published_or_final_version / Business Administration / Master / Master of Business Administration

M.Comm. / The fundamental objective of this paper is to effectively analise and forecast currency option volatility in the South African derivative market. The study of Dollar/Rand volatility is based in the domain of quantitative and international economics. It focuses on the monetary aspect of international finance, where currency volatility is of critical significance in the hedging of open currency option positions used in investment strategies as well as in active currency risk management. Topics covered in this study include firstly a theoretical discussion of option pricing and volatility to provide the necessary financial and statistical background: Advanced volatility issues are secondly addressed to define the volatility matrix and to explain the appearance of volatility smiles and cones as well as the characteristics of the time structure of volatility. The use of volatility as an important risk management tool is also depicted. Various time-series techniques such as the Box Jenkins methodology and decomposition of Dollar/Rand historical and implied volatility are assessed and used to forecast volatility. Univariate and multivariate regression analysis is in addition described and used to find the best estimate for subsequent Dollar/Rand volatility. Finally, the paper is concluded by an analysis of time varying stochastic volatility models such as the models for autoregressive conditional heteroscedasticity. The techniques apply a regression on the variance and include a function to allow for the asymmetric nature of movements in Dollar/Rand volatility. Up to date, no formal in-depth academical research on high frequency currency volatility has been conducted in the South African derivative market. It is therefor crucial to research the unique characteristics of Dollar/Rand option volatility. If the study concludes that Dollar/Rand volatility is predictable, it will have important implications for currency option pricing and portfolio management. Investors seeking to avoid risk, may choose to adjust their portfolios by reducing their commitments to assets whose volatilities are predicted to increase, or by using dynamic diversification approaches to hedge predicted volatility increases. This is particularly true of currency derivative markets where the volatility of the underlying asset has a profound effect on the value of the derivative.

The thesis contains two chapters which address questions important both for the economic theory and applications. In Chapter I we show that inequalities are an important tool in the theory of production functions. Various notions of internal economies of scale can be equivalently expressed in terms of upper or lower bounds on production functions. In the problem of aggregation of efficiently allocated goods, if one is concerned with two-sided bounds as opposed to exact expressions, the aggregate production function can be derived from some general assumptions about production units subject to aggregation. The approach used does not require smoothness or convexity properties. In Chapter II we introduce a new forecasting techniques essential parts of which include using average high-order polynomial estimators for in-sample fit and low-order polynomial extension for out-of-sample fit. We provide some statements following the Gauss-Markov theorem format. The empirical part shows that algebraic polynomials treated in a proper way can perform very well in one-step-ahead prediction, especially in prediction of the direction of exchange rate movements. / Graduation date: 1995

M.Com. (Financial Economics) / Exchange rate forecasting has been an important and complex field of study originating mainly from the introduction of floating exchange rates in the 1970s. Since then, various models have been developed to explain exchange rate behaviour, all contributing in their own way to the understanding of what economic and financial information reveal about the future price of exchange rates. To measure the performance of a variety of exchange rate models, researchers in exchange rate forecasting almost always use the random walk model as benchmark to evaluate the forecasting performance of exchange rate models. An exchange rate model is regarded as superior if it can outperform a random process. The random walk model, a special case of the unit root process, helps us to identify the kinds of disturbances that drive the exchange rate to follow an independent successive process. If the exchange rate follows a random walk process, it has no mean reversion tendency and a directional shock in the exchange rate will cause it to deviate from its long-run equilibrium. Conversely, if the exchange rate does not follow a random walk, it has mean reverting tendencies, and will follow a stationary process which allows us to accurately forecast the exchange rate based on historic observations (Lam, Wong and Wong, 2005:1). However, it seems unrealistic that exchange rates will follow either a random walk process or a stationary process. If we assume that the exchange rate follows a random walk, we also assume that the order flow information from exchange rate trades follows a random walk, and by implication that macroeconomic exchange rate information follows a random walk [see Lyons (2001) for the link between order flow and macroeconomic fundamentals]. It seems unrealistic that exchange rates will follow an identifiable mean reverting (stationary) process, as daily exchange rates are exposed to risk, news and speculation which functions independent from long-run exchange rate fundamentals. Ironically, Meese and Rogoff (who laid the foundation for the use of random walk models as benchmark in exchange rate forecasting) emphasize that exchange rates do not follow an exact random walk (Meese and Rogoff, 1983:14). However, if it is known that exchange rates do not follow a random process explicitly, alternative exchange rate benchmark models should be considered. Yet, judging by the universal...

