Thesis (MComm (Statistics and Actuarial Science))--University of Stellenbosch, 2006. / An overview of modern and historical interest rate model theory is given with the specific aim of derivative pricing. A variety of stochastic interest rate models are discussed within a South African market context. The various models are compared with respect to characteristics such as mean reversion, positivity of interest rates, the volatility structures they can represent, the yield curve shapes they can represent and weather analytical bond and derivative prices can be found. The distribution of the interest rates implied by some of these models is also found under various measures. The calibration of these models also receives attention with respect to instruments available in the South African market. Problems associated with the calibration of the modern models are also discussed.

This thesis studies interest rates (even negative), interest rate derivatives and term structure of interest rates. We review the different types of interest rates and go through the evaluation of a derivative using risk-neutral and forward-neutral methods. Moreover, the construction of interest rate models (term-structure models), pricing of bonds and interest rate derivatives, using both equilibrium and no-arbitrage approaches are discussed, compared and contrasted. Further, we look at the HJM framework and the LMM model to evaluate and simulate forward curves and find the forward rates as the discount factors. Finally, the new framework (after financial crisis in 2008), under the collateral agreement (CSA) has been taken into consideration.

Dans le Chapitre 1, nous présentons une nouvelle approche pour évaluer des options dites à barrières basée sur une méthode connue sous le nom de méthode Vanna-Volga. Cette nouvelle méthode nous permet une calibration simple et rapide sur le marché des options à barrières directement ce qui permet d'évaluer ces options avec un outil en accord avec le marché. Nous comparons également nos résultats avec ceux provenant d’autres modèles célèbres et nous étudions la sensibilité de cette méthode par rapport aux données du marché. Nous donnons une nouvelle justification théorique associée à la méthode Vanna-Volga comme étant une approximation de Taylor du premier ordre du prix de l'option autour de la volatilité dite à la monnaie.<p><p><p>Dans le Chapitre 2 de la thèse nous allons développer un modèle qui compte de la volatilité implicite du marché et de la variabilité des taux d'intérêts. Nous travaillons dans le marché particulier des taux de changes, avec un modèle à volatilité locale pour la dynamique du taux de change dans lequel les taux d'intérêts domestiques et étrangers sont également supposé stochastiques. Nous dérivons l'expression de la volatilité locale et dérivons divers résultats particulièrement utiles pour la calibration du modèle. Finalement, nous développons un nouveau modèle hybride où la volatilité du taux de change possède une composante locale et une composante stochastique et nous dérivons une méthode de calibration pour ce nouveau modèle.<p><p><p>Dans le Chapitre 3, nous allons appliquer le modèle à volatilité locale et taux d'intérêts stochastiques développé dans le précédent chapitre mais dans le cadre d'évaluation de produits dérivés associés aux assurances vie. Nous utilisons une méthode de calibration développée dans le Chapitre 2. Les produits étudiés étant exotiques, nous allons également comparer les prix obtenus dans différents modèles, à savoir le modèle à volatilité locale, à volatilité stochastique et enfin à volatilité constante pour le sous-jacent, les trois modèles étant combinés avec des taux d'intérêts stochastiques.<p><p><p>Finalement, dans le Chapitre 4 nous allons travailler avec un modèle dit de Lévy pour modéliser le sous-jacent. Nous nous intéressons à l'évaluation d'options Asiatiques arithmétiques. Comme de nombreuses options exotiques, il n'est pas possible d'obtenir un prix analytique et dans ce cas seules les méthodes numériques permettent de résoudre le problème. Dans ce Chapitre 4, nous développons une méthode basée sur la méthode de simulations de Monte Carlo et nous employons deux types de variables de contrôle permettant d'améliorer la convergence du programme. Nous développons également une méthode permettant d'obtenir une borne inférieure au prix de l'option avec une efficacité qui surpasse les autres méthodes.<p> / Doctorat en Sciences / info:eu-repo/semantics/nonPublished

This thesis is made of two parts. Part I (Chapter 1 to 3) focuses on the ethical aspects of the current challenges in microfinance. Chapter 1 addresses the question of the place and importance of credit in development policies, through the debate on the right to credit. Chapter 2 and 3 then question the fairness of the interest rates charged by the microfinance institutions. Chapter 2 analyzes whether the fairness criteria depend on more basic principles of justice, such as Rawls’ principles described in A Theory of Justice (Rawsl, 1976). Chapter 3 then reviews some of the implicit and explicit definitions of fair interest rates and proposes an original methodology, with David Gauthiers’ contractuarian theory. It determines what a fair interest rate would be when lending to the poor. <p><p>Based on the results of the two first chapters, Part II (Chapter 4 to 6) focuses on the role of donors in microfinance. Chapters 4 and 5 use two original databases, of 67 and 100 MFIs respectively to study the impact of subsidies on the MFIs’ management, through their rating evaluation (Chapter 4) and MFIs’ performance and management decisions (Chapter 5). Chapter 4 will analyze the relationship between the quality of management, as rated by a specialized agency, and the amount of subsidies. Chapter 5 will study pricing policy, the clientele and the potential moral hazard of subsidized institutions. Concluding this analysis, Chapter 6 gives some guidelines on the use of donor subsidies, especially in their interaction with the new private commercial actors, such as investment funds. <p> / Doctorat en sciences de gestion / info:eu-repo/semantics/nonPublished

