Introduction
The Financial Statistics stream of the MSc Statistics programme is mainly intended for students wishing to pursue careers in the finance industry or as a stepping stone towards PhD study in statistics for finance. Students will receive a thorough grounding in the theory and methods of statistical inference, the statistical analysis of time series as well as a selection of important concepts in statistical finance, such as financial time series, asset pricing and portfolio choice, and some aspects of continuous-time finance. Students will also learn to code in the R statistical computing environment. Optional modules from the Statistics, Finance and Economics departments (among others) will be available. The research branch of the Financial Statistics programme will be open to students wishing to take the dissertation option.
Entry Requirements
The normal entry requirement is an upper second class honours degree, or equivalent, with a significant mathematical content. Well-qualified applicants who do not meet this requirement will be considered on merit.
Course Structure
Our taught postgraduate courses are based around lectures, with problem classes and computer workshops. Most courses are assessed by a two-hour exam in the summer term although some contain an element of course work.
The courses in the programme are divided into two categories: compulsory courses and optional courses. Students must take courses to the value of four full units.
MSc in Statistics (Financial Statistics)
i. Three compulsory courses (two full units)
ii. Courses to the value of two full units from the following:
The maximum of one unit's worth of non-ST and non- MY courses is permitted.
Other non-ST course(s) may be taken, with permission.
MSc in Statistics (Financial Statistics) (Research)
Applicants have the option to register for the MSc in Statistics (Financial Statistics) (Research) branch of the programme in the first few weeks of the Michaelmas (Autumn) term. The research branch of the course involves a dissertation, completed over the year.
Students must take courses to the value of four full units.
i. Four compulsory courses (3 full units):
ii. Courses to the value of one full unit from the following:
The maximum of one unit's worth of non-ST courses is permitted.
Other non-ST course(s) may be taken, with permission.
Courses
Compulsory Courses
Core syllabus
A comprehensive coverage of fundamental aspects in probability and statistics. Data illustration using package R constitutes an integral part of the course, providing hands-on experience in simulation and data analysis.
Content
Random variables, Probability distributions, Probability inequality, Convergence of random variables, Point estimation, Hypothesis testing, Interval Estimation, Linear regression.
Core syllabus
A broad introduction to statistical time series analysis for postgraduates
Content
What time series analysis can be useful for; autocorrelation; stationarity; basic time series models: AR, MA, ARMA; trend removal and seasonal adjustment; invertibility; spectral analysis; estimation; forecasting. If time permits, we will also discuss some of the following topics: financial time series and the (G)ARCH model; nonstationarity; bivariate time series.
Core syllabus
An introduction to the theory and application of modern multivariate methods used in the Social Sciences.
Content
A selection from the following topics: cluster analysis, multi-dimensional scaling, principal components analysis, correspondence analysis, factor analysis, latent variable models, multivariate normal distribution, exponential family, and structural equations models.
Core syllabus
A broad introduction to stochastic processes for postgraduates with an emphasis on financial and actuarial applications.
Content
Martingales, Markov Chains, Poisson Processes, Brownian motion, stochastic differential equations and diffusion processes. Applications in Finance. Actuarial applications.
Core syllabus
Regression analysis and generalized linear modelling with an emphasis on diagnostics and the exponential family.
Content
One variable and multiple regression. Factorial design. Variable selection and model building. Deletion diagnostics. Transformation of the response, constructed variables. The use of R for data analysis. Exponential family and generalized linear models. Loglinear models, contingency tables, exact tests.
Core syllabus
A practical introduction to multilevel modelling with applications in social research.
Content
This course deals with the analysis of data from hierarchically structured populations (eg individuals nested within households or geographical areas) and longitudinal data. Multilevel (random-effects) extensions of standard statistical techniques, including multiple linear regression and logistic regression, will be considered. The course will have an applied emphasis with computer sessions using appropriate software (eg Stata).
Core syllabus
An introduction to the dynamics of non-linear deterministic systems with a practical focus, including case studies, of use of time series data in industry.
Content
Analysis and modelling of real data, involving an introduction to the dynamics of non-linear systems. Focus is on evaluating which methods to employ (linear/non-linear, deterministic/stochastic) in a given problem. Concrete applications in economics (electricity demand) and environment (weather derivatives) as well as analytically tractable illustrations.
Syllabus: Dynamics of nonlinear systems. Analysis and forecasting of nonlinear stochastic systems. Fractal dimensions and Lyapunov exponents. Concrete applications in forecasting electricity demand and pricing weather derivatives. Practical focus on the use of time series data in industry.
Core syllabus
Our aim is to teach students important statistical methodologies that reflect the exciting development of the subject over the last ten years, which include empirical likelihood, MCMC, bootstrap, local likelihood and local fitting, model Assessment and selection methods, boosting, support vector machines. These are computationally intensive techniques that are particularly powerful in analysing large-scale data sets with complex structure.
