected value no longerseems valid. Instead, the predictability of the spot rate capturedby forward rates seems to be due to mean reversion toward atime-varying expected value that is subject to a sequence ofapparently permanent shocks that are on balance positive tomid-1981 and on balance negative thereafter.     

The information in the term structure

This paper presents a regression approach to measuring the information in forward interest rates about time varying premiums and future spot interest rates. Like earlier work, the regressions identify variation in the expected premiums on longer-maturity Treasury bills. The more novel evidence concerns the forecasts of future spot rates in forward rates. The regressions provide evidence that the one-month forward rate has power to predict the spot rate one month ahead. During periods preceding 1974, forward rates have reliable forecast power for one-month spot rates up to five months in the future.     

Random walk and efficiency tests in the Asia-Pacific foreign exchange markets: Evidence from the post-Asian currency crisis data

This paper empirically tests the random walk and efficiency hypothesis for 12 Asia-Pacific foreign exchange markets. The hypothesis is tested using individual as well as panel unit root tests and two variance-ratio tests. The study covers the high (daily) and medium (weekly) frequency post-Asian crisis spot exchange rate data from January 1998 to July 2007. The inferential outcomes do not differ substantially between the unit root tests and the variance-ratio tests when using daily data but differ significantly when using weekly data. With the daily data, both types of unit root tests identify unit root components for all the series and two variance-ratio tests provide the evidence of martingale behavior for majority of the exchange rates tested. With the weekly data, panel unit root tests identify unit root component for the exchange rates and, the unit root tests on a single series basis identify unit root component for 10 foreign exchange markets. However, the variance-ratio tests reject the martingale null for the majority of the exchange rates when using weekly data.     

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 .     

Nonlinear trends in real exchange rates: A panel unit root test approach

We analyze the possibility of nonlinear trend stationarity as the alternative to unit roots in 23 OECD real exchange rates, 1974–1998, by adding nonlinear time terms to the CIPS panel unit root test of Pesaran (2007). We follow a thorough bootstrapping approach and propose a technique to adjust statistical significance for the use of multiple tests over several time trend orders. The unit root null that all real exchange rates have unit roots is rejected at better than the 0.05 level. Bootstrapped results from a procedure of Chortareas and Kapetanios (2009) suggest that the hypothesis that all are stationary is reasonable. We argue that nonlinear trend stationarity is the most likely alternative hypothesis for at least some of the real exchange rates because: (1) the strongest CIPS rejection occurs when quadratic trends are specified; (2) nonlinear time terms are statistically significant at the 0.10 level; (3) the actual CIPS statistics are more consistent with CIPS sampling distributions from bootstrapped nonlinear trend stationary processes than from linear trend or mean stationary processes.     

Resuscitating real interest rate parity: new evidence from panels

This paper considers the real interest rate parity (RIRP) in OECD countries applying a sequential panel selection (SPS) method on alternative panel unit-root tests. Our approach exploits the enhanced power of panels to uncover evidence of stationarity, but also identifies the exact countries for which the RIRP holds in a panel. Moreover, we construct real interest rate measures using alternative approaches, including a Markov regime-switching procedure, which is consistent with the forward-looking nature of inflation expectations formation. Considering US as the benchmark economy, we produce strong evidence of stationarity in real interest rate differentials, which resuscitates RIRP, especially given the inconclusive results in the related literature. Our results are robust to different panel unit-root tests, measures of inflation expectations, and interest rate maturities. The RIRP appears quite resilient in the face of the global financial crisis and the low real interest rate environment after the great recession. The SPS allows to calculate half-lives, which avoid the pitfalls of over/underestimating the speed of adjustment and are lower as compared to the typical estimates in the literature.     

Equilibrium exchange rate determination and multiple structural changes

The large appreciation and depreciation of the US Dollar in the 1980s stimulated an important debate on the usefulness of unit root tests in the presence of structural breaks. In this paper, we propose a simple model to describe the evolution of the real exchange rate. We then propose a more general smooth transition (STR) function than has hitherto been employed, which is able to capture structural changes along the (long-run) equilibrium path, and show that this is consistent with our economic model. Our framework allows for a gradual adjustment between regimes and allows for under- and/or over-valued exchange rate adjustments. Using monthly and quarterly data for up to twenty OECD countries, we apply our methodology to investigate the univariate time series properties of CPI-based real exchange rates with both the U.S. Dollar and German Mark as the numeraire currencies. The empirical results show that, for more than half of the quarterly series, the evidence in favor of the stationarity of the real exchange rate was clearer in the sub-sample period post-1980.     

Financial integration in the pacific basin region: RIP by PANIC attack?

We exploit advances in panel data econometrics to test whether real interest parity holds in the Pacific Basin region. We test for a unit root in the difference between either the US, Japanese or Euro area real interest rate and the real interest rates from a panel of eleven Pacific Basin economies. Unlike extant studies that test for RIP using panel data, we use Bai and Ng’s (2004) PANIC test which allows for a very general model of cross-section dependence, including the possibility of cross-unit cointegration. Ignoring the possibility of cross-unit cointegration can lead to severe size distortions and to an over-rejection of the null hypothesis of a unit root. We overturn earlier findings based on first-generation panel tests, and demonstrate that cross-unit cointegration leads to incorrect conclusions. We find that RIP holds in the Pacific region. Real interest rates converge to the US rate. We find no support for the hypothesis that Pacific Basin real interest rates converge to either the Japanese or Euro area 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.     

IS THE REAL INTEREST RATE REALLY UNSTABLE?

If nominal interest rates have a unit root, but inflation and inflation forecast errors do not, ex-ante real interest rates are argued to have a unit root and are therefore nonstationary. I show that empirical tests for nonstationarity of real interest rates using such a deductive method can be misleading when the stationary inflation forecast errors are large relative to the variation of nominal interest rates.     

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.