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We begin by examining the accumulated value functions of some annuities-certain. We then investigate the accumulated value of these annuities where the interest is a random variable under some restrictions. Calculations are derived for the expected value and the variance of these accumulated values and present values. In particular we will examine an annuity-due of k yearly payments of 1. Then we will consider an increasing annuity-due of k yearly payments of 1, 2, ⋯ , k. And finally, we examine a decreasing annuity-due of k yearly payments of n, n - 1, ⋯ , n - k + 1, for k ≤ n. Finally we extend our analysis to include a contingent annuity. That is an annuity in which each payment is contingent on the continuance of a given status. Specifically, we examine a life annuity under which each payment is contingent on the survival of one or more specified persons. We extend our methods from the previous sections to derive the formula of the expected value for the present value of the life annuities of a future life time at a random rate of interest.

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This dissertation is comprised of four chapters. Chapter 1 provides an introduction to<br />Economic application of time series analysis and discusses the topics covered in each of the following chapters along with some main results therein. <br />    In Chapter 2, I construct a measure of information asymmetry in the financial markets in U.S., by estimating an index of agency cost pertaining to U.S. manufacturing firms. The cyclical behavior of the unobservable agency cost is derived by a novel application of the Kalman filter within a Bayesian framework, using firm level data from 1984-2006. The preliminary results provide support to the financial accelerator mechanism in the business cycle literature. <br />    In Chapter 3, I show that people\'s expectation of uncertainty in financial markets is a significant factor impacting short-term real exchange rate movements. Specifically, a sudden increase in expectation of stock market volatility in a low interest rate country tends to appreciate their currencies against high interest rate currencies. I construct a measure of conditional expected uncertainty from volatility of returns of the dominant portfolio (indices) of 7 industrialized countries. I identify uncertainty shocks and its impact on dollar real exchange rate, and explain my results in the context of currency carry trade.<br />    Chapter 4 of my dissertation documents the presence of significant non-linearity in the deficit-interest rate relationship in the U.S. economy. Using an asymptotic threshold test as per Hansen (2000), I find strong evidence for threshold effects in the impact of expected deficit on future long-term interest rates. I find that a percentage point increase in expected deficit in a regime where the expected deficit/GDP ratio is above 1.8 percent (the estimated threshold value) increases future nominal long term interest rates by 29-30 basis point, and a "news shock" to expectation of future deficit increases future real long term interest rates by 12-18 basis points. When expected deficit/GDP ratio is below 1.8 percent, an increase in expected deficit has no impact on future long-term interest rates. <br /> / Ph. D.

Hace tan solo unos años se introdujo el euro como moneda de pleno derecho en once países de la Unión Europea. Sin embargo, a lo largo del tiempo, este proyecto se ha enfrentado a diversos obstáculos, y uno de los más relevantes es el no conocer precisamente el efecto que la Unión Monetaria podría tener en las economías de la región. Las tasas de interés son variables fundamentales en el desempeño coyuntural de cualquier nación, por lo que su manejo por parte del Banco Central implica consecuencias importantes. A partir del mes de Enero de 1999, la difícil tarea de fijar los tipos de interés comunes para todos los países miembros de la Zona Monetaria Europea, independientemente sus características particulares, está a cargo del Banco Central Europeo. En esta investigación se busca determinar las variables más importantes que afectan el comportamiento de las tasas de interés, y al mismo tiempo saber que efecto ha ocasionado la introducción