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September 2012 Course handbook MSc in Quantitative Finance MSc in Financial Mathematics

Course handbook MSc in Quantitative Finance MSc in Financial … · 2015-03-02 · The MSc programmes in Quantitative Finance / Financial Mathematics aim: • To develop a good knowledge

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Page 1: Course handbook MSc in Quantitative Finance MSc in Financial … · 2015-03-02 · The MSc programmes in Quantitative Finance / Financial Mathematics aim: • To develop a good knowledge

September 2012

Course handbookMSc in Quantitative FinanceMSc in Financial Mathematics

Page 2: Course handbook MSc in Quantitative Finance MSc in Financial … · 2015-03-02 · The MSc programmes in Quantitative Finance / Financial Mathematics aim: • To develop a good knowledge
Page 3: Course handbook MSc in Quantitative Finance MSc in Financial … · 2015-03-02 · The MSc programmes in Quantitative Finance / Financial Mathematics aim: • To develop a good knowledge

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Table of Contents Page

Section 1 Course Director’s Welcome 2

Section 2 Programme Information

Programme Aims 3

Programme Structure 3

Assessment Matrix 5

Term Dates and Assessment Periods 7

Section 3 Module Descriptions

SMM306 Advanced Stochastic Modelling Methods in Finance 8

SMM265 Asset Pricing 10

SMM527 Business Research Project 12

SMM254 Derivatives 14

SMM271 Econometrics of Financial Markets 16

SMM269 Fixed Income Securities 19

SMM270 Foundations of Econometrics 21

SMM301 Mathematical Models for Financial Derivatives 23

SMM312 Numerical Methods 1: Foundations 25

SMM313 Numerical Methods 2: Applications in Finance 26

SMM522 Research Project Management Skills 28

SMM272 Risk Analysis 29

SMM302 Stochastic Calculus 31

Elective Information 33

Section 4 Regulations Degree Requirements 34

Assessment Calculations 34

Coursework 35

Failure and Re-sitting of Modules 35

Award of Merit and Distinction 35

Grade Related Criteria 37

Section 5 Additional Information

MSc Course Office 38

Virtual Learning Environment (Moodle) 38

Personal Tutors 39

Staff Contact Details 39

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Section 1 Course Director’s Welcome

Dear Student

On behalf of the Faculty of Finance and the members of staff who work on the MSc Quantitative Finance and MSc Financial Mathematics programme, we welcome you to Cass Business School. The Faculty has one of the largest concentrations of expertise in the areas of Finance, Economics, Econometrics and Mathematical Finance, and we have an international reputation for research and teaching excellence in those areas.

While business schools should concentrate on “relevant” and “practical” aspects of knowledge, the task of a university is not just to train a workforce, but to educate; to develop an understanding of a particular discipline so as to gain a wider perspective that will help you to solve real world problems, and that will help you to develop a broader set of skills which have practical relevance.

This course handbook summarises most of the information you will need to know about the programmes. It is your guide to what will be a busy, but rewarding, twelve months of study ahead. Certain information (e.g. teaching and examination timetables, tutorial lists) is available separately. You should keep the course handbook safe and refer to it if you have any questions about the operation of the programmes. If the handbook does not answer your questions, do not hesitate to speak to your tutor, the course officer, or myself.

The programmes have been carefully designed to prepare students to pursue successful careers in quantitative areas of finance, both in the City or for further studies at PhD level. To ensure this, the content of the programmes are frequently discussed with practitioners, alumni and academics. Compared to last year the programmes remain largely unchanged as they have been very successful according to the students’ feedback and feedback from my colleagues.

This year I am very excited about the new partnership which we have established with Singapore Management University (SMU). As part of this partnership we will welcome a small cohort of MSc Quantitative Finance students from Singapore in London after the Christmas break who are joining the MSc Quantitative Finance programme to study at Cass the term 2 modules.

Finally, can I remind you that the programmes are very demanding and you will have to work really hard over the next 12 months. Don’t forget this. But I should also say the rewards are huge.

My colleagues and I will help you to realise your potential so that you can derive the maximum benefit from your MSc programme. Enjoy the programme. My team and I are looking forward to working with you over the next 12 months.

Dr Dirk Nitzsche

Course Director MSc Quantitative Finance and MSc Financial Mathematics September 2012

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Section 2 Programme information

Programme aims

The MSc programmes in Quantitative Finance / Financial Mathematics aim: • To develop a good knowledge and understanding in the field of financial mathematics

(FM), financial econometrics (QF), financial engineering and risk management

• To develop an understanding of the respective roles of stochastic theory (FM) and forecasting (QF) in pricing securities, as well as numerical methods and computer programming

• To enable students to acquire the sophisticated mathematics and computer-modelling skills required to employ newly developed investment products and financial strategies for pricing, hedging, trading and portfolio management decisions.

Programme structure

The MSc programmes are organised in eight core subject-specific modules of 15 credits, and five elective modules of 10 credits. In addition, students will take a 10 credit core module in Research Project Management Skills during the second term.

The core modules are being taught in the first two terms, (October to December and January to March respectively), with the electives being taught in the third term of May to June.

