Alexander McNeil

Quantitative Methods for Risk Management

Time and Place

SS 2004. Monday 11-12 and Thursday 10-12 in HG D7.2.

Target Audience

This course is an optional specialisation for students of the Master of Advanced Studies in Finance program and is designed with these students in mind; it is however open to all students who have the necessary background knowledge (see below).

Required Knowledge

This course will build on the course Empirical Methods for Finance in WS2003-04 and it will be assumed that students are familiar with the material in that course. This includes: standard methods of statistical inference; rudiments of multivariate analysis; univariate time series analysis (ARMA and GARCH).

The course will be taught in English.

Course Description

We look at mathematical and statistical methods for the problem of modelling market risk. Typically we consider a large portfolio, representing the position in risky assets of a financial institution or one of its sub-units, whose value is impacted by numerous underlying risk factors such as stock prices, exchange rates, interest rates and spreads. The problem is to estimate the loss distributiuon for a future time interval, such as a day or fortnight, and associated risk measures that describe the tail of the loss distribution. The statistical problems that arise require techniques in multivariate analysis, time series and extreme value theory. Of particular interest is the phenomenon of simultaneous extreme moves in many risk factors and the models that may be used to capture this behaviour.

In style the course will offer a combination of theory, statistical methods and practical examples with real data using S-Plus and S+FinMetrics.

Contents

Slides are downloadable by ETH students.
  1. Basics of Risk Management
  2. Standard Statistical Methods for Market Risk
  3. Multivariate Models for Risk Factors: Basics
  4. Multivariate Models: Normal Mixtures and Elliptical Distributions
  5. Financial Time Series
  6. Conditional Risk Measurement
  7. Multivariate Time Series
  8. Copulas and Dependence
  9. Modelling Maxima and Worst Cases
  10. POT Method
  11. Advanced EVT

Practical Examples with S-Plus

A feature of the course will be the integration of practical examples using S-Plus and S+FinMetrics. This software is installed in the student computer rooms in E floor and is also available as part of the Neptun project for installation on students' own notebook computers.

It is intended that students should be able to reproduce the analyses demonstrated in the lecture room. For some of the scripts you will need my extra library of scripts known as QRMLib. For Windows version download the zipped file here, unpack in the library directory of Splus and attach using the commmand "library".
  1. Standard Methods for Market Risks
  2. Normal Mixtures Models (output only; this script cannot be run by students)
  3. Conditional Risk Measurement
  4. VAR (vector autoregressive) Models
  5. Multivariate GARCH
  6. Copulas
  7. Copula Fitting
  8. Modelling Maxima
  9. POT Method

Recommended Literature