Reducible Diffusions with Time-Varying Transformations with Application to Short-Term Interest Rates

Reducible diffusions (RDs) are nonlinear transformations of analytically solvable Basic Diffusions (BDs). Hence, by construction RDs are analytically tractable and flexible diffusion processes. Existing literature on RDs has mostly focused on time-homogeneous transformations, which to a significant extent fail to explore the full potential of RDs from both theoretical and practical points of view. In this paper, we propose flexible and economically justifiable time variations to the transformations of RDs. Concentrating on the Constant Elasticity Variance (CEV) RDs, we consider nonlinear dynamics for our time-varying transformations with both deterministic and stochastic designs. Such time variations can greatly enhance the flexibility of RDs while maintaining sufficient tractability of the resulting models. In the meantime, our modeling approach enjoys the benefits of classical inferential techniques such as the Maximum Likelihood (ML). Our application to the UK and the US short-term interest rates suggests that from an empirical point of view time-varying transformations are highly relevant and statistically significant. We expect that the proposed models can describe more truthfully the dynamic time-varying behavior of economic and financial variables and potentially improve out-of-sample forecasts significantly.

Are there non-linearities 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.

Forecasting the term structure when short-term rates are near zero

This paper compares the experience of forecasting the UK government bond yield curve before and after the dramatic lowering of short-term interest rates from October 2008. Out-of-sample forecasts for 1, 6 and 12 months are generated from each of a dynamic Nelson-Siegel model, autoregressive models for both yields and the principal components extracted from those yields, a slope regression and a random walk model. At short forecasting horizons, there is little difference in the performance of the models both prior to and after 2008. However, for medium- to longer-term horizons, the slope regression provided the best forecasts prior to 2008, while the recent experience of near-zero short interest rates coincides with a period of forecasting superiority for the autoregressive and dynamic Nelson-Siegel models. © 2014 John Wiley & Sons, Ltd.

Modeling Multivariate Interest Rates Using Time-Varying Copulas and Reducible Nonlinear Stochastic Differential Equations

We propose a new approach for modeling nonlinear multivariate interest rate processes based on time-varying copulas and reducible stochastic differential equations (SDEs). In the modeling of the marginal processes, we consider a class of nonlinear SDEs that are reducible to Ornstein--Uhlenbeck (OU) process or Cox, Ingersoll, and Ross (1985) (CIR) process. The reducibility is achieved via a nonlinear transformation function. The main advantage of this approach is that these SDEs can account for nonlinear features, observed in short-term interest rate series, while at the same time leading to exact discretization and closed-form likelihood functions. Although a rich set of specifications may be entertained, our exposition focuses on a couple of nonlinear constant elasticity volatility (CEV) processes, denoted as OU-CEV and CIR-CEV, respectively. These two processes encompass a number of existing models that have closed-form likelihood functions. The transition density, the conditional distribution function, and the steady-state density function are derived in closed form as well as the conditional and unconditional moments for both processes. In order to obtain a more flexible functional form over time, we allow the transformation function to be time varying. Results from our study of U.S. and UK short-term interest rates suggest that the new models outperform existing parametric models with closed-form likelihood functions. We also find the time-varying effects in the transformation functions statistically significant. To examine the joint behavior of interest rate series, we propose flexible nonlinear multivariate models by joining univariate nonlinear processes via appropriate copulas. We study the conditional dependence structure of the two rates using Patton (2006a) time-varying symmetrized Joe--Clayton copula. We find evidence of asymmetric dependence between the two rates, and that the level of dependence is positively related to the level of the two rates. (JEL: C13, C32, G12) Copyright The Author 2010. Published by Oxford University Press. All rights reserved. For permissions, please e-mail: journals.permissions@oxfordjournals.org, Oxford University Press.

Linkages between property asset returns and interest rates: evidence for the UK

This paper considers the effect of short- and long-term interest rates, and interest rate spreads upon real estate index returns in the UK. Using Johansen's vector autoregressive framework, it is found that the real estate index cointegrates with the term spread, but not with the short or long rates themselves. Granger causality tests indicate that movements in short term interest rates and the spread cause movements in the returns series. However, decomposition of the forecast error variances from VAR models indicate that changes in these variables can only explain a small proportion of the overall variability of the returns, and that the effect has fully worked through after two months. The results suggest that these financial variables could potentially be used as leading indicators for real estate markets, with corresponding implications for return predictability.

Spread trading strategy for intraday short term interest rate futures markets

Neste trabalho analisaram-se estratégias de spread calendário de contratos futuros de taxa de juros de curto prazo (STIR – Short Term Interest Rate) em operações de intraday trade. O spread calendário consiste na compra e venda simultânea de contratos de STIR com diferentes maturidades. Cada um dos contratos individualmente se comporta de forma aleatória e dificilmente previsível. No entanto, no longo prazo, pares de contratos podem apresentar um comportamento comum, com os desvios de curto prazo sendo corrigidos nos períodos seguintes. Se este comportamento comum for empiricamente confirmado, há a possibilidade de desenvolver uma estratégia rentável de trading. Para ser bem sucedida, esta estratégia depende da confirmação da existência de um equilíbrio de longo prazo entre os contratos e a definição do limite de spread mais adequado para a mudança de posições entre os contratos. Neste trabalho, foram estudadas amostras de 1304 observações de 5 diferentes séries de spread, coletadas a cada 10 minutos, durante um período de 1 mês. O equilíbrio de longo prazo entre os pares de contratos foi testado empiricamente por meio de modelos de cointegração. Quatro pares mostraram-se cointegrados. Para cada um destes, uma simulação permitiu a estimação de um limite que dispararia a troca de posições entre os contratos, maximizando os lucros. Uma simulação mostrou que a aplicação deste limite, levando em conta custos de comissão e risco de execução, permitiria obter um fluxo de caixa positivo e estável ao longo do tempo.

