Statistical Modelling in Finance

MATH48191 Statistical Modelling in Finance 15 Semester 1 Undergraduate Level 4 Jingsong Yuan Unit coordinator 1 FHEQ level (Framework for Higher Education Qualifications) ' Masters/Integrated Masters P4 ' European Credit Transfer & Accumulation System Rating : 7.5 This course unit is set up to support the finance pathway of the BSc in Mathematics and Statistics. No previous knowledge of finance is required. This course unit is set up to support the Financial Statistics pathway of the MSc in Statistics. No previous knowledge of finance is required. Students should gain an insight into statistical models and methods to fit financial data and assess risk. As a result they should be able to analyse financial data using statistical methods. On successful completion of the course, students will be able to:  <ul> <li> calculate values and derive statistical properties of returns and log returns from those of prices, portfolio returns from asset returns, and asset returns from market returns;</li> <li> formulate statistical models for returns data, find maximum likelihood estimators, and make inferences using fitted models;</li> <li> construct optimal portfolios with or without the presence of a risk-free asset and produce sketches of feasible region, efficient frontier, etc;</li> <li> evaluate value at risk and expected shortfall for a single asset/index and a portfolio of assets under various distributions and interpret the results;</li> <li> derive basic properties of stationary ARMA models, use them to identify correlation structures in regression models with correlated errors, fit such models and validate them;</li> <li> formulate models in state space form and write down procedures of using the Kalman filter/smoother for maximum likelihood estimation/smoothing,    </li> <li> derive properties of basic ARCH-type models and use fitted models to forecast volatility.  </li> </ul>    <ul> <li> Asset returns and log returns. Mean, variance, skewness, kurtosis, heavy tails. [3]    </li> <li> Distributions with Pareto tails. Maximum likelihood estimation and inference. [3]   </li> <li> Portfolio Theory. Risk versus expected return. The minimum variance portfolio. Efficient portfolios. Portfolios with a risk-free asset. Tangency portfolio and Sharpe ratio. [6]    </li> <li> The Capital Asset Pricing Model. Estimation of Beta and testing of CAPM. [3]     </li> <li> Factor models. The random walk model. Market efficiency and test [3]    </li> <li> Value at risk and expected shortfall. [3]</li> <li> Time series of asset returns. Stationarity. Correlations and partial correlations. Tests of uncorrelatedness. Regression models with correlated errors. [3]     </li> <li> State space models and Kalman filtering/smoothing. Dynamic linear models and time-varying betas in CAPM. [3]    </li> <li> Volatility models and forecasting. [3]</li> </ul> 0 Other 20% 1 Written exam 80% <ul> <li> Coursework; two-week take-home assignment: 20%</li> <li> Written examination: 80%</li></ul>   Feedback tutorials will provide an opportunity for students' work to be discussed and provide feedback on their understanding.  Coursework or in-class tests (where applicable) also provide an opportunity for students to receive feedback.  Students can also get feedback on their understanding directly from the lecturer, for example during the lecturer's office hour.   MATH20701 Probability 2 Pre-Requisite Compulsory MATH20802 Statistical Methods Pre-Requisite Compulsory MATH48191 pre-requisitesStudents are not permitted to take more than one of MATH38191 or MATH48191 for credit in the same or different undergraduate year. Students are not permitted to take MATH48191 and MATH68191 for credit in an undergraduate programme and then a postgraduate programme. BSc Maths with Financial Maths BSc (Hons) Maths w Fin Maths Fourth Year Optional BSc Maths with Financial Maths BSc (Hons) Maths w Fin Maths P Fourth Year Optional MMath Maths with Financl Maths MMath (Hons) Math w Fin Math Fourth Year Optional MMath (Hons) Mathematics MMath (Hons) Mathematics Fourth Year Optional MMath (Hons) Mathematics MMath (Hons) Mathematics w PY Fourth Year Optional MMath(Hons) Maths & Stats MMath(Hons) Maths & Stats Fourth Year Optional N Ruppert D (2010). Statistics and Data Analysis for Financial Engineering. Springer. Recommended.Lai TL and H Xing (2008). Statistical Models and Methods for Financial Markets. Springer. Recommended.Shumway RH and DS Stoffer (2011). Time Series Analysis and Its Applications: With R Examples. Springer. Recommended. Lectures 11 Tutorials 11 0 128 The independent study hours will normally comprise the following. During each week of the taught part of the semester:·         You will normally have approximately 75-120 minutes of video content. Normally you would spend approximately 2.5-4 hrs per week studying this content independently·         You will normally have exercise or problem sheets, on which you might spend approximately 2-2.5hrs per week·         There may be other tasks assigned to you on Blackboard, for example short quizzes, short-answer formative exercises or directed reading·         In some weeks you may be preparing coursework or revising for mid-semester testsTogether with the timetabled classes, you should be spending approximately 9 hours per week on this course unit.The remaining independent study time comprises revision for and taking the end-of-semester assessment.The above times are indicative only and may vary depending on the week and the course unit. More information can be found on the course unit’s Blackboard page.