Postgraduate Certificate in Quantitative Finance (Distance Learning)

Econometric Analysis and Applications is the second econometrics module offered to MSc students who need to broaden their understanding of the application of quantitative methods to inquiry in finance or economics. This module assumes that you have studied the classical linear regression model at an introductory level and that you are familiar with the assumptions that underlie that model. You will be aware that there are many cases in which these assumptions are not satisfied, and know how such problems as heteroscedastic disturbances and autocorrelated errors can be detected, and what can be done about them.

The purpose of this module is to broaden your knowledge and extend your understanding of econometrics. In doing this, you will work with data. The first two units extend your knowledge of single equation methods. Unit 1 considers how to make progress with dummy – that is, qualitative – regressors. Unit 2 introduces dynamic models by showing how lags and expectations can be incorporated. The following three units focus on models that consist of two or more equations – simultaneous equation models. The nature of such systems is explained and their identification and estimation discussed. The analysis of dynamic models is extended in Unit 6, where the time series properties of variables are discussed. By understanding the time series properties of variables, you will be able to specify dynamic econometric models that capture both short-run and long-run effects. These are discussed in Unit 7. The final unit, Unit 8, focuses on forecasting with both econometric and time series models.

We recommend that you study Econometric Principles and Data Analysis prior to this module.

Learning outcomes

After studying this module you will be able to:

• explain the use of intercept and slope dummy variables
• use and interpret the Chow test of parameter stability
• explain the nature of the ‘dummy variable trap’ and how to avoid it
• explain finite distributed lag models, including immediate impact, long-run reactions and mean lag
• discuss the properties of estimators of distributed lag and autoregressive models
• implement both Durbin’s h test and the LM test of autocorrelation and interpret the results
• explain ‘simultaneous equation bias’
• interpret in a model the behavioural equations, definitions or identities, and equilibrium conditions
• examine the structural form, reduced form and final form of a simultaneous equation system
• identify conditions for stability in dynamic simultaneous equation systems
• explain the identification problem
• discuss the implications of equations which are exactly identified, overidentified, and not identified
• explain and apply indirect least squares
• explain the method of instrumental variable estimation, and discuss the properties of IV estimators
• explain and apply the method of two stage least squares (TSLS or 2SLS), and discuss the properties of 2SLS estimators
• discuss what is meant by stationary and nonstationary time series, and provide examples of each
• explain and implement the Dickey–Fuller and augmented Dickey–Fuller tests of the hypothesis that a series is I(1)
• explain the nature of cointegration and the relationship between spurious regression and cointegration
• discuss and implement tests of cointegration
• explain, interpret and estimate error correction models
• explain the nature of vector autoregressions (VARs)
• define an autoregressive integrated moving average (ARIMA) model, and use it to forecast
• interpret measures of forecast evaluation.

Tuition and assessment

Students are individually assigned an academic tutor for the duration of the module, with whom you can discuss academic queries at regular intervals during the study session.

You are required to complete two Assignments for this module, which will be marked by your tutor. Assignments are each worth 15% of your total mark. You will be expected to submit your first assignment by the Tuesday of Week 6, and the second assignment at the end of the module, on the Tuesday after Week 10. Assignments are submitted and feedback given online. In addition, queries and problems can be answered through the Virtual Learning Environment.

You will also sit a three-hour examination on a specified date in September/October, worth 70% of your total mark. An up-to-date timetable of examinations is published on the website in July each year.

Study resources

• Study guide: The module study guide is carefully structured to provide the main teaching, defining and exploring the main concepts and issues, locating these within current debate and introducing and linking the assigned readings.
• Key text: Jeffrey M Wooldridge (2020) Introductory Econometrics. 7th Edition. Boston MA: Cengage.
• Software: This module will use R. This is a widely used programming environment for data analysis and graphics. You will use this software to do the exercises in the units, and also the data analysis part of your assignments. The results presented in the units are also from R.
• Exercises: There are exercises in every unit. Many of these exercises require you to work with R and data files, available from the VLE, to do your own econometric analysis.
• Virtual learning environment: You will have access to the VLE, a web-accessed study centre. Via the VLE, you can communicate with your assigned academic tutor, administrators and other students on the module using discussion forums. The VLE also provides access to the module Study Guide and assignments, as well as a selection of electronic journals available on the University of London Online Library.

Study calendar 2022/23

Study calendars are subject to change.