Term 1

SMM265 Asset Pricing SMM254 Derivatives (QF only) SMM270 Foundations of Econometrics (QF only) SMM301 Mathematical Models for Financial Derivatives (FM only) SMM312 Numerical Methods I: Foundations SMM302 Stochastic Calculus (FM only)

Term 2

SMM306 Advanced Stochastic Modelling Methods in Finance (FM only) SMM271 Econometrics of Financial Markets (QF only) SMM269 Fixed Income Securities SMM313 Numerical Methods II: Applications in Finance SMM522 Research Project Management Skills SMM272 Risk Analysis

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Term 3

Option 1: Students can opt to write a 10,000 word business research project (40 credits) and take one specialist elective module (1 x 10 credits).

Option 2: Students can take five specialist elective modules (5 x 10 credits).

In light of the recent turmoil in financial markets, it is of fundamental importance to understand the role banks play in the financial system and to be aware of the regulatory constraints they face.

The programme aims to bring students the most up-to-date and factual information backed by solid academic research and a deep understanding of the banking and financial industry.

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Assessment Matrix – MSc Financial Mathematics

Module Title Module Code

Credits Assessment weightings used to calculate module

k Coursework Examination

Term One

Asset Pricing SMM265 15 25% 75%

Mathematical Models of Financial Derivatives

SMM301 15 25% 75%

Numerical Methods 1: Foundations

SMM312 15 100%

Stochastic Calculus SMM302 15 25% 75%

Term Two

Advanced Stochastic Modelling Methods in Finance

SMM306 15 25% 75%

Fixed Income Securities SMM269 15 25% 75%

Numerical Methods 2: Applications in Finance

SMM313 15 100%

Research Project Management Skills

SMM522 10 100%

Risk Analysis SMM272 15 25% 75%

Term Three

Option One

Elective 1 SMMXXX 10 100%

Elective 2 SMMXXX 10 100%

Elective 3 SMMXXX 10 100%

Elective 4 SMMXXX 10 100%

Elective 5 SMMXXX 10 100%

Option Two

Business Research Project SMM527 40 100%

Elective 1 SMMXXX 10 100%

Degree Total 180

ECTS equivalencies

Each MSc course is worth between 180 - 210 CAPS credits. As a general rule two CAPS credits equal one ECTS credit. (For example, a course with 180 CAPS credits is worth 90 ECTS credits.)

*CAPS (Credit Accumulation of Programme Specification)

*ECTS (European Credit Transfer and Accumulation System)

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Assessment Matrix – MSc Quantitative Finance

Module Title Module Code

Credits Assessment weightings used to calculate module

k Coursework Examination

Term One

Asset Pricing SMM265 15 25% 75%

Derivatives SMM254 15 25% 75%

Foundations of Econometrics SMM270 15 25% 75%

Numerical Methods 1: Foundations

SMM312 15 100%

Term Two

Econometrics of Financial Markets

SMM271 15 25% 75%

Fixed Income Securities SMM269 15 25% 75%

Numerical Methods 2: Applications in Finance

SMM313 15 100% 75%

Research Project Management Skills

SMM522 10 100%

Risk Analysis SMM272 15 25% 75%

Term Three

Option One

Elective 1 SMMXXX 10 100%

Elective 2 SMMXXX 10 100%

Elective 3 SMMXXX 10 100%

Elective 4 SMMXXX 10 100%

Elective 5 SMMXXX 10 100%

Option Two

Business Research Project SMM527 40 100%

Elective 1 SMMXXX 10 100%

Degree Total 180

ECTS equivalencies

Each MSc course is worth between 180 - 210 CAPS credits. As a general rule two CAPS credits equal one ECTS credit. (For example, a course with 180 CAPS credits is worth 90 ECTS credits.)

*CAPS (Credit Accumulation of Programme Specification)

*ECTS (European Credit Transfer and Accumulation System)

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Term Dates and Assessment Periods

Induction

16 – 28 September 2012

Term One

01 October – 07 December 2012

Term One Examinations

14 – 25 January 2013

Term Two

28 January – 09 April 2013

Term Two Examinations

29 April – 10 May 2013

Term Three

13 May – 28 June 2013

Term Three Assessments

01 – 12 July 2013

Re-sit Examinations and Assessments (terms one, two and three)

19 – 30 August 2013

Business Research Project Submission Date

02 September 2013

Students are expected to be in attendance at lectures and other classes during term time; attend all invigilated tests and examinations. Students should not make travel arrangements during term time or assessment periods. Any absence from any form of assessment, which does not constitute valid extenuating circumstances, will result in the student re-sitting the module as a second attempt.

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Section 3 Module Descriptions

Advanced Stochastic Modelling Methods in Finance SMM306

Module Leader Prof. Ales Cerny

Sessions 10 x 3 hour sessions

Module Assessment Coursework 25% Examination 75%

Educational aims

• Introduce students to more recent advances in financial mathematics.

• To provide students with the mathematical tools required for the setting up of more sophisticated financial models and valuation framework.

• To introduce students to pricing frameworks beyond the Black&Scholes model

• To introduce concepts and applications of stochastic optimal control.

Learning outcomes

• Provision of knowledge and understanding of the more recent developments in the field of financial mathematics.

Syllabus

• Levy processes: the Levy-Khintchine formula, the fine structure of Levy processes and the Levy decomposition.

• Classes of Levy processes used in finance: jump diffusion processes and time changed Brownian motions.

• Stochastic calculus for Levy processes with finance in view: stochastic differential equations, the Girsanov theorem and market incompleteness.

• Derivative pricing: numerical approximations and calibration to market data.

• Stochastic optimal control in discrete time: Dynamic Programming.

• Stochastic optimal control in continuous time: the Hamilton-Jacobi-Bellman approach.

