## Statistical Modelling in Finance

 Unit code: MATH48191 Credit Rating: 15 Unit level: Level 4 Teaching period(s): Semester 1 Offered by School of Mathematics Available as a free choice unit?: N

#### Requisites

Prerequisite

MATH48191 pre-requisites

Students 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.

#### Aims

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.

#### Overview

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.

#### Learning outcomes

On successful completion of the course, students will be able to:

• 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;
• formulate statistical models for returns data, find maximum likelihood estimators, and make inferences using fitted models;
• construct optimal portfolios with or without the presence of a risk-free asset and produce sketches of feasible region, efficient frontier, etc;
• evaluate value at risk and expected shortfall for a single asset/index and a portfolio of assets under various distributions and interpret the results;
• 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;
• formulate models in state space form and write down procedures of using the Kalman filter/smoother for maximum likelihood estimation/smoothing,
• derive properties of basic ARCH-type models and use fitted models to forecast volatility.

#### Assessment Further Information

End of semester examination: three hours weighting 80% plus 20% coursework.

#### Syllabus

• Characteristics of financial data. Mean, variance, skewness, kurtosis, heavy tails. [2]
• Distributions with Pareto tails. Maximum likelihood estimation and inference. [2]
• Correlation and dependence. Regression methods. [2]
• Asset returns. The random walk model. Market efficiency and tests. [3]
• Portfolio Theory. Risk versus expected return. The minimum variance portfolio. Efficient portfolios. [5]
• The Capital Asset Pricing Model. Estimation of Beta and testing of CAPM. Factor Models. [5]
• Value at risk. [3]
• Time series of asset returns. Stationarity. Estimation of variance and correlation. Tests of uncorrelatedness. Regression models with correlated errors. [3]
• State space models and Kalman filtering. Dynamic linear models and time-varying betas in CAPM. [4]
• Dynamic models of asset returns and volatility. [4]

• Lai TL and H Xing (2008). Statistical Models and Methods for Financial Markets. Springer. Available at http://rylibweb.man.ac.uk/cgi-bin/doip.pl?10.1007+978-0-387-77827-3.
• Ruppert D (2004). Statistics and Finance: An Introduction. Springer.

#### Feedback methods

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.

#### Study hours

• Lectures - 33 hours
• Tutorials - 11 hours
• Independent study hours - 106 hours

#### Teaching staff

Jingsong Yuan - Unit coordinator