MSc Financial Engineering 
Programme Content Part 1 (Compulsory Modules)


Securities, Futures and Options

Convenor: John Board    Credits: 20

Introduces techniques for analysing and valuing different classes of risky assets. It also develops ways of optimally selecting portfolios of such assets and develops models of how these portfolios may be priced in financial markets. The techniques introduced in this module are widely applied in other elements of the programme.

Outline Content: Financial assets and investing in securities markets; Investors and their objective; Risk and capital allocation; Optimal portfolio selection; Capital asset pricing model; Single index and multifactor models; Arbitrage pricing theory; Derivative securities and the no-arbitrage principle; Forwards and Futures contracts (simple hedging); Options basic properties and trading strategies; Option pricing.

Quantitative Methods for Finance

Convenor: Carol Alexander    Credits: 20

The objective of the module is to give students a thorough grounding in the essential mathematical methods used in finance, including basic principles of calculus, linear algebra, statistics, probability and regression. Students apply these skills to the fundamental problems in finance, such as compounding interest, pricing and hedging options, portfolio volatility, portfolio beta and simulation. The theory is illustrated by numerous examples and Excel spreadsheets.. The very high practical content will make it accessible to all students, even those with little previous training in mathematics.

Outline Content: Foundation; Descriptive Statistic; Calculus; Linear Algebra; Probability Theory in Finance; Regression; Numerical Methods.

Financial Markets

Convenor: Alfonso Dufour    Credits: 20

Provides knowledge of global financial markets, the importance of liquidity, the distinction between exchange versus OTC markets, primary and secondary markets and the role of intermediaries in their various forms. Participants will gain an understanding of: international stock and bond markets, ‘repo’ markets (for borrowing/lending on a secured basis); an introduction to foreign exchange and money markets, and to futures markets (which are developed in more detail in optional Part 2 modules); finally specific markets for commodity and energy are studied in more detail.

Outline content: General introduction to world financial markets; Liquidity, the distinction between exchange versus OTC markets and the role of intermediaries in their various forms; Short-term debt securities issued by government and corporations; Classification of bonds according to issuer: government, agencies, corporate and municipa; Comparison of bond markets in major countries and a description of the main intermediaries and their role; Foreign exchange market – quotation conventions, types of brokers, central banks’ policies; Primary and secondary stock markets; Futures markets; Commodities markets; Energy markets.

Derivatives Pricing

Convenor: Emese Lazar    Credits: 10 

The aim of the module is to convey the basic concepts and analytical methodology for the valuation of derivatives in the standard Black-Scholes framework. By the end of the module, it is expected that the student will be able to: derive the price and the hedging parameters for a variety of equity based derivatives; digest literature on equity based derivatives at the introductory level; work in a support function, such as product structuring, in a derivatives business and use this as a platform for further research.

Stochastic Calculus for Finance

Convenor: Mathematics Dept    Credits: 10

Presents the basics of stochastic calculus for Brownian motion as used in contemporary finance, in an elementary fashion with plenty of practice. By the end of the module, it is expected that the student will be able to work with the principal stochastic differential equations that are used in derivative modelling and other areas of quantitative finance, and understand the theoretical concepts of stochastic integration.

Outline content:Outline of where stochastic calculus is used in finance; Brownian motion; Martingales; Itô Stochastic Integration; Itô Calculus; Stochastic Differential Equations used in finance; Change of probability, change of numeraire, and its use in derivative valuation.

Mathematical and Numerical Methods

Convenor: Emese Lazar and Dept. Mathematics    Credits: 10

This module introduces students to the mathematical tools needed for derivatives pricing. Namely, it covers special topics in calculus for finance, optimization and the numerical implementation of the models covered in “Derivatives Pricing”. It also presents the latest methodologies in calibration and interpolation. The module puts emphasis on presenting the methodologies and the possible applications will also be covered, using computer programmes.

Outline content: ODE’s, PDE’s and their application in finance (including the heat equation); Transform methods (Laplace, Fourier); Optimization, Calibration and Interpolation; Binomial and trinomial trees, using backward recursion and forward induction; Finite difference methods for solving parabolic partial differential equations for derivative prices; Random number generation; Simulation methods; variance reduction methods; Simulation of stochastic differential equations.

Probability for Financial Engineering

Convenor: Tobias Kuna    Credits: 10

This module introduces students into the mathematical tools of probability underlying the understanding of probabilistic approaches to finance and necessary for understanding stochastic analysis. Namely, it covers basic concepts and methods of modern probability placing emphasis on presenting the methodologies and the possible applications in finance. 

Outline Content: Concept of Probability; Standard Distributions; Random Variables, their Distributions and their Characteristics; Joint Distribution; Independence; Conditional Probability and Expectation; Expectation, Variance, Covariance, and Correlation; Law of Large Numbers and Central Limit Theorem.