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Reading List

• Cont, R. and P. Tankov (2004). Financial modelling with jump processes, Chapman and Hall/ CRC Press.

• Björk, T. Arbitrage Theory in Continuous Time (Oxford Finance Series, 3rd edition, 2009: OUP)

• Further references for this module will be disseminated at the start of term.

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Asset Pricing SMM265

Module Leader Dr Dirk Nitzsche

Sessions 10 x 3 hour sessions

Module Assessment Coursework 25% Examination 75%

Educational aims

The course introduces students to the basic concepts used for pricing and analysing financial securities, focusing on spot markets. The efficiency of financial markets is discussed together with the question of whether stock prices are predictable. The importance of the risk and its trade-off with return will be analysed in debts. Portfolio theory and the conceptual idea of factor models such as the CAPM and how they can be used to assess the riskiness of financial securities are introduced. Some basic utility analysis is also covered in the course which helps to explain mathematically different ‘attitudes’ towards risk by different investors. The Module also includes an overview of the mutual fund industry and discusses issues such as performance, persistence of performance and market timing. The course is both rigorous in presenting the theoretical models, but also focuses on the practical applications and empirical findings.

Learning outcomes

On completion of this module students will be able to: • Demonstrate broad knowledge of the functioning and behaviour of spot markets

• Understand the importance of risk and return of financial assets

• Understand in depth portfolio theory and management and its application to real-world situations

• Understand systematically asset pricing models and their application to practical situations

• Demonstrate sound understanding of the full range practical asset pricing and asset management issue

• Given the nature of the subject matter – theoretical knowledge and ability to apply to practical situations are developed in tandem through a mixture of lectures, computer exercises and technical case studies.

Syllabus

• Financial securities, financial markets: The basics

• Utility Analysis

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• Valuation of spot securities

• Efficiency of financial markets and stock return predictability

• Efficient frontier, diversification and portfolio theory

• The CAPM and other asset pricing models

• Topics in Asset Pricing: Mutual fund performance

Reading List

• Cuthbertson, K. and Nitzsche, D. (2004). Quantitative Financial Economics, 2nd

edition, J. Wiley.

• Elton, E.J. and Gruber, M.J. (1995). Modern Portfolio Theory and Investment Analysis, J.

Wiley, 5th edition.

• Cuthbertson, K. and Nitzsche, D. (2008). Investments, J. Wiley.

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Business Research Project SMM527

Module Leader A project supervisor will be allocated

Sessions This is an individual project which students will develop in their own time with support from their project supervisor.

Module Assessment Coursework 100%

Delivery of the final project, indicative length: 10,000 words

Educational aims

• To train students to undertake individual research and provide them with an opportunity to specialise in a contemporary business or finance topic related to their future career aspirations

• To integrate and apply concepts from different aspects of their MSc.

Learning outcomes

On completing the project students will be able to:

• Identify specific business or finance related issues which would be useful to research and shape an achievable research question around them.

• Develop a research question and plan and carry out a research programme to address the question.

• Understand the theories and recent research relating the project topic.

• Understand how to apply research methodologies to practical business and commercial issues.

• Show confidence in overcoming problems raised in the course of a practical research project and

• Accept the challenge of carrying out a piece of research with elements of originality.

Project requirements

The choice of project is your responsibility. It is most important that you choose an area you are happy to work in, and in which you are confident of your abilities.

Students are encouraged to start thinking about project ideas at the beginning of their studies. By the end of the first term you will have gained sufficient knowledge to start to develop ideas that can be discussed with faculty. We expect you to identify the basic idea or research question, though this is likely to be modified after discussion with academic staff.

Make effective use of the RPMS module. This module can be used to help to formulate your ideas and design an appropriate methodology. It can also help you develop a specific

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project topic – the greater clarity you have about the topic of your project the more successful it is likely to be.

The types of project allowed are:

What you can do. What you can’t do

• Business report on a contemporary issue

• Business plan

• Statistical test of literature driven hypothesis

• Empirical feasibility of a financial strategy

• Development of a new product/ service /

finance strategy

• Market survey

• Case study on a specific issue within a particular company / organisation

• Numerical project that describes and implements one or more numerical methods for pricing, hedging or reserving for derivatives or portfolios.

• Pure literature surveys

• Some evidence that the writer has learnt a new subject, a sort of extra elective

• A synthesis of other writing or a piece of journalism

• A mere compendium of facts and statistics

• Projects totally unrelated to relevant academic discipline and literature.

Reading list

Student research and reading list will be defined by the subject matter of the project.

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Derivatives SMM254

Module Leader Professor Keith Cuthbertson

Sessions 10 x 3 hour sessions

Module Assessment Coursework 25% Examination 75%

Educational aims

The course will develop an in-depth understanding of forwards, futures, swaps, options and exotic options and their application in risk management, to develop student knowledge to the level of a highly valued professional qualification. The course will:

• Develop student appreciation of the ubiquity of derivative securities throughout commercial life

• Develop student understanding of risk management.

Learning outcomes

On completion of this module students will be able to: • Select the appropriate derivative security for hedging, insurance and other risk

management applications

• Understand derivatives trading strategies

• Understand the valuation of derivative securities using closed form and numerical methods

• Understand the measurement of market risk (Value at Risk) in complex portfolios.

Syllabus

• Commodity forwards and futures, Stock Index futures, interest rate futures

• Practical examples of pricing and hedging with futures contracts

• Swaps (interest rate and currency) – pricing, valuation and hedging.

