On the modeling of asset returns and calibration of European option pricing models

- Robbertse, Johannes Lodewickes

**Authors:**Robbertse, Johannes Lodewickes**Date:**2008-07-07T09:11:28Z**Subjects:**Options (Finance) , Distribution (Probability theory) , Gaussian distribution , Levy processes , Parameter estimation , Goodness-of-fit tests , Prices , Mathematical models**Type:**Thesis**Identifier:**uj:10194 , http://hdl.handle.net/10210/756**Description:**Prof. F. Lombard**Full Text:**

**Authors:**Robbertse, Johannes Lodewickes**Date:**2008-07-07T09:11:28Z**Subjects:**Options (Finance) , Distribution (Probability theory) , Gaussian distribution , Levy processes , Parameter estimation , Goodness-of-fit tests , Prices , Mathematical models**Type:**Thesis**Identifier:**uj:10194 , http://hdl.handle.net/10210/756**Description:**Prof. F. Lombard**Full Text:**

On the modelling of ultra high frequency financial data on the Johannesburg Stock Exchange

- Van Rooy, Herculaas Frederik

**Authors:**Van Rooy, Herculaas Frederik**Date:**2008-07-07T09:27:52Z**Subjects:**Finance , Time and economic reactions , Johannesburg Stock Exchange , Mathematical models**Type:**Thesis**Identifier:**uj:10238 , http://hdl.handle.net/10210/760**Description:**This thesis considers the modelling of ultra high frequency (UHF) nancial data from South African markets. The approach to be taken is that such irregularly spaced data can be viewed as a realization of a marked point process. We propose a statistical model that incorporates both the unequally spaced transaction times (the points) as well as the movements of the associated returns (the marks). In all data sets investigated, no change in the value of the mark accounts for more that half the observations. If no change is considered as the censoring of some underlying process, we can explicitly model both the censoring of marks and the underlying process by utilizing methods for Markov chains and missing values. All models considered hitherto in the literature assume homogeneity of structure within a UHF data set. Data analyses indicate strongly that such an assumption is not justi ed. The proposed model aims to exploit this observation. The diurnal (time of day) e¤ect is a form of non-stationarity commonly found in UHF data sets. We show that the method currently considered standard practice is inadequate and we will propose modi cations of it. Consideration is given to the classi cation of heterogeneous subsets that arises naturally in UHF data, for instance daily subsets of a UHF data set. We nd evidence in support of some market microstructure theories, but no theory is supported by all data sets considered. We pay attention to technical issues surrounding the application of certain tests to large samples. As large samples are common in UHF data sets methods that are sensitive to large sample size, for example the Ljung-Box test, are not suitable. , Professor Freek Lombard**Full Text:**

**Authors:**Van Rooy, Herculaas Frederik**Date:**2008-07-07T09:27:52Z**Subjects:**Finance , Time and economic reactions , Johannesburg Stock Exchange , Mathematical models**Type:**Thesis**Identifier:**uj:10238 , http://hdl.handle.net/10210/760**Description:**This thesis considers the modelling of ultra high frequency (UHF) nancial data from South African markets. The approach to be taken is that such irregularly spaced data can be viewed as a realization of a marked point process. We propose a statistical model that incorporates both the unequally spaced transaction times (the points) as well as the movements of the associated returns (the marks). In all data sets investigated, no change in the value of the mark accounts for more that half the observations. If no change is considered as the censoring of some underlying process, we can explicitly model both the censoring of marks and the underlying process by utilizing methods for Markov chains and missing values. All models considered hitherto in the literature assume homogeneity of structure within a UHF data set. Data analyses indicate strongly that such an assumption is not justi ed. The proposed model aims to exploit this observation. The diurnal (time of day) e¤ect is a form of non-stationarity commonly found in UHF data sets. We show that the method currently considered standard practice is inadequate and we will propose modi cations of it. Consideration is given to the classi cation of heterogeneous subsets that arises naturally in UHF data, for instance daily subsets of a UHF data set. We nd evidence in support of some market microstructure theories, but no theory is supported by all data sets considered. We pay attention to technical issues surrounding the application of certain tests to large samples. As large samples are common in UHF data sets methods that are sensitive to large sample size, for example the Ljung-Box test, are not suitable. , Professor Freek Lombard**Full Text:**

