Doctoral Degrees (Statistics and Actuarial Science)

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Browsing Doctoral Degrees (Statistics and Actuarial Science) by browse.metadata.advisor "Conradie, W. J. (Willem Johannes)"

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    Classifying yield spread movements in sparse data through triplots
    (Stellenbosch : Stellenbosch University, 2020-03) Van der Merwe, Carel Johannes; De Wet, Tertius; Inghelbrecht, Koen; Vanmaele, Michele; Conradie, W. J. (Willem Johannes); Stellenbosch University. Faculty of Economic and Management Sciences. Dept. of Statistics and Actuarial Science.
    ENGLISH SUMMARY : In many developing countries, including South Africa, all data that are required to calculate the fair values of financial instruments are not always readily available. Additionally, in some instances, companies who do not have the necessary quantitative skills are reluctant to incorporate the correct fair valuation by failing to employ the appropriate techniques. This problem is most notable with regards to unlisted debt instruments. There are two main inputs with regards to the valuation of unlisted debt instruments, namely the the risk-free curve and the the yield spread. Investigation into these two components forms the basis of this thesis. Firstly, an analysis is carried out to derive approximations of risk-free curves in areas where data is sparse. Thereafter it is investigated whether there is sufficient evidence of a significant change in yield spreads of unlisted debt instruments. In order to determine these changes, however, a new method that allows for simultaneous visualisation and classification of data was developed - termed triplot classification with polybags. This new classification technique also has the ability to limit misclassification rates. In the first paper, a proxy for the extended zero curve, calculated from other observable inputs, is found through a simulation approach by incorporating two new techniques, namely permuted integer multiple linear regression and aggregate standardised model scoring. It was found that a Nelson Siegel fit, with a mixture of one year forward rates as proxies for the long term zero point, and some discarding of initial data points, performs relatively well in the training and testing data sets. This new method allows for the approximation of risk-free curves where no long term points are available, and further allows for the determinants of the yield curve shape by considering other available data. The changes in these shape determining parameters are used in the final paper as determinants for changes in yield spreads. For the second paper, a new classification technique is developed that was used in the final paper. Classification techniques do not easily allow for visual interpretation, nor do they usually allow for the limitation of the false negative and positive error rates. For some areas of research and practical applications these shortcomings are important to address. In this paper, classification techniques are combined with biplots, allowing for simultaneous visual representation and classification of the data, resulting in the so-called triplot. By further incorporating polybags, the ability of limiting misclassification type errors is also introduced. A simulation study as well as an application is provided showing that the method provides similar results compared to existing methods, but with added visualisation benefits. The paper focuses purely on developing a statistical technique that can be applied to any field. The application that is provided, for example, is on a medical data set. In the final paper the technique is applied to changes in yield spreads. The third paper considered changes in yield spreads which were analysed through various covariates to determine whether significant decreases or increases would have been observed for unlisted debt instruments. The methodology does not specifically determine the new spread, but gives evidence on whether the initial implied spread could be left the same, or whether a new spread should be determined. These yield spread movements are classified using various share, interest rate, financial ratio, and economic type covariates in a visually interpretive manner. This also allows for a better understanding of how various factors drive the changes in yield spreads. Finally, as supplement to each paper, a web-based application was built allowing the reader to interact with all the data and properties of the methodologies discussed. The following links can be used to access these three applications: - Paper 1: https://carelvdmerwe.shinyapps.io/ProxyCurve/ - Paper 2: https://carelvdmerwe.shinyapps.io/TriplotSimulation/ - Paper 3: https://carelvdmerwe.shinyapps.io/SpreadsTriplot/