Are there nonlinearities in short‐term interest rates?

The present paper investigates the characteristics of short‐term interest rates in several countries. We examine the importance of nonlinearities in the mean reversion and volatility of short‐term interest rates. We examine various models that allow the conditional mean (drift) and conditional variance (diffusion) to be functions of the current short rate. We find that different markets require different models. In particular, we find evidence of nonlinear mean reversion in some of the countries that we examine, linear mean reversion in others and no mean reversion in some countries. For all countries we examine, there is strong evidence of the need for the volatility of interest rate changes to be highly sensitive to the level of the short‐term interest rate. Out‐of‐sample forecasting performance of one‐factor short rate models is poor, stemming from the inability of the models to accommodate jumps and discontinuities in the time series data.     

Purchasing power parity: Modeling and testing mean reversion

A model of mean reversion of exchange rates to purchasing power parity is developed and tested where exchange rates are assumed to follow a mean reverting elastic random walk toward a stochastic PPP rate. The model recognizes the possibility that mean reversion towards PPP may be nonlinear which allows greater flexibility in the adjustment process. Regression equations consistent with the theoretical model are derived. The model is tested using long- and short-term data for six countries. While the results are generally consistent with the findings of previous studies, evidence is presented which demonstrates that the mean reversion process is not linear for some countries.     

REGIME-SWITCHING IN AUSTRALIAN SHORT-TERM INTEREST RATES

This paper applies a generalized regime-switching (GRS) model of the short-term interest rate to Australian data. The model allows the short rate to exhibit both mean reversion and conditional heteroscedasticity and nests the popular generalized autoregressive conditional heteroscedasticity (GARCH) and regime-switching specifications. It is shown that empirical estimates of many popular interest rate models provide curious results which imply that innovations to the short rate process are extremely persistent, and that the short rate is potentially non-stationary. The source of these curious results, which are also present in US and European interest rates, is identified in the context of the GRS model, which is shown, via specification and forecasting tests, to capture the features of Australian short-term interest rate data better than existing models. The stochastic process of short-term interest rates in Australia is compared with evidence from the US and Europe, highlighting a number of important differences.     

Mean Reversion across National Stock Markets and Parametric Contrarian Investment Strategies

For U.S. stock prices, evidence of mean reversion over long horizons is mixed, possibly due to lack of a reliable long time series. Using additional cross-sectional power gained from national stock index data of 18 countries during the period 1969 to 1996, we find strong evidence of mean reversion in relative stock index prices. Our findings imply a significantly positive speed of reversion with a half-life of three to three and one-half years. This result is robust to alternative specifications and data. Parametric contrarian investment strategies that fully exploit mean reversion across national indexes outperform buy-and-hold and standard contrarian strategies.     

Real exchange rate adjustment in European transition countries

In single-equation tests, real exchange rates show mean reversion for nine of 10 Central and Eastern European transition countries for the period January 1993 to December 2005. Because of the shift from controlled to market economies and accompanying crises, failed policy regimes and changes in exchange rate regimes, unit root tests for transition countries often require allowance for structural changes. Accounting for structural breaks gives substantially faster mean-reversion speeds than those found for major industrialized countries. These fast adjustment speeds are plausible: Transition countries had perhaps 10 years to make unprecedented adjustments required for accession to the European Union. A number of papers have applied non-linear models to the Central and Eastern European countries. This paper investigates four non-linear models and compares them with piece-wise linear break models. The break models appear superior in detecting mean reversion for the Central and Eastern European transition countries.     

Macroeconomic announcements, volatility, and interrelationships: An examination of the UK interest rate and equity markets

This study investigates the intraday and daily pricing behavior of UK interest rate and equity index futures contracts. The paper initially examines the response of Short Sterling, Long Gilt, and FTSE100 to the release of scheduled macroeconomic announcements before employing dynamic time series techniques in order to reveal the nature of causal transmission patterns between these variables. In brief, short-term interest rates were found to be highly sensitive to indicators of prevailing economic conditions. However, the release of data important in the formation of inflationary expectations had a relatively subdued impact on long-term rates. Announcement effects appear somewhat ambiguous for the stock market. The analysis also reveals the bid-ask bounce and swift mean reversion in volatility to be important behavioral features of the return-generating process. Whilst the three variables appear to be bound by two cointegrating relationships, the tests for lead/lag relationships produce mixed results.     

