M.Com. (Financial Economics) / Recently, there has been a growth in the bond market. This growth has brought with it an ever-increasing volume and range of interest rate depended derivative products known as interest rate derivatives. Amongst the variables used in pricing these derivative products is the short-term interest rate. A numbers of short-term interest rate models that are used to fit the short-term interest rate exist. Therefore, understanding the features characterised by various short-term interest rate models, and determining the best fitting models is crucial as this variable is fundamental in pricing interest rate derivatives, which further determine the decision making of economic agents. This dissertation examines various short-term interest rate models in continuous time in order to determine which model best fits the South African short-term interest rates. Both the linear and nonlinear short-term interest rate models were estimated. The methodology adopted in estimating the models was parametric approach using Quasi Maximum Likelihood Estimation (QMLE). The findings indicate that nonlinear models seem to fit the South African short-term interest rate data better than the linear models

Much depends on the future course of interest rates. The decisions of families to make major purchases, the willingness of businesses to expand and invest, the rise and fall of the economy and stock market, the ability of lesser developed countries to repay their debts, the tenure of presidents and prime ministers--all of these may turn on whether interest rates increase or decrease in the months ahead. Several decision functions developed in the dissertation permit the direction of change of interest rates on long-term U. S. government bonds to be forecast correctly about 60% of the time. When the different models are combined, effectiveness is increased, and when the forecasts are dollar-weighted, performance in excess of 70% is possible. The results are evaluated in comparison with a Bayesian forecasting model and a 10,000-event Monte Carlo simulation of a random decision rule. The forecasting ability of the models is statistically significant at the 99% level of confidence. The dissertation reports on one of the first application of powerful techniques recently developed in cybernetics and engineering to forecasting the direction of change in interest rates. Two forecasting algorithms, called linear decision functions or linear classifiers, are derived using the principles of pattern recognition. Because they are recursively updated, both algorithms operate dynamically and adapt their performance to changes in the economic environment. One classifier, a modification of the widely used least-mean-squared-error algorithm, is adapted to permit monthly revision and to allow larger movements of interest rates to have greater weight in future decisions. The second algorithm permits refinement of the parameter estimates generated by the first. These formal, mathematical constructs are then supplied with financial variables--leading indicators of inflation and investment activity--to permit unconditional, ex-ante forecasts of the direction of change of interest rates on long-term government bonds over a one-month time horizon throughout the period 1969-82. The results should be of interest to investment managers, speculators, corporate treasurers, policymakers, economists and forecasters.

Thesis (MSc)--Stellenbosch University / ENGLISH ABSTRACT : In this thesis, we first review the traditional pre-credit crunch approach that considers a single curve to consistently price all instruments. We review the theoretical pricing framework and introduce pricing formulas for plain vanilla interest rate derivatives. We then review the curve construction methodologies (bootstrapping and global methods) to build an interest rate curve using the instruments described previously as inputs. Second, we extend this work in the modern post-credit framework. Third, we review the calibration of the SABR model. Finally we present applications that use interest rate curves and SABR model: stripping implied volatilities, transforming the market observed smile (given quotes for standard tenors) to non-standard tenors (or inversely) and calibrating the market volatility smile coherently with the new market evidences. / AFRIKAANSE OPSOMMING : Geen Afrikaanse opsomming geskikbaar nie

Research Report: BUSA7167 (MM Finance and Investment Management). Submitted in Partial Fulfillment of the Requirements for the (Master of Management in Finance and Investments). Submitted on 06th June 2016 / The findings of the research have implications on the efficiency of the South African exchange rate market, and by extension, the efficiency of similar emerging foreign exchange markets. The study used Ordinary Least Square Approach and Johansen cointegration. Despite their theoretical appeal, and in line with a dozen of related past literature, the findings of the research generally favour the rejection UIP, PPP and IFE. The findings have implications on some regulatory measures that can be undertaken by the financial authority to improve the efficiency of the foreign exchange market. While there have been extensive studies on uncovered interest parity (UIP), purchasing power parity(PPP), and the international Fisher effect(IFE), research has scarcely tested these hypotheses in the context of emerging markets. This study attempts to bridge the existing gap by testing the three related parity condition for South Africa. / MT2016