• Options. Delta hedging, portfolio replication.

• Speculation and arbitrage (pricing) of derivatives – risk neutral valuation, BOPM, MCS and Black&Scholes.

• Exotic derivatives – Asians, knockout, path dependent

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• Energy and Weather Derivatives

• Interest rate derivatives, caps, floors, collars, swaptions, forward swaps

• Value at Risk

Reading List

• Cuthbertson, K. and Nitzsche, D. (2001), Financial Engineering: Derivatives and Risk Management, Wiley, Chichester.

• Hull, J.C. (2010), Options, Futures and Other Derivatives, 7th edition, Prentice Hall.

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Econometrics of Financial Markets SMM271

Module Leader Professor Giovanni Urga

Sessions 10 x 3 hour sessions

Module Assessment Coursework 25% Examination 75%

Educational aims

• To provide a detailed knowledge of the tools of financial econometrics.

• To build / illustrate the techniques with actual examples of applied works using high frequency data.

• To show how econometrics can be applied to get useful insights about financial-world behaviour.

Learning outcomes

• Demonstration of systematic knowledge and understanding of the essential technical tools required to carry out advanced econometric research on financial data.

• Demonstration of sound understanding of leading edge research in empirical finance and related econometric theory.

• Appreciation of the implications of financial theories and the practical insights they can offer into practical financial issues.

• Development and execution of complex empirical financial analyses.

• Familiarise with the techniques by studying empirical papers, and undertaking practical works which may be asked of most applied financial economists to model the main characteristics of financial time series.

Syllabus

• Preliminaries: high frequency finance and data types

• Linear time series models and forecasting

• GMM and maximum likelihood estimation methods in finance.

• Modelling volatility: univariate (G)ARCH models.

• Modelling volatility: MGARCH models.

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• Dynamic conditional correlations (DCC) models, multivariate risk and contagion.

• Realized volatility. Forecasting risk and returns

• The impact of macro-announcements on the term structure, foreign exchange rates and asset prices.

• Fractional integration and long memory processes in finance: a short introduction.

Reading List

The material covered during the lectures will be drawn from parts of the textbooks listed below and various papers. Relevant reading material and notes prepared by the lecturer will be distributed during each lecture.

• Andersen, T.G., Davis, R.A., KreiB, J.P., Mikosch, T. (2009). Handbook of Financial Time Series, Springer-Verlag.

• Campbell, J. Y., Lo, A.W. and MacKinlay, A.C. (1997). The Econometrics of Financial Markets, Princeton University Press.

• Dacorogna, M.M., R. Gencay, U. Muller, R.B. Olsen and O.V. Pictet (2001). An Introduction to High Frequency Finance, Academic Press.

• Dunis, C. (eds.) (1996). Forecasting Financial Markets, Wiley.

• Gourieroux, C. and Jasiak, J. (2001). Financial Econometrics, Princeton University Press.

• Hall, A. (2005). GMM Estimation Methods, Oxford University Press.

• Laurent, S. (2009). Estimation and Forecasting ARCH Models Using G@RCH 6, Timberlake Consultants Ltd.

• McNeil, A.J., R. Frey, and P. Embrechts (2005). Quantitative Risk Management. Concepts, Techniques and Tools, Princeton University Press.

• Mills, T.C. (1999). The Econometric Modelling Of Financial Time Series, Cambridge University Press.

• Mills, T. C. and R. N. Markellos (2008). The Econometric Modelling Of Financial Time Series, 3rd Edition, Cambridge University Press.

• Rachev, S.T., S. Mittnik, F. J. Fabozzi, S.M. Focardi, T. Jasic (2007). Financial Econometrics. From Basics to Advanced Modelling Techniques. Wiley Finance.

• Taylor, S. (2008). Modelling Financial Time Series, World Scientific Publishing Co. Pte. Ltd.

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• Tsay, S. R. (2005). Analysis of Financial Time Series, Wiley (2nd

Edition)

• Valdez, S. and P. Molyneux (2010). An Introduction to Global Financial Markets, 6th Edition, Palgrave MacMillan.

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Fixed Income Securities SMM269

Module Leader Dr. Max Bruche

Sessions 10 x 3 hour sessions

Module Assessment Coursework 25% Examination 75%

Educational aims

• To acquaint students with the main modelling streams in fixed income securities.

• To enable students to use models in this area in practical applications.

• To transmit to students the fundamental mathematical modelling techniques underpinning the subject.

Learning outcomes

• In-depth systematic knowledge of theory used in mathematical modelling of fixed income and credit for valuation and hedging.

• Demonstration of comprehensive understanding of application of models to practical situations, including their strengths and limitations.

• Understanding of the theoretical and practical differences between models and their distinct applications to live corporate or market situations.

• Development of intuitive but accurate interpretations of data through fixed income models.

Syllabus

• Basic bond math, forward rates, term structure of interest rates

• Interest rate swaps and swap rates

• Caps, floors and swaptions

• The standard market models (the Black approach)

• Short-rate models

• Introduction to affine models

• The HJM approach

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• The LIBOR-market model

• Credit risk instruments and concepts

• Reduced-form and structural models of credit risk

• Default dependence

Reading List

• Hull, J., 2006, Options, Futures, and Other Derivatives, Prentice Hall, 6th edn. or later

• Shreve, S. E., 2004, Stochastic Calculus for Finance II: Continuous-Time Models, Springer-Verlag, New York NY USA.