del euro en las mismas, por lo que el trabajo se ha dividido en dos partes. En la primera parte se estudian diversas ecuaciones, creadas con base en ciertas teorías relacionadas con el tema (Akthar 1987, Fischer 1990, Cohen y Wennigen 1994, Lee y Prasad 1994, Patterson 1999, Haley 2000.) por lo que se obtienen las variables más significativas en cada una de ellas. En la segunda parte se analizan las variables de la primera parte, y se definen cuales fueron afectadas por la introducción del euro. Para ambas secciones se utiliza una Base de Datos del Boletín Mensual del Mes de Enero del 2001 del Banco Central Europeo. El período estudiado comprende desde el mes de Enero de 1997 hasta Octubre del 2000. Para efectuar el análisis se emplean los modelos de regresión lineal y split regression, de forma que es posible determinar la relación entre las variables, su nivel de significación en los modelos empleados, y el efecto sufrido por la introducción del euro. El resultado del análisis muestra que la introducción de la moneda única tuvo un fuerte impacto en la mayoría de las variables analizadas y por consecuencia en las tasas de interés de la zona euro. La introducción de la divisa comunitaria implicó la disminución de los tipos de interés promedio en la región, sin embargo fue posible observar un incremento en los mismos durante los últimos meses analizados. Este comportamiento ha sido la respuesta del Banco Central Europeo para mantener la estabilidad de precios ante los fenómenos presentados en el segundo semestre del año 2000, como han sido la debilidad del euro con relación al dólar americano, los elevados precios del petróleo, falta de interés y confianza en la moneda común por parte de Dinamarca, Suecia y el Reino Unido, el prolongado e ininterrumpido crecimiento sostenido de la economía estadounidense hasta antes de Enero del 2001, crisis agropecuarias y la caída de los índices bursátiles.

Thesis (MSc)--Stellenbosch University, 2014. / ENGLISH ABSTRACT: This work analysis the main macro-finance models of the term structure of interest rates that determines the joint dynamics of the term structure and the macroeconomic fundamentals under no-arbitrage approach. There has been a long search during the past decades of trying to study the relationship between the term structure of interest rates and the economy, to the extent that much of recent research has combined elements of finance, monetary economics, and the macroeconomics to analyse the term structure. The central interest of the thesis is based on two important notions. Firstly, it is picking up from the important work of Ang and Piazzesi (2003) model who suggested a joint macro- finance strategy in a discrete time affine setting, by also imposing the classical Taylor (1993) rule to determine the association between yields and macroeconomic variables through monetary policy. There is a strong intuition from the Taylor rule literature that suggests that such macroeconomic variables as in inflation and real activity should matter for the interest rate, which is the monetary policy instrument. Since from this important framework, no-arbitrage macro-finance approach to the term structure of interest rates has become an active field of cross-disciplinary research between financial economics and macroeconomics. Secondly, the importance of forecasting the yield curve using the variations on the Nelson and Siegel (1987) exponential components framework to capture the dynamics of the entire yield curve into three dimensional parameters evolving dynamically. Nelson-Siegel approach is a convenient and parsimonious approximation method which has been trusted to work best for fitting and forecasting the yield curve. The work that has caught quite much of interest under this framework is the generalized arbitrage-free Nelson-Siegel macro- nance term structure model with macroeconomic fundamentals, (Li et al. (2012)), that characterises the joint dynamic interaction between yields and the macroeconomy and the dynamic relationship between bond risk-premia and the economy. According to Li et al. (2012), risk-premia is found to be closely linked to macroeconomic activities and its variations can be analysed. The approach improves the estimation and the challenges on identication of risk