by O'Yang Wiley. / Thesis (M.B.A.)--Chinese University of Hong Kong, 1990. / Bibliography: leaves 44-45. / ABSTRACT --- p.ii / TABLE OF CONTENTS --- p.iv / ACKNOWLEDGEMENTS --- p.v / Chapter / Chapter I. --- INTRODUCTION --- p.1 / Chapter II. --- TIME SERIES AND UNIT ROOT --- p.5 / Definitions --- p.5 / Difference Between 1(0) and 1(1) Processes --- p.8 / Chapter III. --- FORMULATION OF LONG RUN FISHER OPEN HYPOTHESIS … --- p.10 / Chapter IV. --- UNIT ROOT TESTS --- p.14 / Dickey and Fuller Test --- p.14 / Augmented Dickey and Fuller Test --- p.16 / Phillips and Perron Test --- p.16 / Finite Sample Properties of Regression / Unit Root Tests --- p.18 / Chapter V. --- UNIT ROOT TEST RESULTS --- p.20 / Tentative ARIMA Model for the Interest Rate Series --- p.21 / Hong Kong --- p.21 / Singapore --- p.22 / Malaysia --- p.22 / Philippines and Japan --- p.23 / Tentative ARIMA Model for the Interest Rate Differentials --- p.23 / Hong Kong-Malaysia --- p.23 / Hong Kong-Singapore --- p.24 / Singapore-Malaysia --- p.24 / Others --- p.24 / Unit Root Test Results --- p.24 / Discussions and Findings --- p.36 / Chapter VI. --- CONCLUSIONS AND AREAS OF FURTHER RESEARCH --- p.40 / APPENDIX --- p.43 / BIBLIOGRAPHY --- p.44

Zhang Haiyan. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2001. / Includes bibliographical references (leaves 48-50). / Abstracts in English and Chinese. / Chapter 1 --- Introduction --- p.1 / Chapter 2 --- Literature Review --- p.6 / Chapter 2.1 --- An Introduction to the Uncovered Interest Parity (UIP) and previous works on UIP --- p.6 / Chapter 2.2 --- Previous empirical works applying Band Spectrum Regression(BSR) --- p.15 / Chapter 3 --- Basic Band Spectral Regression (BSR) Techniques --- p.20 / Chapter 3.1 --- BSR Based on the complex Fourier transform --- p.20 / Chapter 3.2 --- BSR based on the real-valued Fourier transform --- p.24 / Chapter 3.3 --- Testing for parameter stability in the frequency domain --- p.26 / Chapter 4 --- Data and Standard Time Series Analysis in the Time Domain --- p.29 / Chapter 5 --- Analyze the UIP relation in the frequency domain --- p.33 / Chapter 5.1 --- An overview of the UIP relation across frequency --- p.33 / Chapter 5.2 --- Testing parameter stability across different time horizons --- p.37 / Chapter 6 --- Test of UIP with the forward premium --- p.42 / Chapter 7 --- Conclusion --- p.45

This thesis focuses on the non-arbitrage (fair) pricing of interest rate derivatives, in particular caplets and swaptions using the LIBOR market model (LMM) developed by Brace, Gatarek, and Musiela (1997) and Swap market model (SMM) developed Jamshidan (1997), respectively. Today, in most financial markets, interest rate derivatives are priced using the renowned Black-Scholes formula developed by Black and Scholes (1973). We present new pricing models for caplets and swaptions, which can be implemented in the financial market other than the Black-Scholes model. We theoretically construct these "new market models" and then test their practical aspects. We show that the dynamics of the LMM imply a pricing formula for caplets that has the same structure as the Black-Scholes pricing formula for a caplet that is used by market practitioners. For the SMM we also theoretically construct an arbitrage-free interest rate model that implies a pricing formula for swaptions that has the same structure as the Black-Scholes pricing formula for swaptions. We empirically compare the pricing performance of the LMM against the Black-Scholes for pricing caplets using Monte Carlo methods.