M.Comm. / The object of this study is to critically appraise the fundamental models, technical methods and statistical techniques that constitute the bulk of exchange rate forecasting methodology. Specifically, can any single approach, or combination of techniques, predict or explain the volatile currency movements characterising exchange rate behaviour in the modern international currency market? International currency markets are indeed complex in nature, and the layperson may be excused for not grasping the distinction between the fundamental, technical and statistical techniques described in the hypothesis. It is vital, however, for the comprehension of this study that the distinction between these approaches be explained, and the logic underlying their individual methodologies examined. It may prima facie seem that this study is based on a contradiction. Surely if one wants to predict an economic variable of any kind, one should refer to the economic theory upon which it is based as the starting point of an analysis. Consequently, if the objective is to forecast the future value of a currency, surely there are a great many economic texts that deal with this very question in voluminous detail. Why, then, should yet another paper be written when so much literature already exists? The answer lies not so much in the scope as in the purpose of this work. The aim of this study can be paraphrased. as follows: to provide a comprehensive and critical examination of the various methods of exchange rate forecasting and to explain why economic theory is still deficient in this important area. The question of whether or not short-term' exchange rates are able to be forecast at all will also be critically examined. This study will attempt to elucidate that while fundamental currency speculation models do provide a certain degree of guidance to currency-traders in their daily prognostications, these models are, in the context of modern capital markets, inadequate. At best, these models will be shown as trackers of long-term exchange rate trends, and not always accurate ones at that. Further, it will be demonstrated that the modern trading floors are characterised (if not defined) by split-second price changes, where the long-term'' can mean a minute, and he who hesitates is lost. It is in this setting that traders must do battle for profit, and where the fundamental models that seem to serve so well in textbooks are anachronisms. The study then shifts its focus to a subset of technical analysis known as charting, the objective being to fill the void which arises due to the fundamental models' inadequacies in the short-term. The charting techniques utilised in this study deviate from their fundamental counterparts in that they attempt to explain future exchangerate trends in terms of past performance. That is, exogenous changes are factored out of the forecasting equation, to give way to a methodology based on trendextrapolation. The performance of these models, especially as they pertain to the medium- and short-term., will then be determined. Finally, in an attempt to supplement the use of charts as a forecasting tool, statistical analysis will be considered. The model utilised in this section will be a rudimentary auto-regressive process. Its simplicity, however, belies its consequence. That is, considering that no ubiquitous statistical model dominates exchange rate theory, it is reasonable to assume that an auto-regressive process, such as the one contributed by this study, will not be subordinate to other, more complex, quantitative offerings. Thus this study attempts to provide the necessary insights in order to perspicaciously 1 It should be noted here that the terms "short-term" and "short run" are interchangeable. For the purposes of consistency, only the former term shall be employed throughout this study. 2 The terms "long-term" and "long run" are also interchangeable. For the purposes of consistency, only the former term shall be employed throughout this study. ascertain the proficiency of statistical analysis as an accurate forecaster of exchange rate fluctuations. All of the models and methods examined in this study adopt a pragmatic acid-test. That is to say, if the predictions made as a result of adherence to the models do not comply accurately and consistently with real findings, then the models themselves should be revised. This revision can be in terms of the time-frame to which the model pertains, the application of the model, or the model itself. It must, however, be stressed that a model whose very raison d'etre lies in its ability to predict exchange rate movements must be able to do so without qualifications or exceptions. The methodology adopted in analysing the models themselves is therefore positive as opposed to normative. Thus, even in the "organised chaos" of the modern exchange rate markets, the application of the models should yield satisfactory results. In other words, despite the unprecedented volumes, speed and volatility of the currencies that are traded in the modern arena, the models themselves should still be able to achieve their purpose - to forecast the extent and direction of changes in the par value of a currency. The next logical question is: what is meant by the "organised chaos", and specifically why should this influence the predictive ability of the fundamental, technical and statistical methods of exchange rate forecasting? The answer to this can be introduced as follows. On an almost daily basis, currency traders move an excess of one trillion dollars throughout the world. Adding to the gravity of this somewhat overwhelming statistic is that most of these are intercomputer transactions occurring instantaneously via inter-bank wire-transfers. In fact, the volume of currency traded is so great that if one were to sum the trading of all the Saudi oil, American wheat, European aircraft and Japanese cars, the monetary result would seem pithy in comparison (Millman, 1995:xxi). It is, however, not only the sheer volumes of currencies traded that characterise the international money markets. It is perhaps more importantly the unanticipated and unparalleled volatility of the markets themselves which provides the greatest quandary for those who conform to 'traditional' methods of exchange rate determination. It is all too common, in fact, for currency prices to change on a minute-to-minute or even second-to-second basis. Exchange rates are thus in a constant state of flux. The significant though infrequent changes of past years have been terminally disposed of. The inception of the microcomputer and the floating exchange rate system currently dominating the greater world economy has irrevocably altered what was considered a flawed order. It is this very metamorphosis which will be examined in detail, specifically how fundamental models have assumed a differing purpose to those used by modern speculators, hedgers and arbitrageurs in their specific fields of application. Thus it will be shown how the changing paradigm of the world economy and consequently the currency trading floors themselves necessitate neoteric predictive powers, that is, the power to forecast currency changes not in terms of years, months or even weeks, but rather in terms of days, minutes and seconds. The object of this thesis will therefore be to show that a definite dichotomy has developed between the exchange rate models espoused in economic textbooks and the techniques upon which the de facto day-to-day buying and selling of currencies depend. The efficacy of this study consequently hinges on one decisive question - is there truly a consistent and precise method of forecasting exchange rates?

