Statistics and Actuarial Science
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Nagraadse Finansiële Risikobestuur

Aansoeke vir 2021 nagraadse studies is nou gesluit.  Sluitingsdatum vir nagraadse studies in 2021 was 31 Oktober 2020. Besoek vir verdere besonderhede omtrent die aansoek-prosedures.

Hier vind u meer inligting oor die volgende programme in Finansiële Risikobestuur:

'n Kort omskrywing en opsomming van die verskillende nagraadse modules word verkry deur op die module te klik of na onder op hierdie bladsy te gaan.

Die R module begin reeds 3 Februarie 2021. Verpligtende module vir all honneurs studente in die Departement.

Honneursprogram in Finansiële Risikobestuur

54690 – 778 (120) HonsBCom in Finansiële Risikobestuur 

Sien die Jaarboek hier vir 'n volledige omskrywing van die program.

Modules wat aangebied word in hierdie program:

Module Kode Semester (2021) Krediete Verpligte Modules
Finansiële Risikobestuur A​10459-731​1​12​****
​Finansiële Risikobestuur B​10460-761​2​12​****
Stogatiese Simulasie​65250-718​1​12​****

Praktiese Finansiële Modellering & Introduction to R

Portefeuljebestuurteorie A​10660-733​1​12​****
Portefeuljebestuurteorie B​10661-763​2​12​****
Finansiële Wiskundige Statistiek​11164-7322​12​****
​Navorsingswerkstuk: Finansiële Risikobestuur11218-793​1 & 2​30​****


Magisterprogramme in Finansiële Riskobestuur

54690 – 879 (180) MCom (Finansiële Risikobestuur) – tesis opsie  

54690 – 889 (180) MCom (Finansiële Risikobestuur) – werkstuk opsie

Sien die Jaarboek hier vir 'n volledige omskrywing van die programme. Modules wat aangebied word in hierdie programme:

Module Kode Semester (2021) Krediete Verpligte Module
​Esktreemwaardeteorie A​10441-813​1​15​****
Ekstreemwaardeteorie B​10442-843​2​15****​
Gevorderde Finansiële Risikobestuur A​10501-831​1​15​****
Gevorderde Finansiële Risikobestuur B*​10503-861​2​15​****
Gevorderde Finansiële Risiko Programmatuur​10504-835​1​15​****
Gevorderde Portefeuljebestuurteorie A​10517-833​2​15​****
Gevorderde Portefeuljebestuurteorie B (VaR)​10518-863​1​15​****
Krediet Afgeleide Instrumente A​10575-834​2​15​****
Krediet Afgeleide Instrumente B​10576-864​NVT​15
​Tesis: Finansiële Risikobestuur​11237-891 ​1 & 2​90saam met 879
​Navorsingswerkstuk: Finansiële Risikobestuur​11218-893​1 & 2​60​saam met 889

  NVT - Hierdie module word nie aangebied in 2021 nie.

* Statistiese Leerteorie (Honneursmodule) - sien inhoud by Honneurs Wiskundige Statistiek


Module Inhoud - Honneurs

Financial Risk Management A & B (10459-731 & 10460-761)


Objectives and content (FRM-A): The following topics are covered: Different models to estimate volatility, covariances and correlations of financial time series. Value-at-Risk (vaR): Definitions, foundations of VaR measurement, Decomposition of VaR, Parametric Linear VaR Models (normal- and t- distributions). Martingales and Measures: Market price of risk, Equivalent martingale measure result, Change of numeriare and applications. Interest Rate Derivatives, the Standard Market Model: Bond Options, Interest Rate Caps and Floors, European Swap options. Convexity-, timing- and quanto adjustments.

Objectives and content (FRM-B): The following topics are covered: Interest Rate Derivatives - Models of the Short Rate: Equilibrium models, No Arbitrage models, Options on bonds, Volatility structures, Interest rate tree-building models. The Heath, Jarrow and Morton model. The Libor Market Model. Rachet-, Sticky-  and Flexi caps and European Swap options. Credit risk - Different models to estimate default probabilities: Historical default probabilities, Using Bond prices, Using equity prices, Gaussian copula models, Binomial models, Merton’s model, KMV Approach. Credit VaR. Credit default swaps.