• Rebonato, R., 1998, Interest-rate Option Models, John Wiley & Sons Ltd., Chichester, England, 2 edn.

• Schönbucher, Philip, Credit Derivatives Pricing Models, Wiley, 2003

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Foundations of Econometrics SMM270

Module Leader Vincenzo Maini

Sessions 10 x 3 hour sessions

Module Assessment Coursework 25% Examination 75%

Educational aims

• To provide the essential statistical and econometric techniques based on Least Squares estimation which will enable the students to understand and interpret empirical findings in a range of financial markets.

• To ensure that students are comfortable with the use of standard econometric software such as PcGive to undertake their own research.

Learning outcomes

• Provision of a comprehensive and systematic understanding of the complex analytical tools of financial econometrics.

• Ability to demonstrate sound understanding of how econometrics can be applied to gain useful insights into real-world behaviour.

Syllabus

• Regression: the Classical Linear Regression Model (CLRM) * Assumptions of the CLRM * Least Squares estimation (OLS): definition and properties *Goodness of Fit: residual based statistics, interpretation of the regression output, information criteria

• Violations of the assumptions of the CLRM: * Causes of violations and testing for the validity of assumptions: mis-specification tests * Consequences of mis-specification and solutions

• Time series analysis: * Stochastic processes and stationarity;

* Non stationarity: linear deterministic trends, unit roots and the random walk model, testing for unit roots, cointegration and error correction formulations

*(If time allows) Introduction to Garch models: identification, estimation, diagnostic testing.

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Reading List

Recommended textbook

• Brooks, C. (2002) Introductory Econometrics for Finance, Cambridge University Press

Other useful references are:

• Campbell, J.Y., Lo, A.W. and MacKinlay, A.C. (1997). The Econometrics of Financial Markets, Princeton. Greene, W.H. (1997). Econometric Analysis, Prentice Hall, 3

rd

Edition.

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Mathematical Models for Financial Derivatives SMM301

Module Leader Dr Laura Ballotta

Sessions 10 x 3 hour sessions

Module Assessment Coursework 25% Examination 75%

Educational aims

• To introduce students to financial derivative instruments.

• To analyse the features of the main classes of derivatives traded in the markets, like options, forward and futures.

• To provide a theoretical framework for valuation and hedging of contingent claims.

• To introduce students to the theory of interest rate derivatives.

Learning outcomes

• Provision of the core knowledge of derivatives together with the financial models essential to understand the valuation and applications of this asset class.

Syllabus

• Introduction to financial derivatives: forward and futures, options

• The no-arbitrage principle

• Pricing of linear derivatives

• Pricing of non-linear derivatives: discrete time models

• Pricing of non-linear derivatives: continuous time models

• The Black-Scholes framework, hedging vanilla options (Greeks), hedging exotic options (static hedging), implied volatility, variance and volatility swaps

• American options

• The numéraire pair and pricing applications

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Reading List

• Bjork, T. (2004). Arbitrage Theory in Continuous Time, OUP, 2nd Edition.

• Hull, J.H. (2004), Options, Futures and Other Derivatives, Prentice Hall, 7th/8th Edition

• Shreve, S. (2004). Stochastic Calculus for Finance II – Continuous Time Models, Springer

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Numerical Methods 1: Foundations SMM312

Module Leader Dr Dirk Nitzsche (Matlab programming) Dr Fotis Mouzakis

Sessions 5 x 3 hour computer sessions and 5 x 3 hour lectures

Module Assessment Coursework 100% This module is assessed by an individual Matlab-based test (50%) and by group coursework (50%)

Educational aims

• To give students a working knowledge of Matlab, both as a programming environment and as a programming language.

• To show students the right mindset for writing modular computer programmes.

• To provide theoretical foundation to basic numerical methods.

• To provide simple finance-based applications of those methods.

• By means of simple computer-based exercises allow students to develop their individual problem-solving skills.

Learning outcomes

On completion of this module students will: • Be able to use Matlab independently to write and debug script and function files

• Have theoretical understanding of basic numerical methods and the ability to implement them independently in Matlab.

Syllabus

Computing concepts such as program structure, i/o handling, data types, arrays, expressions, control statements, data structures are taught in parallel with - and applied to numerical methods - such as root finding, non-linear equations, linear systems, interpolation, extrapolation, differentiation, integration, and random number generation techniques.

Emphasis will be placed on the numerical concepts that are particularly applicable in Finance.

Reading List

The reading list for this module will be disseminated at the start of term.

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Numerical Methods 2: Applications in Finance

SMM313 Module Leader Dr Ioannis Kyriakou

Sessions 8 x 3 hour lectures and 2 x 3 hour computer sessions

Module Assessment Coursework 100% This module is assessed by group coursework (50%) and by individual invigilated test (50%)

Educational aims

• Explore examples of numerical methods used in derivatives pricing.

• Apply MATLAB programming skills acquired in SMM312 (Numerical Methods I: Foundations) to implement these methods.

• Learn to analyse the trade-off between computational speed and numerical accuracy.

• Recognise the strengths and limitations of the various numerical methods through hands on examples.

Learning outcomes

• Acquire a comprehensive understanding of how to price derivative instruments and compute price sensitivities using numerical methods such as Monte Carlo simulation, multinomial lattice, fast Fourier transform and finite difference schemes for partial differential equations (PDEs).

• Become aware of practical issues in the implementations of the above mentioned methods and learn how to cope with these/reduce their effect.

