A Nonlinear Model of the Term Structure of Interest Rates

We present an economically motivated two–factor term structure model that generalizes existing stochastic mean term structure models. By allowing a certain parameter to acquire dynamical behavior we extend the two–factor model to obtain a nonlinear three–factor model that is shown, in a deterministic version, to be equivalent to the Lorenz system of differential equations. With reasonable parameter values the model exhibits chaotic behavior. It successfully emulates certain properties of interest rates including cyclical behavior on a business cycle time scale. Estimation and pricing issues are discussed. Standard PCA techniques used to estimate HJM type models are observed to be equivalent to dimensional estimates commonly applied to 'spatial data' in nonlinear systems analysis.
It is concluded that techniques commonly used in the analysis of nonlinear systems may be directly applicable to interest rate models, offering new insights in the development of these models. Tests of nonlinearity in interest rate behavior may need to focus on long cycle times.     

SOLUTION OF THE EXTENDED CIR TERM STRUCTURE AND BOND OPTION VALUATION

The extended Cox-Ingersoll-Ross (ECIR) models of interest rates allow for time-dependent parameters in the CIR square-root model. This article presents closed-form pathwise unique solutions of these unsolved stochastic differential equations (s.d.e.s) in terms of functionals of their driving Brownian motion and parameters. It is shown that quadratics in solution of linear s.d.e.s solve the ECIR model if and only if the dimension of the model is a positive integer and that this solution can be achieved by construction of a pathwise unique generalized Ornstein-Uhlenbeck process from the ECIR Brownian motion. For real valued dimensions an extension of the time-change theorem of Dubins and Schwarz (1965) is presented and applied to show that a lognormal process solves the model through a stochastic time change. Pathwise equivalence to a rescaled time-changed Bessel square process is also established. These novel results are applied to characterize zero-hitting time and to produce transition density and zero-hitting conditions for the ECIR spot rate. the CIR term structure is then extended to ECIR under no arbitrage, and its solutions and the transition density are represented under a new ECIR martingale measure. the findings are employed to derive a closed-form ECIR bond option valuation formula which generalizes that obtained by CIR (1985).     

Comparative cost advantage and trade performance: a panel data approach

This article examines the relationship of the components of labor cost—unit cost, productivity, compensation—to the structure of U.S. trade flows in manufacturing industries for the period 1967-1982. Earlier cross-sectional models do not account for differential trade barriers among industries while time series studies do not include changes in either trade barriers or exchange rates. This study addresses these problems by using a panel data model with fixed time effects. Because this model had limited success in estimating the labor compensation parameter, a panel data model with individual industry effects was also estimated.     

基于季节调整的BP神经网络等三种模型对中国出口研究

本文以出口额、实际汇率、我国GDP、美国IPI及它们的季节变量等六个变量为决定变量,运用BP神经网络、ARIMA及AR-GARCH三种方法,对我国向美国的出口额分别建模,并进行了预测。选取误差指标,分别对三个模型得到的模拟结果和预测结果同真实值进行比较。结果发现,三种模型效果都令人满意,虽在模拟和预测能力上有一定差别,但ARIMA模型优势明显。本文分析了以上结果产生的原因,并结合模型为提高我国出口提出建议。     

Prediction of Ideas Number During a Brainstorming Session

In this paper, we present an approach allowing the prediction of ideas number during a brainstorming session. This prediction is based on two dynamic models of brainstorming, the non-cognitive and the cognitive models proposed by Brown and Paulus (Small Group Res 27(1):91–114, 1996). These models describe for each participant, the evolution of ideas number over time, and are formalized by differential equations. Through solution functions of these models, we propose to calculate the number of ideas of each participant on any time intervals and thus in the future (called prediction). To be able to compute solution functions, it is necessary to determine the parameters of these models. In our approach, we use optimization model for model parameters calculation in which solution functions are approximated by numerical methods. We developed two generic optimization models, one based on Euler’s and the other on the fourth order Runge–Kutta’s numerical methods for the solving of differential equations, and we apply them to the non-cognitive and respectively to the cognitive models. Through some feasibility tests, we show the adequacy of the proposed approach to our prediction context.     

The Relationship between Exchange Rates and Interest Rate Differentials: A Wavelet Approach

This paper uses wavelet analysis to investigate the relationship between the spot exchange rate and interest rate differential for seven pairs of countries, with a small country, Sweden, included in each case. The key empirical results show that there tends to be a negative relationship between the spot exchange rate (domestic‐currency price of foreign currency) and nominal interest rate differential (approximately the domestic interest rate minus the foreign interest rate) at the shortest timescales, while a positive relationship is more frequently found at the longest timescales. This indicates that among models of exchange rate determination using the asset approach, the sticky‐price models are supported in the short run and flexible‐price models in the long run.     