Module overview

Unit 1 Dummy Variables

• 1.1 Ideas and Issues
• 1.2 The Use of Dummy Variables
• 1.3 The Chow Test for Parameter Stability
• 1.4 Unit Study Guide
• 1.5 Example – Long-Term Trends in Terms of Trade
• 1.6 Conclusion
• 1.7 Exercises
• 1.8 Answers to Exercises

Unit 2 Dynamic Models – Lags and Expectations

• 2.1 Ideas and Issues
• 2.2 Lags
• 2.3 Expectations
• 2.4 Properties of OLS Estimators
• 2.5 Causality – The Granger Test
• 2.6 Unit Study Guide
• 2.7 Example – Long-Term and Short-Term Interest Rates
• 2.8 Conclusion
• 2.9 Exercises
• 2.10 Answers to Exercises

Unit 3 Simultaneous Equation Models

• 3.1 Ideas and Issues
• 3.2 Unit Study Guide
• 3.3 Example – The Polak Model
• 3.4 Conclusion
• 3.5 Exercises
• 3.6 Answers to Exercises

Unit 4 The Identification Problem

• 4.1 Ideas and Issues
• 4.2 Unit Study Guide
• 4.3 Example – Bid–Ask Spreads and Trading Activity in Options
• 4.4 Conclusion
• 4.5 Exercises
• 4.6 Answers to Exercises
• Appendix – Estimates of Moore’s 1914 Model

Unit 5 Simultaneous Equation Models – Estimation

• 5.1 Ideas and Issues
• 5.2 Unit Study Guide
• 5.3 Example – Stock Market Returns and Bond Yields
• 5.4 Conclusion
• 5.5 Exercises
• 5.6 Answers to Exercises

Unit 6 Univariate Time Series – Stationarity and Nonstationarity

• 6.1 Ideas and Issues
• 6.2 Stationary and Nonstationary Time Series
• 6.3 Integrated and Trend Stationary Series
• 6.4 The Nature of Financial Data
• 6.5 Correlograms
• 6.6 Unit Root Tests
• 6.7 Examples – Simulated Series
• 6.8 Example – Exchange rate US$ to UK£
• 6.9 A Procedure for Unit Root Tests
• 6.10 Conclusion
• 6.11 Exercises
• 6.12 Answers to Exercises

Unit 7 Multivariate Time Series Analysis

• 7.1 Ideas and Issues
• 7.2 The Engle–Granger Approach
• 7.3 Error Correction Models
• 7.4 The Johansen Approach
• 7.5 Example – The Single Index Model
• 7.6 Example – UK Financial Markets
• 7.7 Conclusion
• 7.8 Exercises
• 7.9 Answers to Exercises
• Appendix – 0.05 Critical Values: Unit Root and Engle–Granger Cointegration Tests

Unit 8 Forecasting

• 8.1 Ideas and Issues
• 8.2 Example – Forecasting Earnings
• 8.3 Conclusion
• 8.4 Exercises
• 8.5 Answers to Exercises

Disclaimer

Important notice regarding changes to programmes and modules

This module provides an introduction to econometric methods. In brief, the module examines how we can start from relationships suggested by financial and economic theory, formulate those relationships in mathematical and statistical models, estimate those models using sample data, and make statements based on the parameters of the estimated models. The module examines the assumptions that are necessary for the estimators to have desirable properties, and the assumptions necessary for us to make statistical inference based on the estimated models. In addition, the module explores what happens when these assumptions are not satisfied, and what we can do in these circumstances. The module concludes with an examination of model selection.

We recommend that you take this module before progressing onto the more advanced econometrics module Econometric Analysis and Applications.

Learning outcomes

After studying this module you will be able to:

• explain the principles of regression analysis
• discuss the assumptions of the classical normal linear regression model
• explain the method of ordinary least squares
• produce and interpret plots of data
• estimate a regression equation, and interpret the results, for bivariate (two-variable) regression models and multiple regression models
• test hypotheses concerning model parameters
• assess the consequences of multicollinearity
• discuss the consequences of heteroscedasticity for the properties of OLS estimators
• assess the methods used to identify heteroscedasticity, and the various techniques to deal with heteroscedasticity
• discuss the consequences of autocorrelated disturbances for the properties of OLS estimators
• outline and discuss the methods used to identify autocorrelated disturbances, and what can be done about it
• assess the consequences of disturbance terms not being normally distributed, tests for nonnormal disturbances, and methods to deal with non-normal disturbances
• examine the consequences of specifying equations incorrectly
• discuss the tests used to identify correct model specification, and statistical criteria for choosing between models.

Tuition and assessment

Students are individually assigned an academic tutor for the duration of the module, with whom you can discuss academic queries at regular intervals during the study session.

You are required to complete two Assignments for this module, which will be marked by your tutor. Assignments are each worth 15% of your total mark. You will be expected to submit your first assignment by the Tuesday of Week 6, and the second assignment at the end of the module, on the Tuesday after Week 10. Assignments are submitted and feedback given online. In addition, queries and problems can be answered through the Virtual Learning Environment.

You will also sit a three-hour examination on a specified date in September/October, worth 70% of your total mark. An up-to-date timetable of examinations is published on the website in July each year.

