Alexander J. McNeil

Quantitative Risk Management I

Time and Place

WS 2005-06. Wednesday 15-16 in HG D7.2 and Thursday 15-17 in HG D1.2.

Target Audience

This course is mandatory for students of the Master of Advanced Studies in Finance program and is designed with these students in mind, but is open to all students.

Required Knowledge

Prior knowledge of probability and statistics at least at the level of a first university course in a quantitative discipline will be assumed. Masters students are certainly expected to be familiar with much of the content of the book "Mathematical Statistics and Data Analysis" by John A. Rice (see references below), and a detailed summary of the recommended preliminary reading from Rice is available.

The course will be taught in English.

Course Description

This course forms the first part of a one-year cycle and leads naturally into the SS06 course Quantitative Risk Management II held by P. Embrechts. Following these courses as a cycle is advisable.

The course is based in the book Quantitative Risk Management: Concepts, Techniques and Tools by Alexander J. McNeil, Rüdiger Frey and Paul Embrechts, published by Princeton University Press 2005. (Note that copies of this book may not be generally available in Switzerland until the end of November. The Polybuchhandlung has them on order.) The first chapter may be downloaded from PUP in the internet.

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

Risk in Perspective.
- risk, history of risk management, regulation, the nature of the challenge
Basic Concepts.
- risk factors and loss distributions, risk measures, standard methods
Multivariate Models.
- multivariate normal distribution, inference based on multivariate normal, normal mixture distributions, elliptical distributions, principal components, factor models
Financial Time Series.
- basic concepts, ARMA models, inference in time domain, GARCH models, conditional risk measurement, backtesting, multivariate GARCH

Slides

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 (see also Maths department Neptun page) for installation on students' own notebook computers.

It is intended that students should be able to reproduce the analyses demonstrated in the lecture room.The vast majority of the analyses could also be performed in R, although some of the more advanced functionality of S+FinMetrics for modelling financial time series will not be available.

For some scripts you will need the library QRMlib. Download and unzip the file in the S-Plus library directory.

Recommended Literature

1. General

McNeil, A.J. and Frey, R. and Embrechts, P. (2005). Quantitative Risk Management: Concepts, Techniques and Tools. Princeton University Press, Princeton. The course text.
Casella, G. and Berger, R.L. (2002). Statistical Inference; 2nd Edition. Duxbury, Pacific Grove, California. A modern introduction to mathematical statistics.

2. Multivariate Statistics

Mardia, K.V., Kent, J.T. & Bibby, J.M. (1995). Multivariate Analysis, Academic Press, Padstow, Cornwall. A standard reference for multivariate statistical analysis.

3. Time Series

Brockwell,P.J. & Davis,R.A. (2002, 2nd edition). Introduction to Time Series and Forecasting. Springer-Verlag, New York. The ideal introductory text for general theory and applications of time series.
Brockwell,P.J. & Davis,R.A. (1991, 2nd edition). Time Series: Theory and Methods. For those who want the full mathematics.

4. Econometric Models

Zivot,E. & Wang,J. (2002). Modeling Financial Time Series with S-Plus. Insightful + Springer Verlag, New York. Extremely useful book - highly recommended for this lecture course. Contains many relevant S-Plus examples.