Content
A selection from the following topics. Robustness of likelihood approaches: distance between working model and "truth", maximum likelihood under wrong models, quasi-MLE, model selection with AIC, robust estimation. Empirical likelihood: empirical likelihood of mean. Bayesian methods and Markov chain Monte Carlo (MCMC) basic Bayes, Gibbs sampler, Metropolis-Hastings algorithm. Elements of statistical learning: global fitting versus local fitting, linear methods for regression, splines, kernel methods and local likelihood. Model Assessment and selection: bias-variance trade-off, effective number of parameters, BIC, cross-validation. Further topics: additive models, varying-coefficient linear models, boosting, neural network, support vector machines. The course will be continuously updated to reflect important new developments in statistics.
ST431.1 Life Insurance
Core syllabus
A self-contained, comprehensive introduction to life and pensions insurance mathematics based on the theory of stochastic processes, notably counting processes and their associated counting martingales. A variety of insurance schemes are analysed, ranging from the traditional participating policy to modern index-linked insurance with benefits dependent on prices of traded securities or other market indices. An introduction to statistical life history analysis is part of the course.
Content
The time continuous non-homogeneous Markov chain model for life histories and developments of life insurance policies. Extension to semi-Markov chains. Diffusion and jump process models for financial markets. Actuarial analysis of basic insurance products: life endowment, life annuity, life assurance, and disability insurance. Extension to the general multi-state policy. The participating policy; surplus and bonus. Index-linked benefits (unit-linked, salary-dependent and others). Pricing of embedded interest and mortality guarantees. Defined benefits v defined contributions. Risk minimization in the framework of theory of incomplete financial markets. Portfolio analysis of combined insurance risk and financial risk; solvency and market value of insurance companies. Pension funding. Statistical life history analysis.
ST431.2 Non-life Insurance
Core syllabus
This module covers the core matter of mathematical risk theory. It gives precise content to the notion of (insurable) risk and presents theories for how to mitigate and possibly eliminate such risk through insurance schemes and, at the level of the insurance companies, through reinsurance. Emphasis is on principles for pricing of insurance products and on solvency control of insurers.
Content
Axiomatic approach to ordering of risks; expected utility; optimal forms of insurance from the insured's and from the insurer's point of view, Pareto-optimal risk exchanges. Premium principles and ordering of risks (stop-loss, convex, and other orders). Ruin theory in various model scenarios including catastrophe risk and investment risk, with application to the issue of optimal reinsurance. Evaluation of total claims distributions for risk portfolios. Value at Risk (VaR). Claims reserving in non-life insurance - a marked point process approach.
ST432.1 Derivatives
Core syllabus
Valuation and hedging of derivative securities.
Content
General principles of mathematical finance. Asset price models. Option pricing by bilateral Laplace transforms as well as integro-partial differential equations. Utlilty indifference valuation. Minimal entropy martingale measures. Foellmer-Sondermann optimal hedging. Entropic hedging
ST432.2 Levy Finance
Core syllabus
Lévy processes with applications in finance.
Content
Lévy processes have stationary and independent increments. They form a surprisingly rich class of processes that comprises Brownian motion, compound Poisson processes, and a huge family of processes with omnipresent jumps. This course gives an introduction to the general theory of such processes and presents a number of special processes commonly used in modelling of financial data. The theory is applied to a range of topics in mathematical finance such as pricing and hedging of options, credit risk models, and interest rate models.
Core syllabus
The purpose of this course is to (a) develop the students' computational skills, (b) introduce a range of numerical techniques of importance in actuarial and financial engineering, and (c) develop the ability of the students to apply the theory from the taught courses to practical problems, work out solutions including numerical work, and to present the results in a written report.
Content
Binomial and trinomial trees. Random number generation, the fundamentals of Monte Carlo simulation and a number of related issues. Finite difference schemes for the solution of ordinary and partial differential equations arising in insurance and finance. Numerical solutions to stochastic differential equations and their implementation.The course ends with an introduction to guidelines for writing a scholarly report/thesis.
Core syllabus
Provides a thorough grounding in the theory of derivatives pricing and hedging.
Content
This course develops the theories of no-arbitrage asset pricing. Particular emphasis is placed on pricing within a multi-period, mostly continuous-time, framework. A special feature of the course is its coverage of the modern theory of contingent claims valuation by PDE and martingale methods. These asset pricing methods are applied to the pricing of vanilla and exotic options and corporate liabilities, forwards, futures, as well as fixed income derivatives. The uses of derivatives in hedging and risk-management are discussed as well
Core syllabus
This course is concerned with a mathematical development of the risk-neutral valuation theory.
Content
In the context of the binomial tree model for a risky asset, the course introduces the concepts of replication and martingale probability measures. The mathematics of the Black & Scholes methodology follow; in particular, the expression of European contingent claims as expectations with respect to the risk-neutral probability measure of the corresponding discounted payoffs, pricing formulae for European put and call options, and the Black & Scholes PDE are derived. A class of exotic options is then considered. In particular, pricing formulas for lookback and barrier options are derived using PDE techniques as well as the reflection property of the standard Brownian motion.
Core syllabus
This course is concerned with the mathematical foundations of interest rate and foreign exchange theory.