Study resources

• Study guide: The module study guide is carefully structured to provide the main teaching, defining and exploring the main concepts and issues, locating these within current debate and introducing and linking the assigned readings.
• Key texts: Wooldridge JM (2020) Introductory Econometrics. 7^th Edition. Boston MA: Cengage.
• Econometric software: This module will use R. This is a widely used programming environment for data analysis and graphics. You will use this software to do the exercises in the units, and also the data analysis part of your assignments. The results presented in the units are also from R.
• Virtual learning environment: You will have access to the VLE, a web-accessed study centre. Via the VLE, you can communicate with your assigned academic tutor, administrators and other students on the module using discussion forums. The VLE also provides access to the module Study Guide and assignments, as well as a selection of electronic journals available on the University of London Online Library.

Study calendar 2022/23

Study calendars are subject to change.

Module overview

Unit 1 An Introduction to Econometrics and Regression Analysis

• 1.1 What is Econometrics?
• 1.2 How to Use the Module Units
• 1.3I deas – The Concept of Regression
• 1.4 Study Guide
• 1.5 An Example – Efficiency in the Foreign Exchange Market
• 1.6 Conclusion
• 1.7 Working with R
• 1.8 Exercises
• 1.9 Answers to Exercises

Unit 2 The Classical Linear Regression Model

• 2.1 Ideas and Issues
• 2.2 Study Guide
• 2.3 Example – the Single-Index Model (SIM)
• 2.4 Conclusion
• 2.5 Exercises
• 2.6 Answers to Exercises
• Appendix 2.1: Derivation of OLS estimators

Unit 3 Hypothesis Testing

• 3.1 Ideas and Issues
• 3.2 Study Guide
• 3.3 Example – The Capital Asset Pricing Model
• 3.4 Conclusion
• 3.5 Exercises
• 3.6 Answers to Exercises

Unit 4 The Multiple Regression Model

• 4.1 Ideas and Issues
• 4.2 Study Guide
• 4.3 Example – A Multi-index Model
• 4.4 Conclusion
• 4.5 Exercises
• 4.6 Answers to Exercises

Unit 5 Heteroscedasticity

• 5.1 Ideas and Issues
• 5.2 Study Guide
• 5.3 Example – Price-Earnings Ratio
• 5.4 Conclusion
• 5.5 Exercises
• 5.6 Answers to Exercises

Unit 6 Autocorrelation

• 6.1 Ideas and Issues
• 6.2 Study Guide
• 6.3 Example – The Single-Index Model
• 6.4 Conclusion
• 6.5 Exercises
• 6.6 Answers to Exercises

Unit 7 Nonnormal Disturbances

• 7.1 Ideas and Issues
• 7.2 Study Guide
• 7.3 Examples
• 7.4 Conclusion
• 7.5 Exercises
• 7.6 Answers to Exercises
• Appendix 7.1: Small-Sample Critical Values for the Jarque-Bera Test
• Appendix 7.2: Stock Market Indices

Unit 8 Model Selection and Module Summary

• 8.1 Ideas and Issues
• 8.2 Study Guide
• 8.3 Example: Stock Returns
• 8.4 Conclusion
• 8.5 Exercises
• 8.6 Answers to Exercises
• 8.7 Module Summary: ‘What you do and do not know’

Module samples

• M430 Module Introduction (PDF)
• M430 Specimen Examination (PDF)
• M430 Unit 1 (PDF)

Disclaimer

Important notice regarding changes to programmes and modules

Welcome to the module on Financial Econometrics. The first objective of this module is to introduce the main econometric methods and techniques used in the analysis of issues related to finance. A module with the title Financial Econometrics assumes that such a field exists.

In this module, we define financial econometrics as ‘the application of statistical techniques to problems in finance’. Although econometrics is often associated with analysing economics problems such as economic growth, consumption and investment, the applications in the areas of finance have grown rapidly in the last few decades.

Before starting this module, we recommend that you first complete the modules Econometric Principles and Data Analysis and Econometric Analysis and Applications.

Learning outcomes

By the end of this module you will be able to:

• define and compute measures of financial returns
• interpret sample moments of financial returns
• discuss the stylised statistical properties of asset returns
• formulate models using matrix notation
• derive the OLS estimators using matrix algebra
• use matrix algebra to analyse sources of variation of risk
• explain the principles of maximum likelihood estimation
• derive the maximum likelihood estimators and discuss their properties
• use maximum likelihood estimation, and apply the hypothesis tests available under maximum likelihood estimation
• analyse and estimate models of autoregressive, moving average, and autoregressive-moving average models
• forecast using AR, MA, and ARMA models
• apply the Box-Jenkins approach to time series models
• model and forecast volatility using autoregressive conditional heteroscedastic (ARCH) models
• estimate, interpret, and forecast with generalised autoregressive conditional heteroscedastic (GARCH) models
• extend GARCH models to analyse the asymmetric effect of shocks on volatility
• construct, estimate and interpret multivariate GARCH models
• test for spill-over of volatility between assets
• use vector autoregressive (VAR) models to analyse and interpret interaction between financial variables
• examine the impact of shocks on financial variables using impulse response analysis
• undertake tests of hypotheses and Granger causality in a VAR framework
• formulate limited dependent variable models, including logit and probit models
• estimate and interpret logit and probit models
• discuss models with multinomial linear dependent variables.