by Hok-hoi Fung. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1995. / Includes bibliographical references (leaves 58-59). / LIST OF TABLES --- p.ii / LIST OF FIGURES --- p.iii / CHAPTER / Chapter 1. --- INTRODUCTION --- p.1 / Chapter 2. --- LITERATURE REVIEW --- p.3 / Chapter 3. --- METHODOLOGY --- p.6 / Formulation of the TVTP Model --- p.6 / Filtered and Smoothed Probabilities --- p.9 / Maximization of the Expected Log-likelihood --- p.13 / Chapter 4. --- EMPIRICAL RESULTS --- p.15 / The Simple 2-state Markov Switching Model --- p.15 / The TVTP Model --- p.17 / The 3-state Markov Switching Model --- p.26 / Chapter 5. --- OUT - OF- SAMPLE FORECASTING --- p.34 / Chapter 6. --- CONCLUSION --- p.40 / APPENDICES --- p.42 / BIBLIOGRAPHY --- p.58

Assignment (MComm)--Stellenbosch University, 2005. / ENGLISH ABSTRACT: Volatilty was originally seen to be constant and deterministic, but it was later realised that return series are non-stationary. Owing to this non-stationarity nature of returns, there were no reliable ex-post volatility measurements. Subsequently, researchers focussed on ex-ante volatility models. It was only then realised that before good volatility models can be created, reliable ex-post volatility measuremetns need to be defined. In this study we examine non-parametric ex-post volatility measurements in order to obtain approximations of the variances of non-stationary return series. A detailed mathematical derivation and discussion of the already developed volatility measurements, in particular the realised volatility- and DST measurements, are given In theory, the higher the sample frequency of returns is, the more accurate the measurements are. These volatility measurements referred to above, however, all have short-comings in that the realised volatility fails if the sample frequency becomes to high owing to microstructure effects. On the other hand, the DST measurement cannot handle changing instantaneous volatility. In this study we introduce a new volatility measurement, termed microstructure realised volatility, that overcomes these shortcomings. This measurement, as with realised volatility, is based on quadratic variation theory, but the underlying return model is more realistic. / AFRIKAANSE OPSOMMING: Volatiliteit is oorspronklik as konstant en deterministies beskou, dit was eers later dat besef is dat opbrengste nie-stasionêr is. Betroubare volatiliteits metings was nie beskikbaar nie weens die nie-stasionêre aard van opbrengste. Daarom het navorsers gefokus op vooruitskattingvolatiliteits modelle. Dit was eers op hierdie stadium dat navorsers besef het dat die definieering van betroubare volatiliteit metings 'n voorvereiste is vir die skepping van goeie vooruitskattings modelle. Nie-parametriese volatiliteit metings word in hierdie studie ondersoek om sodoende benaderings van die variansies van die nie-stasionêre opbrengste reeks te beraam. 'n Gedetaileerde wiskundige afleiding en bespreking van bestaande volatiliteits metings, spesifiek gerealiseerde volatiliteit en DST- metings, word gegee. In teorie salopbrengste wat meer dikwels waargeneem word tot beter akkuraatheid lei. Bogenoemde volatilitieits metings het egter tekortkominge aangesien gerealiseerde volatiliteit faal wanneer dit te hoog raak, weens mikrostruktuur effekte. Aan die ander kant kan die DST meting nie veranderlike oombliklike volatilitiet hanteer nie. Ons stel in hierdie studie 'n nuwe volatilitieits meting bekend, naamlik mikro-struktuur gerealiseerde volatiliteit, wat nie hierdie tekortkominge het nie. Net soos met gerealiseerde volatiliteit sal hierdie meting gebaseer wees op kwadratiese variasie teorie, maar die onderliggende opbrengste model is meer realisties.