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.     

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.     

Mean Reversion and Momentum: Another Look at the Price-Volume Correlation in the Real Estate Market

Based on behavioral finance and economics literature, we construct a theoretical framework in which consumers of newly constructed housing units perceive prices to follow a stochastic mean reversion pattern. Given this belief and the high carrying cost maintained by real estate developers, potential buyers opt to either exercise immediately or defer the purchase. We simulate the model within a real option framework by which we show that the optimal time to wait before exercising a purchase is positively related to the price level; hence, a negative (positive) correlation between transaction volume and price level (yield) emerges. Observing data on housing prices and new construction sales in Israel for the years 1998–2007, we apply an adaptive expectation regression model to test consumers’ belief in both mean reversion and momentum price patterns. The empirical evidence shows that while consumers’ demand pattern is simultaneously consistent with the belief in both momentum and mean reversion processes, the effect of the latter generally dominates. Moreover, while the data does not allow for testing the volume and price-level correlation, it does provide support to the positive volume-price yield correlation.     

Further on nonlinearity,persistence, and integration properties of real exchange rates

Integration, nonlinearity, and persistence dynamics of several quarterly US-Dollar-denominated real exchange rates are investigated by using new unit root tests, simulated p-values for linearity tests, estimation of smooth transition autoregressive (STAR) models, and simulation of autocorrelation functions. This paper uses a simulation-based approach to study covariance stationarity and persistence dynamics of the estimated models. Findings in the paper provide evidence of nonlinear mean reversion for several series albeit with some persistence. Results also reveal considerable variation in the degree of persistence and timing of switches across extreme regimes in ESTAR models between Euro and non-Euro area currencies.     

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.     

Mean reversion of short-run interest rates: empirical evidence from new EU countries

This article deals with the analysis of the mean reversion property of short-term interest rates in Central and Eastern European countries, using daily data from January 2000 to December 2008. For this purpose, we use long memory (fractionally integrated) models, and employ non-parametric, semi-parametric and parametric techniques to check if our results are robust across different methods. The results indicate that the mean reversion only takes place in the case of Hungary. For the remaining countries, the short-term interest rates are clearly non-stationary and non-mean reverting. Allowing for one break in the data, the break date takes place about 2001/2003 in all the series except in Lithuania, where the break occurs in 2007. In general, we observe an increase in the degree of dependence after the break in the majority of the series.     

A Nonparametric Model of Term Structure Dynamics and the Market Price of Interest Rate Risk

This article presents a technique for nonparametrically estimating continuous-time diffusion processes that are observed at discrete intervals. We illustrate the methodology by using daily three and six month Treasury Bill data, from January 1965 to July 1995, to estimate the drift and diffusion of the short rate, and the market price of interest rate risk. While the estimated diffusion is similar to that estimated by Chan, Karolyi, Longstaff, and Sanders (1992) , there is evidence of substantial nonlinearity in the drift. This is close to zero for low and medium interest rates, but mean reversion increases sharply at higher interest rates.     

Mean Reversion in Net Discount Ratios: A Study in the Context of Fractionally Integrated Models

This article introduces a new alternative to the ongoing debate about stationarity and mean reversion of the net discount ratio. Modeling the net discount ratio as a fractionally integrated (I(d)) process, we apply recently developed frequency domain estimation procedures and find evidence that the net discount ratio is an I(d) process with 1/2 ≤d < 1. Although nonstationary, such series behave like stationary processes in one interesting respect; they are mean‐reverting. We present results from a simulation experiment suggesting that the finding of a nonstationary, but mean‐reverting net discount ratio generally supports the validity of current practice in estimating economic damages in personal injury litigation. Moreover, if recognized and accounted for, the presence of long memory in the net discount ratio even offers the potential to significantly improve forecasts of the present value of future earnings.     

Nominal interest rates and stationarity

This paper investigates the (break) stationarity null hypothesis using data for 25 interest rates with different maturities and risk characteristics in Canada and the US. In contrast to a large part of the literature, this paper reports strong empirical evidence in favour of the null hypothesis of stationarity for the interest rate series.     

The Hull and White Model of the Short Rate: An Alternative Analytical Representation

Hull and White extend Ho and Lee's no‐arbitrage model of the short interest rate to include mean reversion. This addition eliminates the problem of negative interest rates and has found wide application. To implement their model, Hull and White employ a sequential search process to identify the mean interest rate in a trinomial lattice at each date. In this article we extend Hull and White's work by developing an analytical solution for the mean interest rate at each date. This solution applies equally well to trinomial lattices, interest rate trees, and Monte Carlo simulation. We illustrate the analytical result by applying it to an example originally used by Hull and White and then for valuing an option on a bond.     