Tuition and assessment

Students are individually assigned an academic tutor for the duration of the module, with whom you can discuss academic queries at regular intervals during the study session.

You are required to complete two Assignments for this module, which will be marked by your tutor. Assignments are each worth 15% of your total mark. You will be expected to submit your first assignment by the Tuesday of Week 6, and the second assignment at the end of the module, on the Tuesday after Week 10. Assignments are submitted and feedback given online. In addition, queries and problems can be answered through the Virtual Learning Environment.

You will also sit a three-hour examination on a specified date in September/October, worth 70% of your total mark. An up-to-date timetable of examinations is published on the website in July each year.

Study resources

• Study guide: The module study guide is carefully structured to provide the main teaching, defining and exploring the main concepts and issues, locating these within current debate and introducing and linking the assigned readings.
• Key texts: Brooks C (2019) Introductory Econometrics for Finance. 4th Edition. Cambridge UK: Cambridge University Press.
• Econometric software: This module will use R. This is a widely used programming environment for data analysis and graphics. You will use this software to do the exercises in the units. The results presented in the units are also from R.
• Readings: You will receive access to a selection of key academic articles which apply the techniques studied in the module to financial data.
• Virtual learning environment:  You will have access to the VLE, a web-accessed study centre. Via the VLE, you can communicate with your assigned academic tutor, administrators and other students on the module using discussion forums. The VLE also provides access to the module Study Guide and assignments, as well as a selection of electronic journals available on the University of London Online Library.

Study calendar 2022/23

Study calendars are subject to change.

Module overview

Unit 1 Statistical Properties of Financial Returns

• 1.1 Introduction
• 1.2 Calculation of Asset Returns
• 1.3 Stylised Facts about Financial Returns
• 1.4 Distribution of Asset Returns
• 1.5 Time Dependency
• 1.6 Linear Dependency across Asset Returns

Unit 2 Matrix Algebra, Regression and Applications in Finance

• 2.1 Introduction
• 2.2 Matrix Algebra: Some Basic Concepts and Applications
• 2.3 OLS Regression Using Matrix Algebra
• 2.4 Applications to Finance

Unit 3 Maximum Likelihood Estimation

• 3.1 Introduction
• 3.2 The Maximum Likelihood Function: Some Basic Ideas and Examples
• 3.3 The Maximum Likelihood Method: Mathematical Derivation
• 3.4 The Information Matrix
• 3.5 Usefulness and Limitations of the Maximum Likelihood Estimator
• 3.6 Hypothesis Testing

Unit 4 Univariate Time Series and Applications to Finance

• 4.1 Introduction
• 4.2 The Lag Operator
• 4.3 Some Key Concepts
• 4.4 Wold's Decomposition Theory (Optional section)
• 4.5 Properties of AR Processes
• 4.6 Properties of Moving Average Processes
• 4.7 Autoregressive Moving Average (ARMA) Processes
• 4.8 The Box-Jenkins Approach
• 4.9 Example: A Model of Stock Returns
• 4.10 Conclusions

Unit 5 Modelling Volatility – Conditional Heteroscedastic Models

• 5.1 Introduction
• 5.2 ARCH Models
• 5.3 GARCH Models
• 5.4 Estimation of GARCH Models
• 5.5 Forecasting with GARCH Model
• 5.6 Asymmetric GARCH Models
• 5.7 The GARCH-in-Mean Model
• 5.8 Conclusions

Unit 6 Modelling Volatility and Correlations – Multivariate GARCH Models

• 6.1 Introduction
• 6.2 Multivariate GARCH Models
• 6.3 The VECH Model
• 6.4 The Diagonal VECH Model
• 6.5 The BEKK Model
• 6.6 The Constant Correlation Model
• 6.7 The Dynamic Correlation Model
• 6.8 Estimation of a Multivariate Model

Unit 7 Vector Autoregressive Models

• 7.1 Introduction
• 7.2 Vector Autoregressive Models
• 7.3 Issues in VAR
• 7.4 Hypothesis Testing in VAR
• 7.5 Example: Money Supply, Inflation and Interest Rate

Unit 8 Limited Dependent Variable Models

• 8.1 Introduction
• 8.2 The Linear Probability Model
• 8.3 The Logit Model
• 8.4 The Probit Model
• 8.5 Estimation using Maximum Likelihood
• 8.6 Goodness of Fit Measures
• 8.7 Example: Dividends, Growth and Profits
• 8.8 Multinomial Linear Dependent Variables
• 8.9 Ordered Response Linear Dependent Variable Models (optional section)

Module samples

• M459 Module introduction (PDF)
• M459 Specimen examination (PDF)
• M459 Unit 1 (PDF)

Disclaimer

Important notice regarding changes to programmes and modules

Welcome to this module on Financial Engineering. The module provides an introduction to the analysis of derivatives in financial markets. You will learn the main features of the most commonly used financial derivatives, and you will understand how to use them for the management of risk.