Portfolio Management Theory A & B (10660-733 & 10661-763)

Objectives and content (PMT-A): This module has been compiled in such a manner that it provides to the student an overview of the nature and scope of Portfolio Management as a subject and its application in practice. Its contents is loosely based on that of the first halve of the CFA level III exam, and the major topics include:  the portfolio management process, the investment policy statement, portfolio management for individual and institutional investors, capital market expectations, asset allocation, financial statement analysis, equity analysis, and equity portfolio management.

Objectives and content (PMT-B): This module has been compiled in such a manner that it provides to the student an overview of the nature and scope of Portfolio Management as a subject and its application in practice. Its contents is loosely based on that of the second halve of the CFA level III exam, and the major topics include:  fixed income portfolio management, alternative investments portfolio management, portfolio risk management, execution of portfolio decisions, monitoring and rebalancing, evaluating portfolio performance, and behavioural finance.

Financial Mathematical Statistics (11164-732)

Objectives and Content: In this module an introduction is given to Extreme Value Theory (EVT) and its role in Financial Risk Management. EVT entails the study of extreme events and for this theory has been developed to describe the behaviour in the tails of distributions. The module will disduss the theory in a conceptual fashion without proving the results. It will be shown how this theory can be used to carry out inferences on the relevant parameters of the underlying distribution. Both the classical approach of block maxima based on the Fisher-Tippett Theorem and the more modern threshold approach based on the Pickands-Balkema-de Haan Theorem will be discussed and applied. Results for both independent and dependent data will be covered.


Practical Financial Modelling & Introduction to R (11166-734)

Objectives and content: The main aim of this module is to teach students how to apply Excel and VBA to solve financial risk problems as well as to teach them some R programming. The following topics are covered with respect to Excel and VBS: An introduction to Excel an VBA; Excel basics and necessities; Using Excel to value bonds and swaps and to determine yield curves; Dates, tables and some Statistical applications in Excel; Applying Excel’s Solver; Some VBA programming; Portfolio optimisation with Excel and VBA; Black Scholes pricing of European options and calculating Greeks with Excel and VBA; Delta hedging with Excel and VBA. The R component of the module is an introduction to programming and data analysis within the R open source environment.

Time series analysis (10751-747)

Objectives and content: This module is a continuation of undergraduate time series analyses and concentrates on more advanced forecasting techniques. Topics that are covered include: 

  • The Box & Jenkins methodology of tentative model identification, conditional and unconditional parameter estimation and diagnostic methods for checking the fit of the series.
  • ARIMA and Seasonal ARIMA-processes.
  • Introduction to Fourier Analysis, spectrum of a periodic time series, estimation of the spectrum, periodogram analysis, smoothing of the spectrum.
  • Case studies using STATISTICA, R and SAS.
  • Forecasting with ARMA models and prediction intervals for forecasts.
  • Transfer function models and intervention analysis.
  • Multiple regression with ARMA errors, cointegration of non-stationary time series.
  • Conditional heteroscedastic time series models, ARCH and GARCH.

Stochastic simulation (65250-718)

Objectives and content: The module probability models and stochastic simulation is devoted to a study of the theory and applications of important probability models and stochastic processes.  Applications are studied analytically, by means of the techniques of mathematical statistics, and are also illustrated by means of stochastic computer simulation. The broad aim of the module is to make students aware of the following important concepts:

  • the way in which probability models and stochastic processes can be used to model phenomena containing a random or stochastic component;
  • the important role played by assumptions in identification of an appropriate model for a given practical situation;
  • the standard techniques of mathematical statistics that can be used in the analysis of probability models;
  • the wide applicability of stochastic simulation in the analysis of probability models.

The specific outcomes of the module are related to the specific topics that receive attention. These topics include the following: Methods for generating random variables from distributions; Monte Carlo integration; Markov chains (including applications to Metropolis-Hastings and Gibbs sampler methods); Homogeneous and non-homogeneous Poisson processes; Markov processes; variance reduction techniques in stochastic simulation.

Module Inhoud - Magister

Extreme Value Theory A & B (10441-813 & 10442-843)

Objectives and content: Extreme value Theory (EVT) entails the study of extreme events, i.e. unusual events rather than usual events as in more traditional statistics. In order to do this, theory has been developed that describes behavior in the tails of distributions. These results are analogous to the results of central limit theory and in a similar way transforms problems of unknown underlying distributions to parametric problems where only parameters are unknown. Techniques have been developed to carry out inference on these parameters and to apply them to data sets where understanding behavior in the tails of distributions, is important. In these modules the mathematical and practical aspects of the theory and inference techniques will be studied.

