published_or_final_version / Economics and Finance / Master / Master of Philosophy

This dissertation is in the form of three essays on the topic of component and long memory GARCH models. The unifying feature of the thesis is the focus on investigating European index option evaluation using these models. / The first essay presents a new model for the valuation of European options. In this model, the volatility of returns consists of two components. One of these components is a long-run component that can be modeled as fully persistent. The other component is short-run and has zero mean. The model can be viewed as an affine version of Engle and Lee (1999), allowing for easy valuation of European options. The model substantially outperforms a benchmark single-component volatility model that is well established in the literature. It also fits options better than a model that combines conditional heteroskedasticity and Poisson normal jumps. While the improvement in the component model's performance is partly due to its improved ability to capture the structure of the smirk and the path of spot volatility, its most distinctive feature is its ability to model the term structure. This feature enables the component model to jointly model long-maturity and short-maturity options. / The second essay derives two new GARCH variance component models with non-normal innovations. One of these models has an affine structure and leads to a closed-form option valuation formula. The other model has a non-affine structure and hence, option valuation is carried out using Monte Carlo simulation. We provide an empirical comparison of these two new component models and the respective special cases with normal innovations. We also compare the four component models against GARCH(1,1) models which they nest. All eight models are estimated using MLE on S&P500 returns. The likelihood criterion strongly favors the component models as well as non-normal innovations. The properties of the non-affine models differ significantly from those of the affine models. Evaluating the performance of component variance specifications for option valuation using parameter estimates from returns data also provides strong support for component models. However, support for non-normal innovations and non-affine structure is less convincing for option valuation. / The third essay aims to investigate the impact of long memory in volatility on European option valuation. We mainly compare two groups of GARCH models that allow for long memory in volatility. They are the component Heston-Nandi GARCH model developed in the first essay, in which the volatility of returns consists of a long-run and a short-run component, and a fractionally integrated Heston-Nandi GARCH (FIHNGARCH) model based on Bollerslev and Mikkelsen (1999). We investigate the performance of the models using S&P500 index returns and cross-sections of European options data. The component GARCH model slightly outperforms the FIGARCH in fitting return data but significantly dominates the FIHNGARCH in capturing option prices. The findings are mainly due to the shorter memory of the FIHNGARCH model, which may be attributed to an artificially prolonged leverage effect that results from fractional integration and the limitations of the affine structure.

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Stocks and similar securities are normally traded in prices which are integral multiples of one-eiqhth of a dollar (a few are traded in one-sixteenths of a dollar). This price constraint may introduce a bias in the estimates of beta for low-priced securities, and the purpose of this dissertation is to examine the bias introduced from this source. The research methodology briefly consists of constructing a price series for a hypothetical stock by computing"true" prices from an assumed"true" beta and alpha, the series of returns generated from a market index, and a random disturbance term. The constructed price series is rounded to the nearest one-eighth of a dollar and an"observed" beta for this rounded price series is calculated. The"observed” beta is compared to the"true" beta to observe the degree of bias. Replications are made which differ in their randomly chosen starting point in the market index series; and the experiment is repeated for various"true" betas and alphas within the range of interest, for different intervals between price observations, and for different initial prices. Chapter I provides an introduction to the study. In Chapter II the relevant literature for this study is reviewed. The first part includes previous studies of the one-eighth effect and the intervalling effect, while the second part of the chapter focuses on the composition and characteristics of common market indexes. The analytical considerations are discussed in Chapter III. The price generating mechanism and the constraint placed upon it by one eighth price rounding are explicitly stated. Alternative rounding procedures are presented and their implications discussed. In the next section the characteristics of the rounding functions are discussed. Finally, expressions for the amount of bias in beta estimates introduced by the one eighth price rounding are derived for both logarithmic returns and holding period (arithmetic) returns. In Chapter IV the methodology used to secure the results presented in Chapter V is reviewed. The simulation itself is discussed as well as the statistical and ad hoc procedures used to evaluate the results. The results presented in the next chapter also include the results pertinent to two ancillary issues discussed in Chapter IV, namely, how many replications are needed and how reproducible are the results. Chapter VI summarizes the findings, draws a conclusion, and suggests extensions of the study. / Ph. D.

published_or_final_version / Business Administration / Master / Master of Business Administration

published_or_final_version / Business Administration / Master / Master of Business Administration

published_or_final_version / Management Studies / Master / Master of Business Administration

published_or_final_version / Statistics / Master / Master of Philosophy

A research report submitted to the School of Economic and Business Sciences, Faculty of Commerce, Law and Management, University of the Witwatersrand, in partial fulfilment (50%) of the requirements for degree of Master of Commerce in Finance. Date of submission: April 2016 / International studies have widely documented the long-run underperformance of firms conducting secondary equity offerings (SEOs), a phenomenon commonly referred to as the ‘new issues puzzle’. Understanding the market’s reaction to SEOs is vital for managers who are commonly tasked with deciding on how to finance their firm’s operations. This study investigates the short-run and long-run performance of firms conducting SEOs on the Johannesburg Stock Exchange (JSE) over the period of 1998 to 2015, by exploring both rational and behavioural models in predicting SEO behaviour. Event-study analysis reveals that the market generally reacts negatively to the announcement of SEOs with a statistically significant average two-day cumulative abnormal return of -2.6%. Using a buy-and-hold abnormal return approach, as well as factor regression analysis to study the long-run share performance of issuing firms, there is no evidence that issuing firms significantly underperform relative to non-issuing firms over a five-year period when testing for abnormal share return performance with the Capital Asset Pricing Model. Furthermore, issuing firms exhibit no consistent signs of operating underperformance in comparison to non-issuing firms over a fiveyear period. Finally, in evidence contradicting the market timing theory, investor sentiment appears to bear no consistently significant influence on either a firm’s decision to issue equity, or on the short-run and long-run performance of SEOs. Overall, the results imply that the longrun performance of SEOs conducted in South Africa is best described by rational explanations centred on the risk-return framework. There is no consistent evidence of any ‘new issues puzzle’ on the JSE. / MT2017

A research report submitted in partial fulfilment of the requirements for the degree M.Com. Masters (Finance) in the School of Economic and Business Sciences at the University of the Witwatersrand, Johannesburg / This study empirically investigates the existence of the Samuelson Hypothesis in South African markets. The Samuelson Hypothesis states that the volatility of futures contracts increase as the expiration of the contracts approaches. It is an important phenomenon to account for when setting margins, creating hedging strategies and valuing options on futures. The study utilizes daily closing prices of agricultural and non-agricultural futures contracts for a period varying from 2002 to 2015. In total, eleven contracts were examined over this period, yet only one (White Maize) consistently shows support for the Samuelson Hypothesis. The Negative Covariance and State Variable Hypothesis were tested, but could not provide an alternative explanation for the lack of relationship between the time to maturity and volatility of futures contracts. / MT2017