These units explain and discuss the theoretical models that are used to analyse derivatives, and you will also see how derivatives are used in practice. You will study spreadsheet models of derivatives, analysing the performance and valuation of derivatives contracts and trading strategies, starting with the simplest options, and extending to more complex strategies and derivatives contracts. These spreadsheet models will help you to develop a deeper and stronger understanding of derivatives and how they work.

This module focuses on the conceptual and analytical aspects of derivatives. After studying this module, you will be able to understand the main characteristics of derivatives, the potential for using derivatives to manage risk, and you should be able to avoid some of the more serious misunderstandings and mistakes associated with using derivatives. The module is not a substitute for the professional expertise that can only be acquired by directly working in financial markets. But you will find that a solid grounding in the principles of derivatives will enable you to understand much better the practical aspects of derivatives investment and risk management.

The module is concerned with financial engineering as the application of statistical and mathematical methods to analyse and use derivatives in financial markets. The term ‘financial engineering’ also refers to the manipulation of the capital structure of a company to attempt to increase shareholder value. Financial engineering in relation to capital structure is studied in the CeFiMS modules Corporate Finance and Introduction to Valuation.

Learning outcomes

When you have completed your study of this module, you will be able to:

• analyse advanced derivative trading strategies for hedging and speculation
• understand the Black–Scholes–Merton model and its applications
• calculate delta and other measures of sensitivity
• discuss volatility, and strategies for trading volatility
• assess the role of credit derivatives in risk management
• apply advanced numerical techniques for valuing complex options
• construct and use spreadsheet models to analyse derivatives.

Tuition and assessment

Students are individually assigned an academic tutor for the duration of the module, with whom you can discuss academic queries at regular intervals during the study session.

You are required to complete two Assignments for this module, which will be marked by your tutor. Assignments are each worth 15% of your total mark. You will be expected to submit your first assignment by the Tuesday of Week 6, and the second assignment at the end of the module, on the Tuesday after Week 10. Assignments are submitted and feedback given online. In addition, queries and problems can be answered through the Virtual Learning Environment.

You will also sit a three-hour examination on a specified date in September/October, worth 70% of your total mark. An up-to-date timetable of examinations is published on the website in July each year.

Study resources

• Study guide: The module study guide is carefully structured to provide the main teaching, defining and exploring the main concepts and issues, locating these within current debate and introducing and linking the assigned readings.
• Key texts: Hull JC (2018) Options, Futures, and Other Derivatives. 9th Edition. Harlow UK: Pearson Education.
  Benninga S (2014) Financial Modeling. 4th Edition. Cambridge MA: The MIT Press.
• Virtual learning environment: You will have access to the VLE, a web-accessed study centre. Via the VLE, you can communicate with your assigned academic tutor, administrators and other students on the module using discussion forums. The VLE also provides access to the module Study Guide and assignments, as well as a selection of electronic journals available on the University of London Online Library.

Study calendar 2022/23

Study calendars are subject to change.

Module overview

Unit 1 Derivatives Contracts

• 1.1 Introduction
• 1.2 Forward Contracts
• 1.3 Futures Contracts
• 1.4 Options
• 1.5 Types of Traders
• 1.6A ‘Health Warning’
• 1.7 Application: Data tables
• 1.8 Conclusion
• 1.9 Solutions to Exercises

Unit 2 Properties of Stock Options

• 2.1 Introduction
• 2.2 Options
• 2.3 Stock Options
• 2.4 Warrants, Employee Stock Options and Convertibles
• 2.5 Basics of Pricing Stock Options
• 2.6 Trading Strategies Involving Options
• 2.7 Application: Profit Patterns for Options and Option Strategies
• 2.8 Conclusion
• 2.9 Solutions to Exercises

Unit 3 The Behaviour of the Stock Price and the Black–Scholes–Merton Model

• 3.1 Introduction
• 3.2 The Wiener Process
• 3.3 The Behaviour of Stock Prices
• 3.4 Itô’s Lemma
• 3.5 The Lognormal Property of Stock Prices
• 3.6 The Black–Scholes–Merton Equation and the Black–Scholes–Merton Formula
• 3.7 Application 1: Simulating a lognormal process
• 3.8 Application 2: Black–Scholes–Merton option pricing
• 3.9 Conclusion
• 3.10 Solutions to Exercises