• Acquire a good understanding of the relationship among the methods and their relative strengths and weaknesses.

• Construct moderately complex MATLAB code involving one script file and several function files in order to implement the above mentioned methods.

Syllabus

• Monte Carlo simulation:

o Generate random samples using the inverse transform method; o Generate multivariate normal samples using Cholesky factorization and Eigenvalue

factorization; o Generate sample paths; o Price path-independent & path-dependent options; o Use variance reduction techniques (control variates, antithetic variates, stratified

sampling/Brownian bridge); o Compute option price sensitivities using the pathwise, likelihood ratio and mixed

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methods. • Multinomial lattices and fast Fourier transform:

o Price path-independent and path-dependent options (Bermudan & Barrier options). • Finite difference schemes for PDEs:

o Price European plain vanilla options.

Reading List

ESSENTIAL READING:

• Černý, A. (2009). Mathematical Techniques in Finance: Tools for Incomplete Markets (2nd ed.). Princeton: Princeton University Press.

• Glasserman, P. (2004). Monte Carlo Methods in Financial Engineering. New York: Springer.

ADDITIONAL READING:

• Cont, R. and P. Tankov (2004). Financial modelling with jump processes. Boca Raton: Chapman & Hall/CRC Press.

• Fishman, G. S. (1996). Monte Carlo: Concepts, Algorithms, and Applications. New York: Springer.

• Wilmott, P., S. Howison, and J. Dewynne (1995). The Mathematics of Financial Derivatives. Cambridge University Press.

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Research Project Management Skills SMM522

Module Leader Dr Dirk Nitzsche

Sessions 3 x 3 hour sessions

Module Assessment Coursework 100% Educational aims

The aim of this module is to produce a research proposal with a comprehensive literature review as its centre piece. Students should demonstrate that they can phrase interesting research questions and are able to search for relevant literature, are aware of the data requirement and other relevant information as well as the appropriate methodologies to address those research questions. Students also need to show a very good understanding of the recent literature in the topic they have chosen.

The module is mainly a self-study module where students gain the knowledge for preparing academically-focused research reports. Developing the aims and objectives, together with the key research questions is at the centre of this process, followed by data considerations and selecting the right methodologies.

Learning outcomes

On completion of this module students will be able to: • Formulate the key questions for a research project

• Search for information and to write a comprehensive critical literature review

• Collect, prepare and use relevant data required for the research report

• Assess different appropriate methodologies

• Organise and manage your time in composing the research proposal.

Syllabus

• Session 1: Introduction to writing a research proposal

• Session 2: Writing a literature and other research skills

• Session 3: Q&A

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Risk Analysis SMM272

Module Leader Dr. Gianluca Fusai

Sessions 10 x 3 hour sessions

Module Assessment Coursework 25% Examination 75%

Educational aims

This module concentrates on approaches to measuring and controlling market risk and credit risk, and also touches on the regulatory framework and the reasons behind the increase of importance of this discipline over the last 10 years.

The students will learn to analyse and quantify risk according to current best practice in the markets, including the RiskMetrics and CreditMetrics methodologies.

The module looks at risk analysis both from a mathematical and an empirical point of view as well as from the viewpoint of practitioners.

Learning outcomes

On completion of this module students will be able to:

• Demonstrate systematic and comprehensive knowledge of the different sources and types of financial risk

• Demonstrate sound appreciation of the different purposes of risk analysis and modelling and the steps involved in defining, measuring and managing risk

• Appreciate the importance of risk management for a wide range of stakeholders at trader, corporation and institution level

• Respect and value the role of financial regulation and understand the issues related to its reform.

Syllabus

• VaR and Expected Shortfall: how to measure market risk

• Univariate analysis: Gaussian, EWMA and GARCH models and applications

• Multivariate analysis; VaR, marginal/incremental VaR, covariance estimation issues.

• Derivatives positions and information from derivatives

• Risk mapping. simulation and bootstrapping

• Backtesting and stress testing; includes coherence

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• Credit risk measurement and types of models

• Portfolio considerations;

• Counterparty Risk Valuation

Reading List

• Jorion, P. (2007). Value at Risk, McGraw-Hill, 3rd Edition.

• Elements of Financial Risk Management, Peter Christoffersen, Academic Press, 2003

• Measuring Market Risk + CD-ROM , 2nd Edition, Kevin Dowd, Wiley; 2 edition, 2005

• RiskMetrics Technical Document, from http://pascal.iseg.utl.pt/~aafonso/eif/RM.html

• CreditMetrics Technical Document, from www.msci.com/resources/technical_documentation/CMTD1.pdf

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Stochastic Calculus SMM302

Module Leader Dr. Laura Ballotta

Sessions 10 x 3 hour sessions

Module Assessment Coursework 25% Examination 75%

Educational aims

• To introduce students to Brownian motion and stochastic calculus.

• To provide examples of applications of stochastic calculus in financial areas.

• To provide the tools required for a rigorous understanding of financial modelling and pricing techniques.

Learning outcomes

• Provision of the necessary mathematical tools on which financial mathematics is based.

Syllabus

• Review of measure theory and probability theory

• Stochastic processes: classes and properties

• Brownian motions: definitions and properties

• Functionals of Brownian motions: the reflection principle and running maxima and minima

• Ito calculus and stochastic differential equations

• Affine processes and applications: the CIR model; the Heston model

• Girsanov theorem and application in finance: changes of measure and numeraire pairs; pricing of barrier options; default structural models

• The Cauchy problem and the Feynman-Kac representation: PDE vs Martingales

• The martingale representation theorem

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Reading List

• Karatzas, I. and Shreve, S. (1987). Brownian Motions and Stochastic Calculus, Springer.