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.

Thesis (MSc)--Stellenbosch University, 2015. / ENGLISH ABSTRACT : The standard-Heath–Jarrow–Morton (HJM) framework is well-known for its application to pricing and hedging interest rate derivatives. This study implemented the extended HJM framework introduced by Eberlein and Raible (1999), in which a Brownian motion (BM) is replaced by a wide class of processes with jumps. In particular, the HJM driven by the generalised hyperbolic processes was studied. This approach was motivated by empirical evidence proving that models driven by a Brownian motion have several shortcomings, such as inability to incorporate jumps and leptokurticity into the price dynamics. Non-homogeneous Lévy processes and the change of measure techniques necessary for simplification and derivation of pricing formulae were also investigated. For robustness in numerical valuation, several transform methods were investigated and compared in terms of speed and accuracy. The models were calibrated to liquid South African data (ATM) interest rate caps using two methods of optimisation, namely the simulated annealing and secant-Levenberg–Marquardt methods. Two numerical valuation approaches had been implemented in this study, the COS method and the fractional fast Fourier transform (FrFT), and were compared to the existing methods in the context. Our numerical results showed that these two methods are quite efficient and very competitive. We have chose the COS method for calibration due to its rapidly speed and we have suggested a suitable approach for truncating the integration range to address the problems it has with short-maturity options. Our calibration results provided a nearly perfect fit, such that it was difficult to decide which model has a better fit to the current market state. Finally, all the implementations were done in MATLAB and the codes included in appendices. / AFRIKAANSE OPSOMMING : Die standaard-Heath–Jarrow–Morton-raamwerk (kortom die HJM-raamwerk) is daarvoor bekend dat dit op die prysbepaling en verskansing van afgeleide finansiële instrumente vir rentekoerse toegepas kan word. Hierdie studie het die uitgebreide HJM-raamwerk geïmplementeer wat deur Eberlein en Raible (1999) bekendgestel is en waarin ’n Brown-beweging deur ’n breë klas prosesse met spronge vervang word. In die besonder is die HJM wat deur veralgemeende hiperboliese prosesse gedryf word ondersoek. Hierdie benadering is gemotiveer deur empiriese bewyse dat modelle wat deur ’n Brown-beweging gedryf word verskeie tekortkominge het, soos die onvermoë om spronge en leptokurtose in prysdinamika te inkorporeer. Nie-homogene Lévy-prosesse en die maatveranderingstegnieke wat vir die vereenvoudiging en afleiding van prysbepalingsformules nodig is, is ook ondersoek. Vir robuustheid in numeriese waardasie is verskeie transformmetodes ondersoek en ten opsigte van spoed en akkuraatheid vergelyk. Die modelle is vir likiede Suid-Afrikaanse data vir boperke van rentekoerse sonder intrinsieke waarde gekalibreer deur twee optimiseringsmetodes te gebruik, naamlik die gesimuleerde uitgloeimetode en die sekans-Levenberg–Marquardt-metode. Twee benaderings tot numeriese waardasie is in hierdie studie gebruik, naamlik die kosinusmetode en die fraksionele vinnige Fourier-transform, en met bestaande metodes in die konteks vergelyk. Die numeriese resultate het getoon dat hierdie twee metodes redelik doeltreffend en uiters mededingend is. Ons het op grond van die motiveringspoed van die kosinus-metode daardie metode vir kalibrering gekies en ’n geskikte benadering tot die trunkering van die integrasiereeks voorgestel ten einde die probleem ten opsigte van opsies met kort uitkeringstermyne op te los. Die kalibreringsresultate het ’n byna perfekte passing gelewer, sodat dit moeilik was om te besluit watter model die huidige marksituasie die beste pas. Ten slotte is alle implementerings in MATLAB gedoen en die kodes in bylaes ingesluit.

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.