Yearbooks

Programme: BScHons (Financial Engineering)

Code Faculty Department
02240277 Faculty of Natural and Agricultural Sciences Department: Mathematics and Applied Mathematics
Credits Duration NQF level SAQA ID
Minimum duration of study: 1 year Total credits: 135 NQF level:  08 SAQA ID:  83929

Admission requirements

1.    Relevant bachelor’s degree
2.    At least 60% for all mathematics and applied mathematics modules at final-year level
3.    A minimum of 60% each in the following subjects/modules (or equivalent) at second-year level: 

  • Calculus
  • Differential equations
  • Linear algebra 
     

Minimum credits: 135

Core credits:  91
Elective credits: 44

The Postgraduate Coordinator has to approve the final programme composition for this programme.

  1. Students who have included Statistics, Mathematical Statistics or Industrial Engineering in their undergraduate degree programme, will not be allowed to take BAN 780. Additional modules from the list of electives should be included in the programme composition.
  2. Lectures for BAN 780 and ISE 780 are scheduled in “blocks” – consult the relevant departments at the Faculty of Engineering, Built Environment and Information Technology.
  3. WTW 732 and WTW 762 will be presented weekly as well as some extra “block” lectures.

Core modules

  • Module content:

    • Monte Carlo Simulation
    • Continuous Simulation
    • System Dynamics
    • Multi-objective Decision-making
    • Operations Research
    • Decision Analysis
    • Discrete Simulation

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  • Module content:

    Introduction to markets and instruments. Futures and options trading strategies, exotic options, arbitrage relationships, binomial option pricing method, mean variance hedging, volatility and the Greeks, volatility smiles, Black-Scholes PDE and solutions, derivative disasters.

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  • Module content:

    Classical optimisation:  Necessary and sufficient conditions for local minima.  Equality constraints and Lagrange multipliers.  Inequality constraints and the Kuhn-Tucker conditions.  Application of saddle point theorems to the solutions of the dual problem.  One-dimensional search techniques.  Gradient methods for unconstrained optimisation.  Quadratically terminating search algorithms.  The conjugate gradient method.  Fletcher-Reeves.  Second order variable metric methods:  DFP and BFCS.  Boundary following and penalty function methods for constrained problems.   Modern multiplier methods and sequential quadratic programming methods.  Practical design optimisation project.

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  • Module content:

    Exotic options, arbitrage relationships, Black-Scholes PDE and solutions, hedging and the Miller-Modigliani theory, static hedging, numerical methods, interest rate derivatives, BDT model, Vasicek and Hull-White models, complete markets, stochastic differential equations, equivalent Martingale measures.

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  • Module content:

    Consult Department.

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Elective modules

  • Module content:

    A company's ability to remain competitive in modern times hinges increasingly on its ability to perform systems engineering. The technology and complexity of a company's products appears to steadily increase and with it, the risks that need to be managed. This module provides specialised knowledge to apply systems engineering by understanding the tools, processes and management fundamentals.

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  • Module content:

    Projection matrices and sums of squares of linear sets. Estimation and the Gauss-Markov theorem. Generalised t- and F- tests.

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  • Module content:

    The singular normal distribution. Distributions of quadratic forms. The general linear model. Multiple comparisons. Analysis of covariance. Generalised linear models. Analysis of categorical data.

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  • Module content:

    Matrix algebra. Some multivariate measures. Visualising multivariate data.  Multivariate distributions. Samples from multivariate normal populations. The Wishart distribution. Hotelling’s T ² statistic. Inferences about mean vectors.

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  • Module content:

    Discriminant analysis and classification. Principal component analysis. The biplot. Multidimensional scaling. Factor analysis. Probabilistic clustering.

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  • Module content:

    An introduction to Markowitz portfolio theory and the capital asset pricing model. Analysis of the deficiencies in these methods. Sensitivity based risk management. Standard methods for Value-at-Risk calculations. RiskMetrics, delta-normal methods, Monte Carlo simulations, back and stress testing.

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  • Module content:

    A selection of special topics will be presented that reflects the expertise of researchers in the Department. The presentation of a specific topic is contingent on student numbers. Consult the website of the Department of Mathematics and Applied Mathematics for more details.

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  • Module content:

    An analysis as well as an implementation (including computer programs) of methods are covered. Numerical linear algebra: Direct and iterative methods for linear systems and matrix eigenvalue problems: Iterative methods for nonlinear systems of equations. Finite difference method for partial differential equations: Linear elliptic, parabolic, hyperbolic and eigenvalue problems. Introduction to nonlinear problems. Numerical stability, error estimates and convergence are dealt with.

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  • Module content:

    Study of main principles of analysis in the context of their applications to modelling, differential equations and numerical computation. Specific principles to be considered are those related to mathematical biology, continuum mechanics and mathematical physics as presented in the modules WTW 772, WTW 787 and WTW 776, respectively.

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  • Module content:

    An analysis as well as an implementation (including computer programs) of methods is covered. Introduction to the theory of Sobolev spaces. Variational and weak formulation of elliptic, parabolic, hyperbolic and eigenvalue problems. Finite element approximation of problems in variational form, interpolation theory in Sobolev spaces, convergence and error estimates.

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The regulations and rules for the degrees published here are subject to change and may be amended after the publication of this information.

The General Academic Regulations (G Regulations) and General Student Rules apply to all faculties and registered students of the University, as well as all prospective students who have accepted an offer of a place at the University of Pretoria. On registering for a programme, the student bears the responsibility of ensuring that they familiarise themselves with the General Academic Regulations applicable to their registration, as well as the relevant faculty-specific and programme-specific regulations and information as stipulated in the relevant yearbook. Ignorance concerning these regulations will not be accepted as an excuse for any transgression, or basis for an exception to any of the aforementioned regulations.

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