## Statistical Modelling in Finance

 Unit code: MATH68191 Credit Rating: 15 Unit level: Level 6 Teaching period(s): Semester 1 Offered by School of Mathematics Available as a free choice unit?: N

#### Requisites

None

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 analyse economic and financial data using statistical models. Emphasis will be placed on model fitting and interpretation.

#### 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