一种新的混沌扩频序列产生方法

本文提出了一种新的混沌扩频序列产生方法。该方法基于神经网络的强大学习能力和副近非线性函数能力,应用具有全局最优的ＢＰ改进算法通过训练学习建立起具有混沌性态的优化神经网络模型,利用网络权值调整的灵活性来产生混沌扩频序列。计算机仿真结果表明,该模型产生的混沌扩频序列调整更容易,比基于单一混沌映射能产生更多符合扩频通信要求的扩频序列。     

A Macroeconomic Model with Hysteresis in Foreign Trade

The continuous non‐linear macro‐hysteresis loop is approximated by a rhombus shaped path which therefore shows a closer affinity to the genuine concept of hysteresis than conventional techniques via difference equations. This linearized model is applied to implement foreign trade hysteresis in a standard macroeconomic simultaneous equation model demonstrating the persisting consequences of only temporary exogenous shocks on national income, interest rate and the determination of the exchange rate. Since hysteresis in foreign trade is analysed in a macroeconomic framework, the feedback of hysteresis caused by exchange rate variations on the exchange rate itself can be illustrated.     

Causes of nonlinearities in low-order models of the real exchange rate

This paper investigates the extent to which modern DSGE models, which feature local currency pricing, home bias, nontraded goods, and incomplete markets, can generate nonlinear real exchange rate dynamics that are consistent with those found in the time series literature using data from the current floating period. Our key findings are as follows. First, if the true model can be appropriately characterized as a set of linear equations, then linearity tests that utilize univariate autoregressions of the real exchange rate suffer from an omitted variables problem, which leads them to overestimate the true incidence of nonlinearity. Consequently, studies that fail to control for this problem may spuriously find evidence of nonlinearities in the data, despite the fact that the data generating process may be linear. Second, we propose a strategy that can largely eliminate this distortion. Finally, we find that DSGE models solved using higher order approximations are capable of generating true structural nonlinearities in real exchange rates both asymptotically and in short samples.     

基于差分空时调制的混沌慢跳频系统

提出一种慢跳频系统中基于差分空时调制的混沌保密通信方法。此方案集成了差分空时编码和混沌跳频扩频技术的优点。一方面,在跳频系统中,使用混沌序列代替伪随机(PN)码,增强了抗截获和抗预测的性能;另一方面,通过差分空时调制产生分集增益,降低了多径衰落效应的影响。仿真结果证实了此方案的有效性。     

Delay Dynamics in a Classical IS‐LM Model with Tax Collections

An IS‐LM model is developed for the dynamics of income, interest rate and money stock with delay in tax revenue. The main aim is to show that the delay matters in macro dynamics. Two different delays, fixed time delays and continuously distributed time delays, are considered explicitly and described by delay‐differential equations and integro‐differential equations, respectively. Conditions for the local stability of the two models are derived and compared. The destabilizing effects caused by the delay are numerically examined. Appearance of wide spectrum of dynamics ranging from simple cyclic oscillations to complex dynamics is described through Hopf bifurctions.     

ON FINITE DIMENSIONAL REALIZATIONS OF TWO-COUNTRY INTEREST RATE MODELS

This paper explores how consistent two-dimensional families of forward rate curves can be constructed on an international market. Applying the approach in Björk and Christenssen (1999) and Björk and Svensson (2001) , we study when a system of inherently infinite dimensional domestic and foreign forward rate processes in a two-country economy with spot (forward) exchange rate possesses finite dimensional realizations. In the system with the forward exchange rate, the forward interest rate equations are supplemented by a third infinite dimensional stochastic differential equation representing the forward exchange rate dynamics. We construct and fit consistent families to observed Euro and USD yields as well as the forward (spot) EUR/USD exchange rate.     

Impact of Exchange Rate Uncertainty on Trade Flows: Evidence from Commodity Trade between the United States and the United Kingdom

Previous studies that investigated the impact of exchange rate volatility on the trade flows employed aggregate trade data and standard estimation techniques. They provided mixed results. In this paper we use disaggregated import and export data for 177 commodities traded between the United States and the United Kingdom to investigate whether volatility of the real bilateral dollar–pound exchange rate has any detrimental effect on trade flows at the commodity level. Additionally, we employ the bounds testing approach to cointegration and error‐correction modelling that is suitable for the models used mostly because it does not require pre‐unit‐root testing and variables in the model could be stationary, non‐stationary or a combination of the two. In most trade flow models estimated, we found a negative effect of exchange rate volatility on commodity trade.     

Subjective Probability Density Functions from FX Option Prices: Predictive Power and Performance on a Carry Trade Strategy

In this article, we extracted the risk‐neutral densities (RNDs) and subjective probability density functions of the US Dollar/Brazilian Real (USD/BRL) exchange rate and evaluated its performance in predicting the future realizations of the USD/BRL exchange rate. The RNDs were estimated using two structural models and three nonstructural models. In the first category, we included the Variance Gamma‐OU model and the CGMY Gamma‐OU model. In the second category, we included the density functional based on confluent hypergeometric function model, the mixture of lognormal distributions model, and the smoothed implied volatility smile. The density functional based on confluent hypergeometric function and the CGMY Gamma‐OU produced 1‐month term densities (RND and subjective probability density function) with the highest forecasting power of the 1‐month USD/BRL exchange rate. Finally, we applied the CGMY Gamma‐OU model to extract a sample of subjective cumulative probabilities of 1‐month USD/BRL movements, and used them as explanatory variables in predictive time series models, whose dependent variable was the 1‐month carry trade return. Its predictive power was then tested and confirmed in three trading strategies that over performed the standard carry trade strategy in terms of annualized cumulative returns.     