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.     

The Stochastic Behavior of Commodity Prices: Implications for Valuation and Hedging

In this article we compare three models of the stochastic behavior of commodity prices that take into account mean reversion, in terms of their ability to price existing futures contracts, and their implication with respect to the valuation of other financial and real assets. The first model is a simple one-factor model in which the logarithm of the spot price of the commodity is assumed to follow a mean reverting process. The second model takes into account a second stochastic factor, the convenience yield of the commodity, which is assumed to follow a mean reverting process. Finally, the third model also includes stochastic interest rates. The Kalman filter methodology is used to estimate the parameters of the three models for two commercial commodities, copper and oil, and one precious metal, gold. The analysis reveals strong mean reversion in the commercial commodity prices. Using the estimated parameters, we analyze the implications of the models for the term structure of futures prices and volatilities beyond the observed contracts, and for hedging contracts for future delivery. Finally, we analyze the implications of the models for capital budgeting decisions.     

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.     

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.     

Stochastic Convenience Yield Implied from Commodity Futures and Interest Rates

We characterize a three‐factor model of commodity spot prices, convenience yields, and interest rates, which nests many existing specifications. The model allows convenience yields to depend on spot prices and interest rates. It also allows for time‐varying risk premia. Both may induce mean reversion in spot prices, albeit with very different economic implications. Empirical results show strong evidence for spot‐price level dependence in convenience yields for crude oil and copper, which implies mean reversion in prices under the risk‐neutral measure. Silver, gold, and copper exhibit time variation in risk premia that implies mean reversion of prices under the physical measure.     

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.     

Investigating the stationarity of insurance premiums: international evidence

This article explores whether there is support for the stationarity hypotheses of life and non-life insurance premiums during the period 1979–2007 for 40 heterogeneous countries. The stationarity of insurance premiums affects insurance companies’ prediction on their future inflow of premium income, which affects the liquidity of insurance companies and their investment plans and thus is relevant to the insurers’ operation. This article employs the advanced nonlinear panel unit-root test with a sequential panel selection method to classify the entire panel into two groups: stationary countries and non-stationary countries. We apply Monte Carlo simulations to derive empirical distributions of the test, which allows us to correct for the finite-sample bias and to consider the cross-country effects. We find relatively stationary life insurance premiums in countries from the following groups: high-income, Europe, and common law origin; relatively stationary non-life insurance premiums exist in the following groups: low-income, Middle East and Africa, and common law origin. Evidence herein shows that different classifications, including income levels, geographic regions, regionally or economically integrated blocs, and legal system, affect the stationarity of life and non-life insurance premiums.     

Do Inventories Matter in Dealership Markets? Evidence from the London Stock Exchange

Using London Stock Exchange data, we test the central implication of the canonical model of Ho and Stoll (1983) that relative inventory differences determine dealer behavior. We find that relative inventories explain which dealers obtain large trades and show that movements between best ask, best bid, and straddle are highly correlated with both standardized and relative inventory changes. We show that the mean reversion in inventories is highly nonlinear and increasing in inventory levels. We show that a key determinant of variations in interdealer trading is inventories and that interdealer trading plays an important role in managing large inventory positions.     

Current account sustainability in the US: What did we really know about it?

We analyze the sustainability of the US current account (CA) deficit by means of unit-root tests. First, we argue that there are several reasons to believe that the CA may follow a non-linear mean-reversion behavior under the null of stationarity. Using a non-linear ESTAR model we can reject the null of non-stationarity favoring the sustainability hypothesis. Second, we ask whether unit-root tests are a useful indicator of sustainability by comparing in-sample results for the 1960–2004 period to the developments observed up to the end of 2008. We find that the non-linear model outperforms the linear and random walk models in terms of forecast performance. The large shocks to the CA observed in the last five years induced a faster speed of mean reversion, ensuring the necessary adjustment to meet the inter-temporal budget constraint.     

How well does nonlinear mean reversion solve the PPP puzzle?

This paper addresses the degree to which models which exhibit nonlinear mean reversion (NMR) present a resolution to the Purchasing Power Parity Puzzle. This paper develops a method of estimating a representative distribution of half lives which is based upon the observed distribution of shocks in a given time series rather than choosing shock sizes arbitrarily which is the current practice in the literature. This approach is implemented with data on five real exchange rates. The empirical analysis shows that half lives shorter than the consensus are observed frequently enough to support the proposition that NMR is a solution to the PPP puzzle.