Unit 4 Greek Letters and Trading Strategies

• 4.1 Introduction
• 4.2 Naked and Covered Positions
• 4.3 Delta Δ Hedging
• 4.4 Theta Θ
• 4.5 Gamma Γ
• 4.6 Vega v
• 4.7 Rho Ρ
• 4.8 Hedging and Portfolio Insurance
• 4.9 Application 1: Delta Hedging a Call
• 4.10 Application 2: VBA Code for Option Pricing and the Greeks
• 4.11 Conclusion
• 4.12 Solutions to Exercises

Unit 5 Volatility

• 5.1 Introduction
• 5.2 Implied Volatility
• 5.3 Volatility Smiles
• 5.4 Trading Volatility
• 5.5 Application 1: Computing implied volatility
• 5.6 Application 2: Options strategies
• 5.7 Conclusion
• 5.8 Solutions to Exercises

Unit 6 Credit Derivatives and Credit Risk

• 6.1 Introduction
• 6.2 Credit Ratings and Default Probabilities
• 6.3 Mitigation of Credit Risk and Default Correlation
• 6.4 Credit Default Swaps
• 6.5 Asset-Backed Securities and Collateralised Debt Obligations
• 6.6 Correlation and the Gaussian Copula
• 6.7 Application: Calculating Default-adjusted Expected Bond Returns
• 6.8 Conclusion
• 6.9 Solutions to Exercises

Unit 7 Further Numerical Procedures

• 7.1 Introduction
• 7.2 Binomial Trees
• 7.3 Alternative Procedures for Constructing Trees
• 7.4 Monte Carlo Simulations
• 7.5 Finite Difference Methods
• 7.6 Alternatives to Black–Scholes–Merton
• 7.7 Stochastic Volatility Models
• 7.8 American Options
• 7.9 Application 1: Binomial Trees
• 7.10 Application 2: Pricing a Simple Call Option Using Monte Carlo Methods
• 7.11 Conclusion
• 7.12 Solutions to Exercises

Unit 8 Some Exotic Options

• 8.1 Introduction
• 8.2 Exotic Options
• 8.3 Barrier, Binary and Lookback Options
• 8.4 Asian Options
• 8.5 Some Other Exotic Options
• 8.6 Weather and Energy Derivatives
• 8.7 Insurance Derivatives
• 8.8 Application 1: Asian Options
• 8.9 Application 2: Barrier Options
• 8.10 Conclusion
• 8.11 Solutions to Exercises

Module samples

• M482 Module Introduction (PDF)
• M482 Specimen Examination (PDF)
• M482 Unit 1 (PDF)

Disclaimer

Important notice regarding changes to programmes and modules

Welcome to the module Modelling Firms and Markets – an introduction to the economics of information and uncertainty. Multi-person decision problems under uncertainty have always played a crucial role in financial markets. For instance, if you buy a stock in a firm, your profit will depend on whether or not its market goes up. To understand decision-making processes and find their possible solutions in real-world problems (such as contracts, mechanisms, bank runs, etc.) you first need to learn how to think strategically. For this, you need to understand some basic and standard market problems among players.

Learning outcomes

By the end of this module you will be able to:

• explain the basic equilibrium concepts such as Nash equilibrium (pure and mixed)
• apply theNash equilibrium in oligopoly competition (Cournot & Bertrand)
• solve simple repeated games using backward induction and define subgame perfect equilibrium
• identify the concept of a Bayesian game and find its equilibrium
• define perfect Bayesian equilibrium and explain the signaling problem
• apply the concepts of adverse selection and moral hazard in different microeconomic contexts and explain how risk and information asymmetry affect the efficiency of contracting
• discuss the role of incentives and optimal contracting in addressing this issue related to asymmetric information
• outline and discuss the various types of auctions and the revenue equivalence principle
• derive the general equilibrium of specific economies.

Tuition and assessment

Students are individually assigned an academic tutor for the duration of the module, with whom you can discuss academic queries at regular intervals during the study session.

You are required to complete two Assignments for this module, which will be marked by your tutor. Assignments are each worth 15% of your total mark. You will be expected to submit your first assignment by the Tuesday of Week 6, and the second assignment at the end of the module, on the Tuesday after Week 10. Assignments are submitted and feedback given online. In addition, queries and problems can be answered through the Virtual Learning Environment.

You will also sit a three-hour examination on a specified date in September/October, worth 70% of your total mark. An up-to-date timetable of examinations is published on the website in July each year.

