This dissertation is based on the papers written by Platen and Rebolledo (1996), and Platen (1999). The papers focuses on modeling the short term interest rate by optimizing relative entropy of two probability measures Q and P. The derivation of the model is done by applying the three principles of market clearing, exclusion of arbitrage and minimization of increase of arbitrage information on a simple financial market model. The last principle is equivalent to minimization of the distance between the risk neutral and the real world probability measures. We test the model on historical data from two countries, United States and South Africa from different time frames. The results are then compared to the findings of Platen (1999). / Dissertation (MSc)--University of Pretoria, 2012. / Mathematics and Applied Mathematics / unrestricted

This thesis is about the causal relationship between interest rates. In chapter 1, with the help of time-series econometrics and by applying linear Granger causality tests based on the Toda-Yamamoto approach, the linear causality directions between the federal funds rate and five different interest rates during the last seven business cycles in the U.S. are investigated. We also examine the linear Granger causality directions between the overnight rate and five other interest rates during the last three business cycles in Canada. In chapter 2, the Diks and Panchenko Granger causality test is applied to explore the nonlinear causality effects between the short-term and long-term interest rates. By combining nonlinear causality effects with the linear ones which are found in the first chapter, it is seen that during the related periods in the U.S. and Canada, the most common Granger causality direction between short-term and long-term interest rates is a bidirectional one. Moreover, our findings show that during recent periods, the federal funds rate and overnight rate Granger cause other interest rates significantly. In chapter 3, the rolling window strategy is employed to detect the linear and nonlinear Granger causality relationship between the federal funds rate and the 10-year government bond rate, during different time horizons, investigating whether these causalities change with the passing of time. Our findings show that during different time horizons, there is a significant two-way Granger causality relationship between these interest rates. Although we have a different interpretation of the existence of bidirectional causation between short-term and long-term interest rates, this conclusion provides some support to some post-Keynesian structuralists viewpoints like Pollin (2008). However, Pollin's claim indicating that with the passing of time the significant causality effects of the federal funds rate to the market rates becomes insignificant is not supported by the current thesis findings because our results demonstrate that these causality effects have not been diminishing over the most recent business cycles.

This thesis is about the causal relationship between interest rates. In chapter 1, with the help of time-series econometrics and by applying linear Granger causality tests based on the Toda-Yamamoto approach, the linear causality directions between the federal funds rate and five different interest rates during the last seven business cycles in the U.S. are investigated. We also examine the linear Granger causality directions between the overnight rate and five other interest rates during the last three business cycles in Canada. In chapter 2, the Diks and Panchenko Granger causality test is applied to explore the nonlinear causality effects between the short-term and long-term interest rates. By combining nonlinear causality effects with the linear ones which are found in the first chapter, it is seen that during the related periods in the U.S. and Canada, the most common Granger causality direction between short-term and long-term interest rates is a bidirectional one. Moreover, our findings show that during recent periods, the federal funds rate and overnight rate Granger cause other interest rates significantly. In chapter 3, the rolling window strategy is employed to detect the linear and nonlinear Granger causality relationship between the federal funds rate and the 10-year government bond rate, during different time horizons, investigating whether these causalities change with the passing of time. Our findings show that during different time horizons, there is a significant two-way Granger causality relationship between these interest rates. Although we have a different interpretation of the existence of bidirectional causation between short-term and long-term interest rates, this conclusion provides some support to some post-Keynesian structuralists viewpoints like Pollin (2008). However, Pollin's claim indicating that with the passing of time the significant causality effects of the federal funds rate to the market rates becomes insignificant is not supported by the current thesis findings because our results demonstrate that these causality effects have not been diminishing over the most recent business cycles.

This thesis focuses on the relationship between short-term interest rate and stock prices. The main idea is that if interest-rate increases, it makes holding stocks less attractive relative to fixed income securities. Therefore, investors change the structure of their portfolios and switch capital from stocks to banks, which results in stock prices decrease. In our thesis, we apply GJR-GARCH-t-M model to study the impact of Czech interest rate (14-day PRIBOR) on the Prague Stock Exchange (the PX index). In contrast to the majority of research on this topic, we have found no impact of the PRIBOR rate on the PX index- neither on its mean nor on its volatility. We attribute the absence of a significant relationship to exceptional composition of the PX index. Furthermore, we have found that the recent crisis has significantly changed the behavior of the Czech stock market.

本文研究目的係以台灣作實證研究，針對這樣一個逐漸開放的小型經濟體系，分析影響其短期利率變動的因素，並驗證其短期利率的變動是否僅受到國外因素（如國外利率）變動的影響，或者是僅受到國內因素（如預期物價膨脹、貨幣供給、景氣、財政及市場資金狀況等）變動的影響，亦或者是兩者皆有。本文以1989年4月到2004年12月這段期間月資料的時間數列為樣本，利用Dickey & Fuller(1981)之ADF單根檢定法來確定變數之數列特性，並採用Johanson (1988)所提出最大概似估計法來分析影響台灣短期利率變動的因素。本文實證結果顯示，台灣31-90天商業本票利率與消費者物價指數年增率、實質經濟成長率、意外貨幣成長、美國三個月國庫券利率、國庫券發行餘額及金融機構平均淨超額準備皆為I(1)數列，並具有一組共整合關係，顯示彼此間具有共同趨勢。其中商業本票與消費者物價指數年增率、實質經濟成長率、意外貨幣成長及美國三個月國庫券利率呈現顯著正向關係，而與金融機構平均淨超額準備呈現顯著負向關係，由此可知，台灣短期利率不僅受到國內因素的影響,亦同時受到國外因素的影響。 / The purpose of this paper is to analyze the determinants of short-term interest rate variation in Taiwan. This paper attempts to examine whether the external factors or internal factors influence the volatility of the short-term rate in Taiwan. ADF unit root test is adopted to check the characteristics of variable series; Johansen’s maximum likelihood method is used to analyze the determinants of short-term interest rate variation in Taiwan based on monthly data from April 1989 to December 2004.The empirical results shows that the rate of commercial paper, consumer price growth rate, real economic growth rate, unanticipated M2 growth rate, U.S. treasury bill rate, balance on treasury bill and net excess reserves are I(1) time series. Besides, those variables have one cointegration relationship with common trend. Specifically, the rate of commercial paper is significantly positively correlated with consumer price growth rate, real economic growth rate, unanticipated M2 growth rate and U.S. treasury bill rate, and is significantly negatively correlated with net excess reserves. Therefore, the variation of short-term interest rate in Taiwan is determined by both external and internal factors.

This study will be investigating the relationship between short-term and long-term interest rates with the OMX30 stock return expressed in percentage, as well as the effect that the interest rates have on the stock return. The data used in this study has been collected from the dataprogram Datastream with monthly observations from January 2003 until December 2022 resulting in 240 different variables within all three factors over a period of 20 years. While performing OLS estimation, the result estimated by using R-studio shows a negative correlation between the interest rates and the percentage return of OMX30. Furthermore, the Granger causality test shows that the short-term interest rate does have an impact on the market whilst the long-term interest rate does not have any direct effect on the stock market in Sweden.