• Filipovic, D. (2009). Term structure models: a graduate course. Springer Finance (Chapter 10)

• Mikosch, T. (1998) Elementary Stochastic Calculus with Finance in View, World Scientific.

• Oksendal, B. (1998). Stochastic Differential Equations, Springer.

• Shreve, S. (2004). Stochastic Calculus for Finance II – Continuous Time Models, Springer.

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Elective Information

Cass Business School provides an extensive range of elective modules for the different MSc programmes. A special elective handbook, regarding your term three selection of modules, will be distributed in the second term and will provide further information.

Electives which have previously been provided by MSc Financial Mathematics and MSc Quantitative Finance include:

Behavioural Finance

Energy and Weather Derivatives

Exotic Options

Introduction to C++

Matlab

Apart from these electives, students will also be able to choose from preselected modules offered by other MSc programmes. In the past these have included, among others:

Hedge Funds

Technical Analysis and Trading Systems

Trading and Hedging in the Forex Market

Please note the School reserves the right to withdraw an elective if demand is insufficient and to add new electives if they are available. Space restrictions and timetable availability may also apply.

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Section 4 Regulations

Described below are the rules governing the award of a master degree in MSc Financial Mathematics and MSc Quantitative Finance. For further information, the City University’s complete set of “Ordinances and Regulations”, including the Assessment Regulations (Regulation 19), are published on the University’s website http://www.city.ac.uk/about/education/academic-services/senate-regulations

Periods of Registration

The periods allowed for completion of the qualifications are:

• Four years for a masters degree, full or part time

• Two years for a postgraduate diploma, full or part time

Degree Requirements

To qualify for a Masters degree a candidate must achieve at least 50% as an aggregate mark for each module and an overall degree average mark of 50%. This will result in the acquisition of 180 credits, which is the number required to achieve a master’s degree in MSc Financial Mathematics and MSc Quantitative Finance.

Assessment Calculations

The rules governing calculation of module and overall degree marks are as follows;

• To receive credits for a MSc all modules must be passed

• There are no minimum mark requirements for separate assessment components (unless specifically stated). However, it is compulsory to complete all components and no module mark can be awarded until these are completed.

• A module mark is calculated by aggregating marks for all assessment components as stated in the module outline (section three).

• Where modules are assessed by both exam and coursework, these are weighted to calculate the module mark. Please see the assessment matrix in section two for the relative weightings.

• Where there are several pieces of coursework, the coursework results are calculated according to the relevant weightings.

• To calculate the overall degree mark, module marks are combined using weightings in line with the relative credit value of each module.

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Coursework

All coursework and invigilated tests are compulsory and count towards the final degree. In some modules presentations or invigilated tests may replace written coursework assignments.

Some subjects may be assessed by coursework only. Precise details concerning examined and non-examined modules are provided in the module outlines.

Please note coursework is required to be submitted for assessment by the specified deadline date. Late coursework will receive imposed penalties. Late coursework will immediately receive a deduction of five marks on the first day of lateness, with one further mark deducted for each day of lateness, for a maximum of five days. After this point coursework will not be accepted and a mark of zero will be awarded.

All coursework should be submitted electronically via the virtual learning environment, Moodle. It is essential that you keep a copy of all coursework submitted.

All sources used should be cited using the Harvard referencing system. Further information about this can be found on the Cass website:

http://www.cass.city.ac.uk/intranet/student/learning-resource-centre/citing-references

Coursework will be returned to students as quickly as possible with the aim of students receiving feedback within three to four weeks of their submission

Failure and the Re-sitting of Modules

• Any module with an aggregate mark of less than 50% is deemed to have been failed and will have to be re-sat.

• To re-sit a failed module, a candidate must re-do all assessment components which gained marks of less than 50%.

• Candidates may re-sit a module only once.

• A candidate who successfully completes a re-sit will be awarded the credits for the module. The mark awarded for the components will be capped at 50%. The mark awarded for other components will be the original mark. This mark will also be used in calculating the overall degree mark

• A candidate who does not pass his or her re-sit by the date specified by the Assessment Board will not progress on the programme and the Assessment Board will normally make a recommendation that they withdraw.

Award of Distinction

To calculate the overall degree mark all module marks are combined using the weighting in the assessment matrix table. The award of distinction for the masters is based on:

• An overall degree mark of at least 70% with no modules failed at first attempt.

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Award of Merit

To calculate the overall degree mark all module marks are combined using the weighting in the assessment matrix table. The award of merit for the masters is based on:

• An overall degree mark between 65% - 69.9% inclusive and no modules failed at first attempt

• Or an overall degree mark of 70% or more and one module failed at first attempt

Postgraduate Diploma

A student who has not accumulated enough credits to be awarded a masters degree may be awarded a postgraduate diploma provided they have satisfied the following conditions:

• The total number of credits gained is equal to or greater than the minimum credits stipulated in the programme specification for the award of a diploma

For the award of a diploma a student may compensate a maximum of twenty core or core elective credits provided the following conditions are met:

• The mark achieved for the module(s) to be compensated is at least 40%

• The average mark of all modules to be counted towards the diploma, including those modules to be compensated, is at least 50%

Note that:

• The diploma average will be calculated in the same way as the masters average as specified in the programme specification;

• The award of distinction and merit will also be calculated in the same way for the masters degree, as specified in the programme specification

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Grade Related Criteria

Class % Literary Knowledge Independent thought, uses of sources and research materials

Presentation Professional

Dis

tinct

ion

85-100 A Outstanding Comprehensive and informative knowledge of subject area, may include - new knowledge derived from which the marker and wider community may learn; addresses the learning outcomes/ assessment criteria in full

Where relevant, evidence of independent reading, thinking and analysis and strong critical ability

Well-constructed

Dis

tinct

ion

80-84 Excellent

75-79 Very good Sophisticated or strong - shows knowledge of complex issues or a broad range of issues and addresses the learning outcomes/assessment criteria well.