This thesis investigates the relationship between expected inflation and nominal interest rates in South Africa and the extent to which the Fisher effect hypothesis holds. The hypothesis, proposed by Fisher (1930), that the nominal rate of interest should reflect movements in the expected rate of inflation has been the subject of much empirical research in many industrialised countries. This wealth of literature can be attributed to various factors including the pivotal role that the nominal rate of interest and, perhaps more importantly, the real rate of interest plays in the economy. The validity of the Fisher effect also has important implications for monetary policy and needs to be considered by central banks. Few studies have been conducted in South Africa to validate this important hypothesis. The analysis uses the 3-month bankers’ acceptance rate and the 10-year government bond rate to proxy both short- and long-term interest rates. The existence of a long-run unit proportional relationship between nominal interest rates and expected inflation is tested using Johansen’s cointegration test. The data is analysed for the period April 2000 to July 2005 as the research aims to establish whether the Fisher relationship holds within an inflation targeting monetary policy framework. The short-run Fisher effect is not empirically verified. This is due to the effects of the monetary policy transmission mechanism and implies that short-term nominal interest rates are a good indication of the stance of monetary policy. A long-run cointegrating relationship is established between long-term interest rates and expected inflation. The long-run adjustment is less than unity, which can be attributed to the credibility of the inflation-targeting framework.

Current economic situation is characterized for deflation and low inflation, low economic growth, and low or negative interest rates, which lead to phenomenon of issuing governments bonds with negative yield. The main goal of this work is to understand the valuation and behavior of bonds with condition of negative interest rates, analyze impacts of negative rates on volatility of bonds. This work also compares the behavior of negative yields of bonds in contrast with positive yields. The contribution of this work consists in the critical evaluation of limitations of the formula for calculating the bond price to fulfill its role if the values of negative interest rates are too low.

Master of Agribusiness / Department of Agricultural Economics / Allen M. Featherstone / Land is typically the highest value category of assets that farmers and ranchers have on their balance sheets. The value of land is affected by inflation. Understanding the effect of inflation on the land market helps farmers make better land pricing decisions and better asset management decisions. Using Treasury Bills and Farm Credit Bonds, future inflation expectations and agricultural risk premiums can be estimated. With the recent government stimulation of the economy and the resulting large amount of money infused into the economy, inflation is becoming an increasing concern with investors. Economic theory suggests that this infusion of money will affect future interest rates and ultimately the value of land given the inverse relationship between interest rates and the value of land. These lingering affects occur with the rise and fall of yield rates for Treasury Bills and Farm Credit bonds. Farm Credit bonds are sold at a premium over Treasury Bills. This premium indicates the market-assessed additional risk that farmers have to pay for their operating loans and other mortgages. Even though land values are affected by inflation, other things affect land values such as recreational use, development, and natural resource exploration. A combination of inflation and these other affects can greatly affect land prices.

Master of Arts / Department of Economics / Lance J. Bachmeier / This thesis examines the properties of two short-term interest rates: the federal funds rate and the rate of return on 90-day Treasury securities (T-Bills). Findings indicate strong evidence of cointegration among the two series. This result leads us to consider whether future movements in T-bill returns are predictable using the same methods used to predict the target federal funds rate. The “Taylor Rule,” introduced by Taylor (1993), assumes the Federal Reserve considers inflation and the output gap in their deliberation of how to adjust the federal funds target rate. We do an in-sample analysis followed by an out-of-sample forecasting comparison. Findings show that, in addition to inflation and the output gap, the unemployment rate and stock market contain valuable information for forecasting future T-bill rates.

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.

This thesis, motivated by my reflections about the failings of monetary policy implementation as a cause of the sub-prime crisis, attempts to answer the following inquiries: (i) whether interest rates have played a major role in generating the house price fluctuations in the U.S., (ii) what are the effects of accommodative monetary policy on the economy given banks' excessive risk-taking, and (iii) whether an optimal monetary policy rule can be found for curbing credit-driven economic volatilities in the model economy with unconventional transmission channels operating. By using a decomposition technique and regression analysis, it can be shown that short-term interest rates exert the most potent influence on the evolution of the volatile components of housing prices. One possible explanation for this is that low policy rates for a prolonged period tend to encourage bankers to take on more risk in lending. This transmission channel, labelled as the risk-taking channel, accounts for the gap to some extent between the forecast and the actual impact of monetary policy on the housing market and the overall economy. A looser monetary policy stance can also shift the preference of economic agents toward housing as theoretically and empirically corroborated in the context of choice between durable and nondurable goods. This transmission route is termed the preference channel. If these two channels are operative in the economy, policy makers need to react aggressively to rapid credit growth in order to stabilize the paths of housing prices and output. These findings provide meaningful implications for monetary policy implementation. First of all, central bankers should strive to identify in a timely fashion newly emerging and state-dependent transmission channels of monetary policy, and accurately assess the impact of policy decisions transmitted through these channels. Secondly, the intervention of central banks in the credit or housing market by adjusting policy rates can be optimal, relative to inaction, in circumstances where banks' risk-taking and the preference for housing are overly exuberant.