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.     

A statistical comparison of the short-term interest rate models for Japan,U.S., and Germany

We propose a simple and practical model selection method for continuous time models. We apply the method to several continuous time short-term interest rate models using discrete time series data of Japan, U.S. and Germany. All the models can be easily estimated from discrete observations, and their performances can be evaluated in a uniform statistical framework. The models that allow dependence of volatility on the level of interest rates tend to perform well empirically. The degree of volatility dependence on the interest rate levels seems to be different across the countries. For the German data, we observe that a model with nonlinear drift performs better than the best linear drift model.     

The Structural Relation Between Mortgage and Market Interest Rates

This paper analyzes the dynamic relationship between primary and secondary mortgage markets and the short-term and long-term market interest rates. Using a series of monthly data on fixed rate mortgage rates and GNMA rates, we explore the dependence and speed of adjustment in these primary and secondary mortgage rates to each other as well as to the long and short-term government rates. The results indicate that residential mortgage rates in general, appear to follow the long-term rate and are not very sensitive to movements in the short-term interest rate.     

Asymmetric Mean Reversion in European Interest Rates: A Two-factor Model

Abstract

This paper tests for asymmetric mean reversion in European short-term interest rates using a combination of the interest rate models introduced by Longstaff and Schwartz (Longstaff, F.A., Schwarts, E.S. (1992) Interest rate volatility and the ferm structure: A two factor general equilibrium model, Journal of Finance, 48, pp. 1259–1282.) and Bali (Bali, T. (2000) Testing the empirical performance of stochastic volatility models of the short-term interest rates, Journal of Financial and Quantitative Analysis, 35, pp. 191–215.). Using weekly rates for France, Germany and the United Kingdom, it is found that short-term rates follow in all instances asymmetric mean reverting processes. Specifically, interest rates exhibit non-stationary behavior following rate increases, but they are strongly mean reverting following rate decreases. The mean reverting component is statistically and economically stronger thus offsetting non-stationarity. Volatility depends on past innovations past volatility and the level of interest rates. With respect to past innovations volatility is asymmetric rising more in response to positive innovations. This is exactly opposite to the asymmetry found in stock returns.     

The Effects of Inflation and Money Supply Announcements on Interest Rates

This paper examines the impact of the money supply and inflation rate announcements on interest rates. Survey data on expectations of the money supply and consumer and producer price indexes are used to distinguish anticipated and unanticipated components of the announcements. This distinction is used to test for the efficiency of the financial market response to the announcements of new information. The results indicate that the unanticipated components of the announced changes in the Producers Price Index and in the money supply have an immediate positive effect on short-term interest rates. The Consumer Price Index announcement has no apparent effect. There is no evidence of a delayed announcement effect. However, there is some indication of a liquidity effect of the money supply change on interest rates. This takes place when reserves are changing and several weeks prior to the information announcement.     

Mean reversion in international stock markets: An empirical analysis of the 20th century

This paper analyzes mean reversion in the stock markets of 18 OECD countries during the years 1900–2009. In this period it takes stock prices about 18.5 years, on average, to absorb half of a shock. However, using a rolling-window approach we establish large fluctuations in the speed of mean reversion over time. The highest mean reversion speed is found for the period including the Great Depression and the start of World War II. Furthermore, the early years of the Cold War and the period containing the Oil Crisis of 1973, the Energy Crisis of 1979 and Black Monday in 1987 are also characterized by relatively fast mean reversion. We document half-lives ranging between 2.0 and 22.6 years. Our results suggest that the speed at which stocks revert to their fundamental value is higher in periods of high economic uncertainty, caused by major economic and political events.     

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.     

Cross‐sectional Restrictions on the Spot and Forward Term Structures of Interest Rates and Panel Unit Root Tests

In this paper we examine the stationarity of all the rates comprising the USD, GBP, DM and JPY spot and forward term structures. Instead of focussing on short maturity interest rates, as most other papers do, we perform a detailed analysis of the whole range of spot and forward interest rates of the 4 main currencies. We investigate the issue of stationarity within the framework of an equilibrium interest rate model such as Vasicek (1977), that defines the cross-sectional and time series properties that interest rates of various maturities must satisfy. We show that within a one-factor interest rate model, such as Vasicek, all interest rates are restricted to exhibit the same mean reverting behaviour. This restriction allows us to apply more powerful panel unit root tests. This methodology increases considerably the number of observations available and as a result the power of the unit root tests. The higher power of these tests allows us to demonstrate that there does exist mean reversion on the spot and forward US interest rates and the forward DM and GBP interest rates.     