parameters that has been faced in recent macro-finance literature. / AFRIKAANSE OPSOMMING: Hierdie werk ontleed die makro- nansiese modelle van die term struktuur van rentekoers pryse wat die gesamentlike dinamika bepaal van die term struktuur en die makroekonomiese fundamentele faktore in 'n geen arbitrage wêreld. Daar was 'n lang gesoek in afgelope dekades gewees wat probeer om die verhouding tussen die term struktuur van rentekoerse en die ekonomie te bestudeer, tot die gevolg dat baie onlangse navorsing elemente van nansies, monetêre ekonomie en die makroekonomie gekombineer het om die term struktuur te analiseer. Die sentrale belang van hierdie proefskrif is gebaseer op twee belangrike begrippe. Eerstens, dit tel op by die belangrike werk van die Ang and Piazzesi (2003) model wat 'n gesamentlike makro- nansiering strategie voorstel in 'n diskrete tyd a ene ligging, deur ook die klassieke Taylor (1993) reël om assosiasie te bepaal tussen opbrengste en makroekonomiese veranderlikes deur middel van monetêre beleid te imposeer. Daar is 'n sterk aanvoeling van die Taylor reël literatuur wat daarop dui dat sodanige makroekonomiese veranderlikes soos in asie en die werklike aktiwiteit moet saak maak vir die rentekoers, wat die monetêre beleid instrument is. Sedert hierdie belangrike raamwerk, het geen-arbitrage makro- nansies benadering tot term struktuur van rentekoerse 'n aktiewe gebied van kruis-dissiplinêre navorsing tussen nansiële ekonomie en makroekonomie geword. Tweedens, die belangrikheid van voorspelling van opbrengskromme met behulp van variasies op die Nelson and Siegel (1987) eksponensiële komponente raamwerk om dinamika van die hele opbrengskromme te vang in drie dimensionele parameters wat dinamies ontwikkel. Die Nelson-Siegel benadering is 'n gerie ike en spaarsamige benaderingsmetode wat reeds vertrou word om die beste pas te bewerkstellig en voorspelling van die opbrengskromme. Die werk wat nogal baie belangstelling ontvang het onder hierdie raamwerk is die algemene arbitrage-vrye Nelson-Siegel makro- nansiele term struktuur model met makroekonomiese grondbeginsels, (Li et al. (2012)), wat kenmerkend van die gesamentlike dinamiese interaksie tussen die opbrengs en die makroekonomie en die dinamiese verhouding tussen band risiko-premies en die ekonomie is. Volgens Li et al. (2012), word risiko-premies bevind om nou gekoppel te wees aan makroekonomiese aktiwiteite en wat se variasies ontleed kan word. Die benadering verbeter die skatting en die uitdagings van identi- sering van risiko parameters wat teegekom is in die afgelope makro- nansiese literatuur.

M.Com. (Financial Economics) / The use of the yield curve spread in forecasting future recessions has become popular as it is a simple tool to use, due to the positive relationship between the yield curve spread and economic activity. The inversion or flattening of the yield curve spread usually signals a future recession. This has been the subject of several studies both internationally and in South Africa. This research provides an analysis of the yield curve spread’s ability to accurately forecast future recessions in South Africa through the use of three probit models. Furthermore, the yield curve spread’s ability to estimate is compared to that of share prices, using the JSE All Share Index. This research extends on studies by Khomo and Aziakpono (2006) and Clay and Keeton (2011), who used the static and dynamic probit models to forecast recessions in South Africa. In addition to these models, this research also makes use of the business cycle conditionally independent probit model for estimation. The findings suggest that share prices improve the yield curve spread’s ability to forecast recessions when estimating using the static probit model; however when comparing the results between the financial variables, the yield curve spread continues to produce the best forecast of recessions in South Africa. These results support those of Khomo and Aziakpono (2006) and Clay and Keeton (2011). Of the three probit models, the dynamic probit model estimate using the yield curve spread produced the most accurate forecast of recessions one quarter ahead. Therefore, the yield curve spread continues to provide the most accurate forecast of recessions in South Africa.