Where relevant, show evidence of wide and comprehensive reading and critical ability

Clearly written

70-74

Mer

it

65-69 B Good Sound knowledge of a broad range of issues or detailed knowledge of a smaller number of issues; makes a good attempt to address the learning outcomes/assessment criteria, realising all to some extent and some well

Evidence of thorough research of the topic(s) but some answers may not be complete or arguments sufficiently explored. Some critical ability will be evident.

Well-structured and logically written

Mer

it

Pass

50-64 C Satisfactory Adequate knowledge of important issues – some level of response to all learning outcomes/assessment criteria but may not include important elements or information that is fully accurate.

Where relevant, development of ideas is limited but attempts will be made to analyse materials critically

Expression and structure may lack clarity

Pass

Fail

(0%

-49%

)

41-49 D Poor Unsatisfactory work - inadequate knowledge of the important issues and doesn’t succeed in grasping key issues, therefore learning outcomes/ assessment criteria will not be realised

No real development of ideas and critical analysis will be very limited.

Presentation is confused or incoherent

Fail

(0%

-49%

)

20-40 E Very poor Knowledge is lacking either through omission, the inclusion of large amounts of irrelevant information or evidence of significant misunderstanding - totally inadequate attempt to address the learning outcomes/ assessment criteria

No critical ability will be displayed

Confused, incoherent or unstructured presentation

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Section 5 Additional Information

MSc Course Office

The MSc course office is here to support both staff and students and each MSc course has its own dedicated Course Officer who you will get to know over the course of your time here at Cass. The Course Office team will provide you with course related information, material and your grades, advice relating to other areas of City University and support throughout the duration of your studies.

Location

The course office is located on the 3rd floor of Cass Business School, 106 Bunhill Row, London EC1Y 8TZ

Contact

You can contact the course office team either in person at the office, by email, telephone or via Moodle, our virtual learning environment.

The MSc Financial Mathematics and MSc Quantitative Finance Course Officer is Helen Young and can be contacted directly via telephone 020 7040 0105 or by email [email protected]

Office Opening Hours

During term time the course office is open to students:

Monday 1300 – 1830

Tuesday 1300 – 2000

Wednesday 1300 – 1830

Thursday 1300 – 2000

Friday 1030 – 1530

Outside of term time the course office is open to students:

Monday to Thursday 1300 – 1700

Friday 1030 – 1530

Moodle: Your Virtual Learning Environment

Moodle is the virtual learning environment used at City University and it provides a wide variety of information and interactive environments to students, including the following:

• Module material and supplementary learning documents, including areas for the submission of coursework and the release of coursework results

• Timetables, including teaching and examination

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• Specialist Masters, MSc specific and module pages providing information relating to each area with supporting documents and forums

• Links to the Learning Resource Centre, Careers, Student Advice and Clubs and Societies

Students are responsible for checking their Moodle pages and their City email account regularly. This is how all information, including changes to teaching, is communicated. Course Officers manage the communications sent to students via Moodle and all administrative enquiries should be directed to them for assistance.

Personal Tutors

Postgraduate Taught students are assigned a personal tutor at the beginning of the year. This personal tutor will be available to provide general academic, professional and pastoral support and will also ensure students are aware of the additional and more specialised support mechanisms available within the University.

Students should have the opportunity to see their personal tutor at least once a term; however it is the student’s responsibility to contact their personal tutor to make an appointment.

The Course Office team is also here to assist should you need any support during the course of your studies.

Academic Staff Contact Details

In addition to their main teaching responsibilities academics also engage in research, administration and external work. As a result staff members may not be able to see you without an appointment.

If the matter is non-urgent please make an appointment or make use of the office hours many academics hold. If the matter is urgent please make this clear when contacting the member of staff to request an appointment.

Lecturer’s contact details and office hours can be found on Moodle.

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Programme Disclaimer

The information in this Specialist Masters Programme Handbook is correct at the time of going to press in August 2012. The University reserves the right to make amendments to:

a) the contents of the Programme Handbook and in particular to the timetable, location and methods of delivery or the content, syllabus and assessment of any of its programmes as set out in the programme and module specifications in this Handbook and/or on the University's website; and

b) its statutes, ordinances, regulations, policies, procedures and fee structures,

provided that such amendments are (i) as a result of student demand (or lack thereof), (ii) as a result of unforeseen events or circumstances beyond the University's control or (iii) are deemed reasonably necessary by the University.

In the event that amendments are made, the University shall take reasonable steps to notify you as soon as is reasonably possible.

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Cass Business School 106 Bunhill Row London EC1Y 8TZ T: +44 (0)20 7040 8600 www.cass.city.ac.uk/masters