Study resources

• Study guide: The module study guide is carefully structured to provide the main teaching, defining and exploring the main concepts and issues, locating these within current debate and introducing and linking the assigned readings.
• Key texts: 
  • Gibbons R (1992) A Primer in Game Theory. Harvester Wheatsheaf.
  • Campbell DE (2018) Incentives: Motivation and the Economics of Information. 3rd Edition. Cambridge University Press.
• Readings: Throughout the module you will be directed to study a selection of readings, including journal articles, book extracts and case studies that are of particular relevance and interest to the topics covered in the module.
• Virtual learning environment: You will have access to the VLE, a web-accessed study centre. Via the VLE, you can communicate with your assigned academic tutor, administrators and other students on the module using discussion forums. The VLE also provides access to the module Study Guide and assignments, as well as a selection of electronic journals available on the University of London Online Library.

Study calendar 2022/23

Study calendars are subject to change.

Module overview

Unit 1 Static Games of Complete Information

• 1.1 Normal (Strategic) Form Game and Iterated Deletion
• 1.2 Nash Equilibrium
• 1.3 Mixed-Strategy Nash Equilibrium
• 1.4 Existence of Nash Equilibrium
• 1.5 Applications of Nash Equilibrium
• 1.6 Conclusion

Unit 2 Dynamic Games of Complete Information

• 2.1 Dynamic Games of Complete and Perfect Information
• 2.2 Subgame Perfection – Generalisation of the Backwards Induction
• 2.3 Repeated Games

Unit 3 Static Games of Incomplete Information

• 3.1 Cournot Competition of Incomplete Information
• 3.2 Normal-Form Representation of Static Bayesian Games and Bayesian Nash Equilibrium
• 3.3 Applications
• 3.4 The Revalation Principle
• 3.5 Conclusion

Unit 4 Dynamic Games of Incomplete Information

• 4.1 Perfect Bayesian Equilibrium
• 4.2 Application
• 4.3 Refinements of Perfect Bayesian Equilibrium
• 4.4 Conclusion

Unit 5 Hidden Action (Moral Hazard)

• 5.1 Introduction
• 5.2 Examples of the Hidden Action Problems
• 5.3 Moral Hazard and Insurance
• 5.4 Principal–Agent Problem: the Model and Optimal Wage Contract
• 5.5 Conclusion

Unit 6 Hidden Characteristics (Adverse Selection)

• 6.1 Responding to Hidden Information – Price Discrimination
• 6.2 Sellers with Private Information – the Market for Lemons
• 6.3 Credit Rationing and the Stiglitz-Weiss Model
• 6.4 Bundling and Product Quality
• 6.5 Adverse Selection and Insurance
• 6.6 Conclusion

Unit 7 Auctions

• 7.1 Four Types of Auctions
• 7.2 Outcome Equivalence for Private Value Auctions
• 7.3 Sealed-Bid Auction
• 7.4 Revenue Equivalence
• 7.5 Common Value Auctions
• 7.6 Conclusion

Unit 8 General Competitive Equilibrium

• 8.1 General Equilibrium in a Pure Exchange Economy
• 8.2 The Arrow-Debreu Model
• 8.3 The Fundamental Theorems of Welfare Economics
• 8.4 Externality
• 8.5 The Issue of Convexity
• 8.6 Common Property Resources
• 8.7 Conclusion

Module samples

• M458 Module Introduction (PDF)
• M458 Specimen Examination (PDF)
• M458 Unit 1 (PDF)

Disclaimer

Important notice regarding changes to programmes and modules

Welcome to this module on Risk Management: Principles and Applications. This module has four main aims, to:

• illustrate the main types of risk
• present the most important ideas and methods used in the analysis of portfolios of financial securities, including stocks and bonds
• explain how rational investors can use financial derivatives (mainly, futures and options) in order to alter the risk of their investment position
• illustrate some more specialised risk management techniques, such as Value at Risk and Credit Risk.

The emphasis throughout is on the general principles behind the investment decisions, rather than on case studies or anecdotal evidence. Thus, you will study, for instance,

• the main features of portfolios, which include stocks and bonds,
• how to calculate their risk, and
• how investors can combine their holdings of different securities to reduce their overall risk without sacrificing return.

Similarly, when you deal with futures and options, you will explore how these instruments can be used to manage risk and to expand the opportunity set of investors.

Learning outcomes

When you have completed this module, you will be able to:

• outline the most important strategies of risk management
• explain how stocks and bonds can contribute to the risk and return of a financial portfolio
• discuss the key principles of diversification of financial investment
• correctly measure the risk of financial portfolios
• explain the risk profile involved in financial derivatives, such as futures and options
• discuss the importance of Value at Risk and scenario analysis
• define and use the principles of credit risk analysis

Tuition and assessment

Students are individually assigned an academic tutor for the duration of the module, with whom you can discuss academic queries at regular intervals during the study session.

You are required to complete two Assignments for this module, which will be marked by your tutor. Assignments are each worth 15% of your total mark. You will be expected to submit your first assignment by the Tuesday of Week 6, and the second assignment at the end of the module, on the Tuesday after Week 10. Assignments are submitted and feedback given online. In addition, queries and problems can be answered through the Virtual Learning Environment.