Effect of exchange rate volatility on industry trade flows between Malaysia and China

This paper investigates the impact of ringgit/yuan volatility on Malaysian trade with her largest trading partner, China. The short- and long-run impacts are estimated using bounds testing approach to cointegration analysis and disaggregated bilateral trade data by industry over the period of 1985–2010. Specifically, we considered a total of 151 importing and 24 exporting industries in Malaysia that traded with China. Our finding indicates that cointegration existed in 94 Malaysian import industry models and 16 Malaysian export industry models. Among these cases, exchange rate volatility has short-run effects on majority of the models. However, the short-run effects shift into the long-run effects in 46 out of 69 industries in import models and 5 out of 10 industries in export models. Results indicate that the exchange rate uncertainty has positive effects on majority of these industries.     

宏观经济因素与人民币汇率浮动

采用协整检验和误差修正模型等计量经济学方法,就当前国内若干热点变动的宏观经济因素变量对汇改后人民币汇率的影响进行了实证研究,研究结果表明热点变动的中美利差水平、通货膨胀率差异水平以及外汇储备增长率与人民币升值幅度之间存在长期稳定的均衡关系。长期来看,利差水平对人民币名义汇率影响程度较大,而短期内,外汇储备因素和人民币汇率自身变动的前期信息对其影响较为显著。     

Nominal rigidity, desired markup variations, and real exchange rate persistence

This paper develops and estimates a dynamic general-equilibrium sticky-price model that accounts for real exchange rate persistence. The key feature of the model is the dependence of the firm's desired markup on its relative price. Desired markup variations exacerbate the nominal rigidity that results from the exogenously imposed frictions in the goods market. The model is estimated by the maximum-likelihood method using Canadian and U.S. data. The estimated model successfully replicates the properties of the Canada-U.S. bilateral real exchange rate. In particular, the model closely matches the persistence found in the real exchange rate series. More importantly, this is achieved with a plausible duration of price contracts and a moderate convexity of the demand function.     

服务出口与实际汇率动态关系分析:基于美国数据的考察

基于代表性家庭追求效用最大化,文中构建了一个由外国实际收入、汇率水平、货物出口以及经GARCH(1,1)模型估计所得条件方差作为汇率风险代理变量组成的服务出口方程。采用自回归分布滞后估计方程参数,并将汇率变动影响货物出口进而传导至服务出口的间接效应纳入分析框架。估计结果显示,汇率水平变动与服务出口之间存在负相关关系,而汇率风险却有助于推动服务出口;汇率变动对服务出口的累积净效应表明,汇率水平变动是汇率变动对服务出口最终影响效应的主导因素。最后从我国汇率变动与服务贸易发展角度也证实了该结论。     

Equilibrium Pricing in the Presence of Cumulative Dividends Following a Diffusion

The paper presents some security market pricing results in the setting of a security market equilibrium in continuous time. The theme of the paper is financial valuation theory when the primitive assets pay out real dividends represented by processes of unbounded variation. In continuous time, when the models are also continuous, this is the most general representation of real dividends, and it can be of practical interest to analyze such models.
Taking as the starting point an extension to continuous time of the Lucas consumption-based model, we derive the equilibrium short-term interest rate, present a new derivation of the consumption-based capital asset pricing model, demonstrate how equilibrium forward and futures prices can be derived, including several examples, and finally we derive the equilibrium price of a European call option in a situation where the underlying asset pays dividends according to an Itô process of unbounded variation. In the latter case we demonstrate how this pricing formula simplifies to known results in special cases, among them the famous Black–Scholes formula and the Merton formula for a special dividend rate process.     

Before the fall: were East Asian currencies overvalued?

Two major approaches to identifying the equilibrium exchange rate are implemented. First, the concept of purchasing power parity (PPP) is tested and used to define the equilibrium real exchange rate for the Hong Kong dollar, Indonesian rupiah, Korean won, Malaysian ringgit, Philippine peso, Singapore dollar, New Taiwanese dollar and the Thai baht. The calculated PPP rates are then used to evaluate whether these seven East Asian currencies were overvalued. A variety of econometric techniques and price deflators are used. As of May 1997, the HK$, baht, ringgit and peso were overvalued according to this criterion. The evidence is mixed regarding the Indonesian rupiah and NT$. Second, a monetary model of exchange rates, augmented by a proxy variable for productivity trends, is estimated for five currencies. An overvaluation for the rupiah and baht is indicated, although only in the latter case is the overvaluation substantial (17%). The won, Singapore dollar and especially the NT$ appear undervalued according to these models.