Applications for 2022 post-graduate studies is now open. Closing date for post-graduate studies in 2022 is 31 October 2021. Please visit www.sun.ac.za for details on the application process.
Here you can find information on the following postgraduate programmes in Financial Risk Management:
Please
note that all our postgraduate programmes are selection programmes.
Apart from adhering to the minimum requirements per programme (Honours
and/or Masters), selection is further done on excellent academic merit
and only a limited number of students may be admitted to any such
programme. Adhering to only the minimum requirements does not guarantee
automatic admission.
A short description and summary of the department's postgraduate modules can be found by clicking on the module or to scroll to the bottom of the page.
The R-module starts two weeks before the official lectures start in 2022. Compulsory module to all honours students in the Department.
Special registration for honours and masters modules
Students
who wish to register for any of these post graduate modules as part of a degree
offered outside the Department of Statistics and Actuarial Science, need to
formally apply to the department for the module(s) by:
· Send personal /
contact details;
· the module(s) you wish to apply for, as well as the degree you will be registered for, to hrandall@sun.ac.za;
· Attach a complete
study record to your e-mail;
· Make sure of the
prerequisites of the modules you wish to apply for at http://www.sun.ac.za/english/faculty/economy/statistics/programmes/mathematical-statistics/math-stats-postgraduate
or http://www.sun.ac.za/english/faculty/economy/statistics/programmes/statistics/stats-postgraduate,
specifically regarding the R block module which takes place roughly two weeks
before normal lecturing starts.
· Closing date for
applications is 31 January each year (and 20 January for 13074-723 Introduction
to R).
Honours Programme in Financial Risk Management
54690 – 778 (120) BComHons in Financial Risk Management
See the Faculty Calendar
here for a detail description of this program. Modules presented in this program:
Masters Programme in Financial Risk Management
54690 – 879 (180) MCom (Financial Risk Management) – thesis option
54690 – 889 (180) MCom (Financial Risk Management) – assignment option
See the Faculty Calendar
here for a detail description of this program. Modules presented in these programmes:
NA - This module is not presented in 2021.
* Statistical Learning Theory (Honours module) - see content at Honours Mathematical Statistics
Module Content - Honours
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.
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 Content - Masters
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 Management 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.
