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# MMath Mathematics and Statistics / Course details

Year of entry: 2021

## Course unit details:Statistical Modelling in Finance

Unit code MATH48191 15 Level 4 Semester 1 Department of Mathematics No

### 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.

### Pre/co-requisites

Unit title Unit code Requirement type Description
Probability 2 MATH20701 Pre-Requisite Compulsory
Statistical Methods MATH20802 Pre-Requisite Compulsory
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.

### 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.

### Syllabus

• Asset returns and log returns. Mean, variance, skewness, kurtosis, heavy tails. [3]
• Distributions with Pareto tails. Maximum likelihood estimation and inference. [3]
• Portfolio Theory. Risk versus expected return. The minimum variance portfolio. Efficient portfolios. Portfolios with a risk-free asset. Tangency portfolio and Sharpe ratio. [6]
• The Capital Asset Pricing Model. Estimation of Beta and testing of CAPM. [3]
• Factor models. The random walk model. Market efficiency and test [3]
• Value at risk and expected shortfall. [3]
• Time series of asset returns. Stationarity. Correlations and partial correlations. Tests of uncorrelatedness. Regression models with correlated errors. [3]
• State space models and Kalman filtering/smoothing. Dynamic linear models and time-varying betas in CAPM. [3]
• Volatility models and forecasting. [3]

### Assessment methods

Method Weight
Other 20%
Written exam 80%
• Coursework; two-week take-home assignment: 20%
• Written examination: 80%

### 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.

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.

### Study hours

Scheduled activity hours
Lectures 32
Tutorials 6
Independent study hours
Independent study 112

### Teaching staff

Staff member Role
Jingsong Yuan Unit coordinator