Markov Switching Risk Premium and the term structure of interest rates. Empirical evidence from US post-war interest rates

This paper considers the basic present value model of interest rates under rational expectations with two additional features. First, following McCallum (1994), the model assumes a policy reaction function where changes in the short-term interest rate are determined by the long-short spread. Second, the short-term interest rate and the risk premium processes are characterized by a Markov regime-switching model. Using US post-war interest rate data, this paper finds evidence that a two-regime switching model fits the data better than the basic model. The estimation results also show the presence of two alternative states displaying quite different features.

Some Implications of the Zero Lower Bound on Interest Rates for the Term Structure and Monetary Policy

In an economy where cash can be stored costlessly (in nominal terms), the nominal interest rate is bounded below by zero. This paper derives the implications of this nonnegativity constraint for the term structure and shows that it induces a nonlinear and convex relation between short- and long-term interest rates. As a result, the long-term rate responds asymmetrically to changes in the short-term rate, and by less than predicted by a benchmark linear model. In particular, a decrease in the short-term rate leads to a decrease in the long-term rate that is smaller in magnitude than the increase in the long-term rate associated with an increase in the short-term rate of the same size. Up to the extent that monetary policy acts by affecting long-term rates through the term structure, its power is considerably reduced at low interest rates. The empirical predictions of the model are examined using data from Japan.

A comparison of tests of non-linear cointegration with an application to the predictability of US interest rates using the term structure

We test whether there are nonlinearities in the response of short- and long-term interest rates to the spread in interest rates, and assess the out-of-sample predictability of interest rates using linear and nonlinear models. We find strong evidence of nonlinearities in the response of interest rates to the spread. Nonlinearities are shown to result in more accurate short-horizon forecasts, especially of the spread.

A comparison of test of non-linear cointegration with an application to the predictability of US interest rates using the term structure

We evaluate the forecasting performance of a number of systems models of US shortand long-term interest rates. Non-linearities, induding asymmetries in the adjustment to equilibrium, are shown to result in more accurate short horizon forecasts. We find that both long and short rates respond to disequilibria in the spread in certain circumstances, which would not be evident from linear representations or from single-equation analyses of the short-term interest rate.

Forecasting multivariate time series under present-value-model short- and long-run co-movement restrictions

It is well known that cointegration between the level of two variables (e.g. prices and dividends) is a necessary condition to assess the empirical validity of a present-value model (PVM) linking them. The work on cointegration,namelyon long-run co-movements, has been so prevalent that it is often over-looked that another necessary condition for the PVM to hold is that the forecast error entailed by the model is orthogonal to the past. This amounts to investigate whether short-run co-movememts steming from common cyclical feature restrictions are also present in such a system. In this paper we test for the presence of such co-movement on long- and short-term interest rates and on price and dividend for the U.S. economy. We focuss on the potential improvement in forecasting accuracies when imposing those two types of restrictions coming from economic theory.

Use of short-term breath measures to estimate daily methane production by cattle

Methods to measure enteric methane (CH4) emissions from individual ruminants in their production environment are required to validate emission inventories and verify mitigation claims. Estimates of daily methane production (DMP) based on consolidated short-term emission measurements are developing, but method verification is required. Two cattle experiments were undertaken to test the hypothesis that DMP estimated by averaging multiple short-term breath measures of methane emission rate did not differ from DMP measured in respiration chambers (RC). Short-term emission rates were obtained from a GreenFeed Emissions Monitoring (GEM) unit, which measured emission rate while cattle consumed a dispensed supplement. In experiment 1 (Expt. 1), four non-lactating cattle (LW=518 kg) were adapted for 18 days then measured for six consecutive periods. Each period consisted of 2 days of ad libitum intake and GEM emission measurement followed by 1 day in the RC. A prototype GEM unit releasing water as an attractant (GEM water) was also evaluated in Expt. 1. Experiment 2 (Expt. 2) was a larger study based on similar design with 10 cattle (LW=365 kg), adapted for 21 days and GEM measurement was extended to 3 days in each of the six periods. In Expt. 1, there was no difference in DMP estimated by the GEM unit relative to the RC (209.7 v. 215.1 g CH4/day) and no difference between these methods in methane yield (MY, 22.7 v. 23.7 g CH4/kg of dry matter intake, DMI). In Expt. 2, the correlation between GEM and RC measures of DMP and MY were assessed using 95% confidence intervals, with no difference in DMP or MY between methods and high correlations between GEM and RC measures for DMP (r=0.85; 215 v. 198 g CH4/day SEM=3.0) and for MY (r=0.60; 23.8 v. 22.1 g CH4/kg DMI SEM=0.42). When data from both experiments was combined neither DMP nor MY differed between GEM- and RC-based measures (P>0.05). GEM water-based estimates of DMP and MY were lower than RC and GEM (P<0.05). Cattle accessed the GEM water unit with similar frequency to the GEM unit (2.8 v. 3.5 times/day, respectively) but eructation frequency was reduced from 1.31 times/min (GEM) to once every 2.6 min (GEM water). These studies confirm the hypothesis that DMP estimated by averaging multiple short-term breath measures of methane emission rate using GEM does not differ from measures of DMP obtained from RCs. Further, combining many short-term measures of methane production rate during supplement consumption provides an estimate of DMP, which can be usefully applied in estimating MY.