You will also sit a three-hour examination on a specified date in September/October, worth 70% of your total mark. An up-to-date timetable of examinations is published on the website in July each year.

Study resources

Study guide: The module study guide is carefully structured to provide the main teaching, defining and exploring the main concepts and issues, locating these within current debate and introducing and linking the assigned readings.

Key texts: Elton EJ, Gruber MJ, SJ Brown & WN Goetzmann (2014) Modern Portfolio Theory and Investment Analysis. 9th Edition. John Wiley & Sons.
Hull JC (2017) Fundamentals of Futures and Options Markets. 9th Edition. Pearson
Crouhy M, D Galai & R Mark (2014) The Essentials of Risk Management. 2nd Edition. McGraw-Hill.

Virtual learning environment: You will have access to the VLE, which is a web-accessed study centre. Via the VLE, you can communicate with your assigned academic tutor, administrators and other students on the module using discussion forums. The VLE also provides access to the module Study Guide and assignments, as well as a selection of electronic journals available on the University of London Online Library.

Study calendar 2022/23

Study calendars are subject to change.

Module overview

Unit 1 Introduction to Risk Management

• 1.1 Introduction to Portfolio Analysis
• 1.2 Risks Faced by Financial and Non-financial Institutions
• 1.3 Financial Securities and Financial Markets
• 1.4 The Mean-Variance Approach
• 1.5 The Opportunity Set under Risk – Efficient Portfolios
• 1.6 Short Sales and Riskless Lending and Borrowing
• 1.7 How to Compute the Efficient Set
• 1.8 Conclusion

Unit 2 Portfolio Analysis

• 2.1 Introduction
• 2.2 The Single-Index Model
• 2.3 Methods for Estimating Betas
• 2.4 Fundamental Betas
• 2.5 Multi-Index Models
• 2.6 Fundamental Multi-Index Models
• 2.7 Conclusion

Unit 3 Management of Bond Portfolios

• 3.1 Introduction
• 3.2 Returns on Bonds
• 3.3 The Term Structure of Interest Rates
• 3.4 Default Risk and Callable Bonds
• 3.5 Duration
• 3.6 Convexity
• 3.7 Passive Bond Portfolio Management – Matching, Immunisation, Indexation
• 3.8 Active Bond Portfolio Management – Index Models
• 3.9 Active Bond Portfolio Management – Swaps
• 3.10 Conclusion

Unit 4 Futures Markets

• 4.1 Introduction
• 4.2 Description of Financial Futures
• 4.3 Pricing of Financial Futures
• 4.4 Futures Strategies
• 4.5 Examples of Using Futures
• 4.6 Interest Rate Futures
• 4.7 Currency Futures
• 4.8 Conclusion

Unit 5 Options Markets

• 5.1 Introduction
• 5.2 Features of Options Contracts
• 5.3 Options on Stocks and Futures
• 5.4 Risk Exposure and Profit Potential of Options and Futures
• 5.5 The Put-Call Parity Formula
• 5.6 Option Pricing – The Black-Scholes Formula
• 5.7 Pricing of Options on Futures
• 5.8 Price Volatility
• 5.9 Conclusion

Unit 6 Risk Management with Options

• 6.1 Introduction
• 6.2 Speculation with Options – Combinations of Calls and Puts
• 6.3 Hedging with Options – against a Price Increase
• 6.4 Hedging with Options – against a Price Decline
• 6.5 Sensitivities of Option Prices
• 6.6 Delta Hedging
• 6.7 The 2007 Credit Crisis and the Role of Derivatives
• 6.8 Conclusion

Unit 7 Value at Risk

• 7.1 Introduction
• 7.2 Definition of Value at Risk
• 7.3 Calculation of Value at Risk – the Variance-Covariance Approach
• 7.4 Delta-Normal VaR
• 7.5 Historical Simulations Approach
• 7.6 Incremental-VaR and DeltaVaR
• 7.7 Stress Testing and Scenario Analysis
• 7.8 Limitations of VaR – EVaR
• 7.9 Conclusion

Unit 8 Credit Risk

• 8.1 Introduction
• 8.2 Credit Rating Systems
• 8.3 Internal Risk Rating
• 8.4 CreditMetrics
• 8.5 Analysis of Credit Migration
• 8.6 Valuation of Bonds
• 8.7 Forward Distribution of Changes in the Value of Bonds
• 8.8 Credit VaR for a Bond or Loan Portfolio
• 8.9 Credit VaR and Calculation of Capital Charge
• 8.10 Conclusion

Module samples

• M423 Module Introduction (PDF)
• M423 Specimen Examination (PDF)
• M423 Unit 1 (PDF)

Disclaimer

Important notice regarding changes to programmes and modules