The overnight interbank market: Evidence from the G-7 and the Euro zone

We study the interbank markets for overnight loans of the major industrial countries, linking the behavior of short-term interest rates to the operating procedures of these countries’ central banks. We find that many of the key behavioral features of US federal funds rates, on which previous studies have focused, are not robust to changes in institutional details, along both cross-sectional and time-series dimensions of the data. Our results indicate that central banks’ operating procedures and intervention styles play a crucial role in shaping empirical features of short-term interest rates’ day to-to-day behavior in industrial countries.     

A jump-diffusion model for the euro overnight rate

In this work we introduce a jump-diffusion process for the euro overnight rate (the European over night index average) that is able to capture the main characteristics of this rate: (i) dynamics constrained to remain in the corridor of official rates fixed by the European Central Bank; (ii) mean reversion towards the official rate on main refinancing operations; and (iii) highly discontinuous pattern (with jumps), also without variations in the official rate. After calibrating the model parameters on historical data, we implement the model to price an overnight indexed swap. Finally, a comparison between our model and the most common short-term interest rate models is presented.     

Mean reversion in long-horizon real exchange rates: Evidence from Latin America

This paper examines mean reversion in real effective exchange rates in six leading Latin American economies during the XXth century using a new data set. A unit-root approach is complemented by an error-correction model including key fundamentals such as terms of trade, trade openness and relative productivities. Unit-root testing shows a very slow process of reversion – if any – to a constant mean in the original series, rejecting the strict PPP hypothesis; however, mean reversion is found after allowing for trends and structural breaks with a half-life average of 1½ years for the six countries. We also found reversion to a conditional mean defined by the co-integrating relationship with an average half-life of 2½ years. Our estimates, although lower than the 3–5 year range that motivated the Rogoff’s puzzle, still indicate the presence of important obstacles to the adjustment process that need further investigation.     

Modeling interest rate volatility: A Realized GARCH approach

We propose using a Realized GARCH (RGARCH) model to estimate the daily volatility of the short-term interest rate in the euro–yen market. The model better fits the data and provides more accurate volatility forecasts by extracting additional information from realized measures. In addition, we propose using the ARMA–Realized GARCH (ARMA–RGARCH) model to capture the volatility clustering and the mean reversion effects of interest rate behavior. We find the ARMA–RGARCH model fits the data better than the simple RGARCH model does, but it does not provide superior volatility forecasts.     

Nonlinear Mean Reversion in the Short-Term Interest Rate

Using a new Bayesian method for the analysis of diffusion processes,this article finds that the nonlinear drift in interest ratesfound in a number of previous studies can be confirmed onlyunder prior distributions that are best described as informative.The assumption of stationarity, which is common in the literature,represents a nontrivial prior belief about the shape of thedrift function. This belief and the use of "flat" priors contributestrongly to the finding of nonlinear mean reversion. Implementationof an approximate Jeffreys prior results in virtually no evidencefor mean reversion in interest rates unless stationarity isassumed. Finally, the article documents that nonlinear driftis primarily a feature of daily rather than monthly data, andthat these data contain a transitory element that is not reflectedin the volatility of longer-maturity yields.     

Combining mean reversion and momentum trading strategies in foreign exchange markets

The literature on equity markets documents the existence of mean reversion and momentum phenomena. Researchers in foreign exchange markets find that foreign exchange rates also display behaviors akin to momentum and mean reversion. This paper implements a trading strategy combining mean reversion and momentum in foreign exchange markets. The strategy was originally designed for equity markets, but it also generates abnormal returns when applied to uncovered interest parity deviations for five countries. I find that the pattern for the positions thus created in the foreign exchange markets is qualitatively similar to that found in the equity markets. Quantitatively, this strategy performs better in foreign exchange markets than in equity markets. Also, it outperforms traditional foreign exchange trading strategies, such as carry trades and moving average rules.