The influence of an educational intervention involving mathematical modelling on the visualisation of engineering students

**Authors:**Kotze, Johanna Hendrina**Date:**2018**Subjects:**Mathematical models , Engineering - Mathematical models**Language:**English**Type:**Doctoral (Thesis)**Identifier:**http://hdl.handle.net/10210/286326 , uj:30980**Description:**Ph.D. (Mathematics Education) , Abstract: Many engineering subjects rely on the interpretation of symbolic, numeric and graphic representations. Engineering students have difficulties with the interpretation of representations generated with a computer algebra system (CAS). For professional engineers, the interpretation of multiple representations is a daily activity and inherent to problem solving. The ability to reason visually and to fluently interpret multiple representations is a cognitive process referred to as visualisation. The use of CAS such as Mathematica has stimulated new mathematical tools desirable for work-place engineers; these include programming, mathematical modelling and visualisation. Step-by-step processes that are automated by CAS create a pragmatic-epistemic gap, an underlying principle of visualisation not yet sufficiently researched in mathematics education. This study assesses the influence of mathematical modelling on the visualisation of engineering diploma students at the University of Johannesburg (UJ), South Africa (SA). The aim is to contribute to research on visualisation within the vocational field, both nationally and internationally. The research is driven by the question: What is the influence of an educational intervention involving mathematical modelling on the visualisation of engineering students? An explanatory sequential mixed methods design was used in three phases. In the first phase, a preliminary pilot study involved two mathematical modelling tasks and an open-ended questionnaire. For the second phase, a pilot study involved a quasi-experiment with a pre-test, mathematical modelling intervention – using the same modelling tasks as in phase one – and a post-test. The quasi-experiment was augmented by two semi-structured reflective group interviews. Phase two was repeated in its entirety for the main study, which was phase three. In each phase, the sample was a different cohort of engineering diploma students in their second year of study at UJ. Quantitative data were analysed with descriptive and inferential statistics, using the Statistical Package for the Social Sciences (SPSS). All qualitative data were analysed with content analysis. Four visualisation dimensions were identified namely translation, visual reasoning, new insights and intuition. While both the experimental and control group could smoothly translate from one representation to another, the experimental group benefited mostly...**Full Text:**

**Authors:**Kotze, Johanna Hendrina**Date:**2018**Subjects:**Mathematical models , Engineering - Mathematical models**Language:**English**Type:**Doctoral (Thesis)**Identifier:**http://hdl.handle.net/10210/286326 , uj:30980**Description:**Ph.D. (Mathematics Education) , Abstract: Many engineering subjects rely on the interpretation of symbolic, numeric and graphic representations. Engineering students have difficulties with the interpretation of representations generated with a computer algebra system (CAS). For professional engineers, the interpretation of multiple representations is a daily activity and inherent to problem solving. The ability to reason visually and to fluently interpret multiple representations is a cognitive process referred to as visualisation. The use of CAS such as Mathematica has stimulated new mathematical tools desirable for work-place engineers; these include programming, mathematical modelling and visualisation. Step-by-step processes that are automated by CAS create a pragmatic-epistemic gap, an underlying principle of visualisation not yet sufficiently researched in mathematics education. This study assesses the influence of mathematical modelling on the visualisation of engineering diploma students at the University of Johannesburg (UJ), South Africa (SA). The aim is to contribute to research on visualisation within the vocational field, both nationally and internationally. The research is driven by the question: What is the influence of an educational intervention involving mathematical modelling on the visualisation of engineering students? An explanatory sequential mixed methods design was used in three phases. In the first phase, a preliminary pilot study involved two mathematical modelling tasks and an open-ended questionnaire. For the second phase, a pilot study involved a quasi-experiment with a pre-test, mathematical modelling intervention – using the same modelling tasks as in phase one – and a post-test. The quasi-experiment was augmented by two semi-structured reflective group interviews. Phase two was repeated in its entirety for the main study, which was phase three. In each phase, the sample was a different cohort of engineering diploma students in their second year of study at UJ. Quantitative data were analysed with descriptive and inferential statistics, using the Statistical Package for the Social Sciences (SPSS). All qualitative data were analysed with content analysis. Four visualisation dimensions were identified namely translation, visual reasoning, new insights and intuition. While both the experimental and control group could smoothly translate from one representation to another, the experimental group benefited mostly...**Full Text:**

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