University of Mines and Technology(UMaT), Tarkwa. Ghana

20.5    Programme Structure

20.5.1 Masters Programme in Financial Engineering

a)    Core and Compulsory Modules

The MSc. coursework comprises four (4) core/compulsory modules namely:

•    Research Methods (MA 501)

•    Computer Programming (MA 507)

•    Financial Engineering (MA 503)

•    Operations Research (MA 505)

In addition, a minimum of three other modules must be selected by the candidate in consultation with his/her Supervisor(s). Applicants without adequate Mathematics or Statistics background will be required to register for the module in Optimisation Techniques and Computer Applications.

b)    Content of Modules

First Semester

Second Semester

FIRST SEMESTER

MA 275 Numerical Methods
Credits: 0

Sources and types of error; round-off errors, truncation error, Basic error analysis. Evaluation of functions. Numerical solution of non-linear algebraic equation; one-point methods; simple iteration, secant and Newton-Raphson methods. Acceleration and relaxation. Bracketing methods; Bisection and false-position methods. Numerical solution of sets of linear algebraic equations: elimination back substitution. Matrix inversion. Instabilities and pivoting. Gaussian elimination. Iterative methods for linear systems: Gauss-Jacobi, Gauss-Siedel and successive over relaxation (SOR). Convergence and error analysis. Order of an iterative process. Use of computer essential. Conjugate Gradient.

Methods for first-order differential equations: Taylor’s method, Euler methods, Runge-Kutta methods, multi-step methods. Methods for higher-order differential equations: Taylor’s, Euler and Runge-Kutta methods.

MA 501 Research Methods
Credits: 3

Introduction to research: Research project formulation/management, the research process, literature review and organization. Epistemology and its implications for research methodology and design. Theoretical framework (variable definition and generation of hypothesis). Scientific research design (differences between qualitative and quantitative methodology, measurement issues: reliability and validity). Qualitative data collection (e.g. in-depth interviews, focus groups, observations). Analysis of qualitative data. Principles of quantitative data analysis (descriptive statistics). Quantitative methods ( hypothesis testing, inferential statistics). Sampling, questionnaire design and methods for pre-testing. Research proposal for competitive research grant. Research presentation (formatting dissertation). Case studies.

MA 503    Financial Engineering
Credits: 3

Introduction and orientation to financial engineering (FE); illustrations of basic research models and applications presented in a lecture series by FE faculty and expert speakers from the finance sector. Project undertaken by students under the supervision of a faculty member with a special focus to design a solution procedure for a real-life problem. (A written midterm progress report and a final report required).

MA 505    Operations Research
Credits: 3

Introduction to Deterministic methods for Optimization, with focus on mathematical programming (linear, nonlinear, integer) and network methods. Introduction to probabilistic methods for modelling and analyzing the performance of complex systems. Topics include Markov chains, queuing, forecasting, discrete event simulation and inventory modelling.

MA 507    Computer Programming
Credits: 3

Input and output procedures. Elementary mathematical functions . User defined functions. Relational and logical operators. Conditional statements . Looping and the switch structure.
Solution of Linear and non linear algebraic equations. Application to differential equations. Symbolic processing with MATLAB.

MA 509    Fundamentals of Economics
Credits: 3

Basics of macroeconomics: money, inflation, income, and unemployment; banking and financial markets; exchange rate determination; emerging markets. Basics of microeconomics: demand, supply, and market equilibrium; perfect competition; imperfect competition; cooperative and non-cooperative solutions in game theory with financial applications.

MA 511    Money and Capital Markets
Credits: 3

Introduction to the Ghanaian economy; facts and figures; information on financial institutions; Central Bank; financial assets, their size, types and issues; legal structure; creation of the Central Bank money and Commercial banks money; government budget and its financing problems; flows and stocks of foreign exchange, balance of payments, international reserves and external debt

MA 513    Mathematics of Uncertainty
Credits: 3

Random variables, expectations and variance, Binomial, Poisson and Normal Distributions, Law of Large Numbers. Methods of data analysis, univariate and multi-variate models, estimation, confidence intervals, hypothesis testing problems, analysis of variance, regression and correlation analysis, goodness of fit tests, maximum likelihood estimation. Central Limit Theorem, generating and characteristic functions, moments, conditional probabilities; Markov Chains, random walks and martingales, discrete to continuous stochastic processes, binomial model of stock prices, Arbitrage Pricing Theory, pricing of a European Call Option, Black-Scholes equation.

SECOND SEMESTER

MA 500 Thesis
Credits: 12

The thesis must be an embodiment of independent research work under the guidance of Supervisor(s) on a topic of the student’s area of specialization. A thesis embodying the results of the research will be presented to the Department for assessment. A panel of examiners will assess the thesis.

MA 502    Financial Econometrics
Credits: 3

Introduction to forecasting techniques; univariate and multi-variate time series; volatility dynamics; Box-Jenkins approach and ARIMA models; seasonal ARIMA models; martingales, random walks and non-linearity; stochastic variance models and ARCH processes; practical modelling and forecasting of financial time series; applications of neural networks and genetic algorithms.

MA 504 Optimization Models in Economics and Finance
Credits: 3

Overview of Optimization concepts: modelling-analysis-decision loop in financial and economic practice; linear, non-linear, integer and dynamic programming applications in finance and economics. Discrete Optimization models in finance: modelling possibilities through binary and integer variables; relaxation methods; branch-and-bound methods; simulated annealing and genetic algorithms. Quadratic and convex programming, applications in portfolio management using linear and nonlinear programming software.

MA 506    Computational Finance
Credits: 3

Simulation methodology; software packages; uniform and non-uniform random variate generation; Monte-Carlo methods; variance reduction techniques; splines; matrix factorizations; finite difference methods; value-at-risk and option pricing computations.

MA 508 Investment Analysis and Portfolio Theory
Credits: 3

Money markets and instruments; debt capital markets; term structure models; bond valuation, duration and convexity; bond ratings; tools of bond portfolio management; equity markets and instruments; common stock valuation; mathematics of portfolio selection; mean-variance and index models; models of market equilibrium; market efficiency; performance measurement and attribution; active and passive portfolio management; uses of derivative assets in portfolio management; global investments.

MA 510    Risk Analysis and Management
Credits: 3

Principles of risk theory; ruin models; credibility premiums and experience rating; operations research techniques in insurance and reinsurance decision making. Financial innovation; new types of risk and evolution of risk management products; sources of risk and risk profile; measuring market risk, credit risk, operational and legal risks; analytical models and estimation problems; using and designing derivative instruments to manage risk; securitization, hedging and arbitrage fundamentals; examples and applications of risk management in financial and non-financial institutions. Design and financing of life insurance products and retirement plans in both the private and public sectors; stochastic investment models for life insurance and pension funds; Wilkie's model.

MA 530 Postgraduate Seminar
Credits: 3

Students will be required to make at least two presentations on the progress and research underway in their areas of specialisation. This will be assessed by a Departmental Panel. Postgraduate students are required to attend the seminar(s).