# Mathematical Approaches to Risk Management (MMath)

## Course summary

Course code: MATH1154
Level: 7
Credits: 15
School: Architecture, Computing and Hums
Department: Mathematical Sciences
Course Coordinator(s): Ana Paula Palacios

## Specification

### Pre and co requisites

Passing Level 6 of the MMath Mathematics or MMath Financial Mathematics programme

### Aims

Acquire knowledge of the building blocks of risk management, stylised facts of financial asset return and the distribution of minima, maxima and tail dependence.
Basic concepts of risk management, risk factors and their measures and credit & counterparty risk.
Acquire knowledge of time series models and volatility modelling and to be able to support decisions on model selection based on the quantifications.
Estimation of time series models, backtesting, and to acquire skills to work with intraday data.
To build knowledge around principal components, applications to term structure of interest rates; dependence measures and copulas.

### Learning outcomes

On successful completion of this course a student will be able to:

1. Quantify risk, work with conditional and unconditional loss distributions; use historical simulation, Monte Carlo and backtesting.

2. Acquire skills to specify, estimate, forecast and model equity and fixed income market returns.

3. Apply continuous-time models, infer realized variance, range-based volatility measures, improving volatility forecasts and VaR models with realized measures.

4. Have an appreciation and awareness of available tools for measuring and identifying risk, counterparty risk and credit default risk.

### Indicative content

Stylised facts, risk, Value-at-Risk, expected shortfall, coherent risk measures, univariate time series, non-normal distributions and extreme value theory, multivariate normal distribution, testing for normality, normal mixture distributions, Monte Carlo estimation and modelling, filtering of latent processes, GARCH models, realised volatility, market price of risk, Volatility and jump risk, Volatility indexes, copulas and mixture copulas.

### Teaching and learning activity

Concepts and techniques will be introduced and demonstrated in lectures and laboratory sessions.

### Assessment

Summative assessment: Coursework - 50%
LO - 1-4
Coursework covering all learning items, which may include selected tutorial exercises.

Summative assessment: Examination - 50%
LO - 1-4
Examination of 3 hours duration covering all learning outcomes.

Formative assessment: Weekly tutorial exercises