Content
The course starts with a development of the multi-dimensional Black & Scholes theory with stochastic market data. This is then used to show how discount bond dynamics modelling can be approached by (a) the modelling of the short-rate process and the market price of risk, which underlies the family of short-rate models, or (b) the modelling of the market price of risk and the discount bond volatility structure, which gives rise to the Heath-Jarrow-Morton (HJM) framework. The course then expands on the theory of interest rate market models, foreign exchange dynamics, and credit risk.
EC484 Econometric Analysis
Core syllabus
An advanced treatment of the theory of estimation and inference for econometric models.
Content
Part (a) Matrix background; symptotic statistical theory: modes of convergence, asymptotic unbiasedness, stochastic orders of magnitude, central limit theorems, applications to linear regression. Part (b) Non-linear-in variables systems: maximum likelihood and instrumental variables estimates, optimal instrumental variables estimates for static and dynamic models, and models with autocorrelated disturbances. Simultaneous equations systems, identification, estimation, asymptotic behaviour of estimators and hypothesis testing. Wald, generalised likelihood ratio and Lagrange multiplier hypothesis tests, asymptotic null and local behaviour and consistency.
Core syllabus
This course provides an introduction to the methodology of the design and analysis of social surveys. It is intended both for students who plan to design and collect their own surveys, and for those who need to understand and use data from existing large-scale surveys.
Content
Topics covered include basic ideas of target populations, survey estimation and inference, sampling error and nonsampling error; sample design and sampling theory; methods of data collection; survey interviewing; cognitive processes in answering survey questions; design and evaluation of survey questions; nonresponse error and imputation for item nonresponse; survey weights; analysis of data from complex surveys; accessing, preparing and working with secondary data from existing social surveys. The course includes computer classes, using the statistical computer package Stata; no previous knowledge of Stata is required.
Core Syllabus
This course provides an introduction to statistical methods used for causal inference in the social sciences.
Content
Using the potential outcomes framework of causality, topics covered include research designs such as randomized experiments and observational studies. We explore the impact of noncompliance in randomized experiments, as well as nonignorable treatment assignment in observational studies. To analyze these research designs, the methods covered include matching, instrumental variables, difference-in-difference, and regression discontinuity. Examples are drawn from different social sciences. The course includes computer classes, where standard statistical computer packages (Stata or R) are used for computation.
Core syllabus
The course will assume a knowledge of standard regression models, to the level covered in MI452. Please note that the exact topic changes every year.
Content
The aim of the course is to introduce students to advanced analytic methods frequently used in leading-edge social research.
OR406 Mathematical Programming: Theory and Algorithms (half-unit)
Core syllabus
To cover the use of mathematical programming models in practice, and an introduction to the theory and computational methods.
Content
As described under the headings of the lecture courses below.
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OR406.1 Foundations of Mathematical Programming: An introduction to the mathematical foundations of mathematical programming
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OR406.2 Mathematical Programming: Introduction to theory and the solution of linear and nonlinear programming problems: simplex and interior point algorithms, integer linear programming (ILP) methods (branch and bound, enumeration, cutting planes), decomposition methods, quadratic programming
Core syllabus
This course covers the basic principles and techniques of population analysis. Topics covered include the analysis of mortality, fertility, nuptiality, and migration, as well as the basic principles of population projection.
Content
The construction, interpretation, and uses of life tables. The measurement and analysis of fertility and birth intervals. Natural fertility and the proximate determinants of fertility, including Bongaarts' framework. Cohort and period approaches to measurement. Nuptiality and reproductivity. The basic measurement of migration. Component population projections. The use of models in demography.
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MA420 Quantifying Risk and Modelling Alternative Markets
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Core Syllabus
This course is concerned with various issues arising in the context of investment risk specification as well as with the mathematical theory of so-called alternative markets, such as commodity and energy markets.
Content
In particular, the course considers the structural credit risk models and the quantification of risk by means of copulas and risk measures. Also, the course expands on the modeling of alternative markets and addresses the problem of valuation of investments in real assets
Core syllabus
The course covers core topics in measure theoretic probability and modern stochastic calculus, thus laying a rigorous foundation for studies in statistics, actuarial science, financial mathematics, economics, and other areas where uncertainty is essential and needs to be described with advanced probability models. Emphasis is on probability theory as such rather than on special models occurring in its applications.
Content
Brief revision of mathematical tools: set theory, logics, techniques of proof, real and complex numbers, sequences, functions, metric spaces, notions of limits and convergence, continuity, differentiation and integration. Brief review of basic probability concepts in a measure theoretic setting: probability spaces, random variables, expected value, conditional probability and expectation, independence. Construction of probability spaces with emphasis on stochastic processes. Operator methods in probability: generating functions, moment generating functions, Laplace transforms, and characteristic functions.
Core syllabus
Independent project work on a subject chosen by the student.
Content
Subjects are chosen and a supervisor assigned by week eight of the Michaelmas term. Students meet with their project supervisor and write an outline of the project before the end of Lent term. Students then spend July, August and September working on their projects.
Further Information
For general information on the MSc programme and advice about academic requirements please email MSc Enquiries at mscstats@lse.ac.uk|.
For advice on your application please refer to the Frequently Asked Questions section of the Graduate Admissions| website.
MSc Statistics (Financial Statistics) brochure coming soon...