by Kwan Wai Kwong. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1997. / Includes bibliographical references (leaves 89-92). / ABSTRACT --- p.1 / Chapter 1. --- INTRODUCTION --- p.2 / Chapter 2. --- LITERATURE REVIEW --- p.5 / Chapter 2.1 --- Traditional and Working's hedging theory --- p.5 / Chapter 2.2 --- Portfolio theory and hedging --- p.5 / Chapter 2.3 --- Selection of proper statistical estimation model --- p.7 / Chapter 2.4 --- StaTIonarIty of optimal hedge ratio --- p.8 / Chapter 2.5 --- time-varying hedging models --- p.9 / Chapter 3. --- MARKETS AND INSTRUMENTS --- p.13 / Chapter 3.1 --- Exchange Fund Bills --- p.13 / Chapter 3.1.1 --- Rationale --- p.13 / Chapter 3.1.2 --- Status and deployment of funds --- p.14 / Chapter 3.1.3 --- Form of Bills --- p.14 / Chapter 3.1.4 --- Pricing of the Bills --- p.15 / Chapter 3.1.5 --- Development of the secondary market --- p.15 / Chapter 3.1.6 --- Investors --- p.17 / Chapter 3.1.7 --- Reasons for the success of the Bills programme --- p.17 / Chapter 3.2 --- eurodollar futures contract --- p.18 / Chapter 3.3 --- Treasury bill futures contract --- p.19 / Chapter 3.4 --- Comparison between eurodollar and treasury bills futures --- p.20 / Chapter 4. --- RESEARCH METHODOLOGY --- p.22 / Chapter 4.1 --- DATA --- p.22 / Chapter 4.2 --- DEFINITION of hedging effectiveness and comparison criterion --- p.23 / Chapter 4.2.1 --- Definition of hedging effectiveness --- p.23 / Chapter 4.2.2 --- Comparison of ex-ante hedging performance --- p.24 / Chapter 4.3 --- Model description --- p.25 / Chapter 4.3.1 --- Conventional hedging model --- p.25 / Chapter 4.3.2 --- Error correction model (ECM) --- p.28 / Chapter 4.3.2.1 --- Unit root test --- p.29 / Chapter 4.3.2.2 --- Test of cointegration --- p.30 / Chapter 4.3.2.3 --- Construction of the error correction model (ECM) --- p.31 / Chapter 4.3.3 --- Time-varying hedging model --- p.32 / Chapter 4.3.3.1 --- Time-varying conditional hedging theory --- p.32 / Chapter 4.3.3.2 --- Test for the ARCH effect --- p.34 / Chapter 4.3.3.3 --- Bivariate ARCH(q) error correction model --- p.35 / Chapter 4.4 --- out-of-sample forecast --- p.37 / Chapter 4.4.1 --- Rolling samples against expanding sample --- p.37 / Chapter 4.4.2 --- Out-of-sample forecast without transaction cost --- p.37 / Chapter 4.4.3 --- Out-of-sample forecast with transaction cost --- p.39 / Chapter 5. --- DATA SUMMARY --- p.42 / Chapter 5.1 --- Preliminary analysis --- p.42 / Chapter 5.2 --- Unit root analysis --- p.43 / Chapter 5.3 --- Co-integration analysis --- p.44 / Chapter 6. --- EMPIRICAL RESULTS --- p.45 / Chapter 6.1 --- Model estimation --- p.45 / Chapter 6.2 --- Ex-ante hedging effectiveness with no transaction cost --- p.47 / Chapter 6.3 --- Ex-ante hedging effectiveness with transaction cost --- p.49 / Chapter 6.4 --- Summary and discussion on empirical findings --- p.50 / Chapter 6.4.1 --- Hedging superiority between the two futures contracts --- p.50 / Chapter 6.4.2 --- Magnitude of hedging performance --- p.51 / Chapter 6.4.3 --- Hedge ratio estimates --- p.56 / Chapter 6.4.4 --- Hedging effectiveness across investment horizon --- p.57 / Chapter 6.4.5 --- Model superiority --- p.57 / Chapter 7. --- CONCLUSION --- p.59 / APPENDIX --- p.84 / Chapter I) --- derivation of optimal hedge ratio under static hedging strategies --- p.84 / Chapter II) --- Derivation of optimal hedge ratios under dynamic hedging strategies --- p.85 / Chapter III) --- Causality test on the lead lag relationship between HKEFB and the two futures contracts --- p.87 / REFERENCES --- p.89