Advance Financial Risk Management A & B(Matlab) (10501-831 & 10503-861)

Objectives and content (Adv FRM-A): The aim of this model is to give the Financial Risk Management Masters students some introductory background to Statistical Learning theory. Statistical learning is a relatively new area in statistics. It is concerned with modeling and understanding patterns in complex datasets. With to the explosion of "Big Data", there is currently a high demand for individuals with expertise in statistical learning. The methods studied in this module include regularised regression by means of ridge regression and the lasso; classification using linear discriminant analysis, logistic regression, quadratic discriminant analysis and k-nearest neighbors; resampling methods such as k-fold cross-validation, leave-one-out cross-validation and the bootstrap; linear model selection and dimension reduction methods; handling non-linearity via regression splines, smoothing splines, local regression, generalised additive models, bagging, random forests and boosting; and non-linear classification and regression by means of support vector machines. The objectives of the module are to equip students with the following knowledge and skills:

  • the theory underlying the above statistical learning techniques;
  • application of statistical learning methods in a programming environment;
  • assessment and comparison of various models;
  • interpretation and effective (written and verbal) communication of results.

We extensively make use of the R programming language, therefore note that the R course is a prerequisite.

Objectives and content (Adv FRM-B{Matlab}): The aim of the model is to teach students how to apply MATLAB in advance Financial Risk modelling. The module consists of a series of lectures, demonstrations, and assignments covering the key ideas and applications in finance and risk management of quantitative modelling. It covers a variety of practical quantitative models and building blocks that will allow you to create your own models using MATLAB. The topics covered include the fundamentals of Monte Carlo and Quasi Monte Carlo simulation techniques, Financial Instrument Pricing models, Interest Rate models, Value at Risk and Principal Components Analysis.

Advance Financial Risk Programming (10504-835)

Objectives and content: This module has been compiled in such a manner that it provides to the student an overview of credit risk from a scoring, accounting impairments and regulatory impairments perspective and the using of SAS in this respect. The major topics that will be covered in this module are as follows:  Introduction to Credit Risk Analytics, Introduction to SAS Software, Exploratory Data Analysis, Data Preprocessing for Credit Risk Modelling, Credit Scoring, IFRS 9 in a nutshell, Probability of Default, Loss Given Default, Basel in a nutshel.

Advance Portfolio Management Theory A & B(VaR) (10517-833 & 10518-863)

Objectives and content (Adv PMT-A): The overriding aim of this module is to provide students with a background to the risks in the asset management. Students will be encouraged to evaluate the relevance of information that is controversial, ambiguous and requires (ethical) discretion in their decision making. The intention is to keep the course substantially less quantitative in its content than the other course offered in the Department. The following topics are covered: Fiduciary preferences/utility function, Habits of Prudence, Benchmarks (Arnott), Generalised Law of Active Management, Investment philosophy (Minahan), Holdings data analysis, Manager’s incentives, Liquidity risk: Forecasting crisis & Risk Management lessons, Strategy for gated assets in Hedge Funds, Liquidity risk & horizon uncertainty, Volatility/Risk management, Commodities and portfolio construction, Currency market operations, Transition management, Portfolio optimization with Black-Litterman.

Objectives and content (Adv PMT-B {VaR}): In this module the underlying theory regarding Value-at-Risk (VaR) is studied and practically applied. The following topics are covered: Value at Risk (VaR) and Other Risk Metrics, Parametric Linear VaR Models, Historical simulation, Monte Carlo VaR, VaR for Option Portfolios, Risk model risk, Scenario analysis and stress testing, Capital allocation.

Credit Derivative Instruments A (10575-834)

Objectives and content: This module has been compiled in such a manner that it provides to the student an overview of the nature and scope of credit related fair valuation adjustments, or in general, xVA. The major topics that will be covered in this module are as follows: Introduction, Global financial crisis, and the general OTC derivatives market, counterparty risk, netting, close-out and related aspects, collateral, credit exposure and funding, capital requirements and regulation, counterparty risk intermediation, quantifying credit exposure, exposure and the impact of collateral, default probabilities, credit spreads and funding costs, discounting and collateral, credit and debit value adjustments, and funding value adjustments.