ETH Zurich

Risk Management

This two-hour course is given by Prof. Dr. Paul Embrechts during the winter 2002/03. It is given in English.

Description: In this course, we discuss some of the main methodological issues underlying risk management in the financial industry. Topics treated include:
  1. Risk management: the basics
  2. Globally accepted risk principles
  3. Coherent risk measures
  4. Market risk: basic definitions
  5. The Greeks
  6. Computational issues
  7. Value-at-Risk and beyond
  8. Modelling extremal events
  9. Methodological issues underlying simulation techniques
  10. Implementation

Course material and selected literature: Students will be directed to selected papers which will be discussed during the course. The list of references below is just an indication of some of the relevant material; it does not constitute as it stands the course material and it is not a compulsory reading list. However, it can provide hints for interested students who want to deepen their knowledge in various areas. For more detailed information and links to additional material, please see Roger Kaufmann's risk management web page.

Grades: The grades for participants of the MAS Finance program will be based on a 30-minutes oral examination during the last week of the semester (February 5 or 7, 2003). Please contact Ms. Aline Strolz by email to sign up for the examination. The examinations will take place in the office of Prof. Dr. Paul Embrechts' office, HG G37.1.
Institutional background
Jorion (1996)
Steinherr (1998)
Pricing and hedging of derivatives with a view towards risk management
Basic books
Cox and Rubinstein (1985)
Hull (1997)
Medium level books, including an elementary introduction to stochastic calculus
Baxter and Rennie (1996)
Bingham and Kiesel (1998)
Björk (1998)
Lamberton and Lapeyre (1996)
Relatively advanced books
Musiela and Rutkowski (1997) (focus on term-structure models)
Karatzas and Shreve (1998) (focus on hedging under market frictions)
Surveys, with a focus on derivative asset analysis beyond Black-Scholes
Frey (1997)
Embrechts, Frey and Furrer (1998) (This paper contains also a discussion of recent advances in actuarial mathematics.)
Eberlein, Keller and Prause (1998)
The basics of VaR
Duffie and Pan (1997)
Riskmetrics (1995)
Dowd (1998)
Risk measures
Artzner, Delbaen, Eber and Heath (1997)
Artzner, Delbaen, Eber and Heath (1998)
Extreme value theory and risk management
Introductory articles
Embrechts, Resnick and Samorodnitsky (1998)
McNeil (1999)
Books
Embrechts, Klüppelberg and Mikosch (1997)
Research papers
McNeil and Frey (1998)
Danielsson and de Vries (1997)
McNeil (1998)
Econometrics and financial time series
Campbell, Lo and McKinlay (1997)
Bollerslev, Chou and Kroner (1992)
Pagan (1996)
Other
Rolski, Schmidli, Schmidt and Teugels (1999) (Relatively advanced introduction to actuarial mathematics)
Embrechts, McNeil and Straumann (1999) (Discusses various dependency concepts arising in risk-management)
Other VaR resources
We find the web-page http://www.gloriamundi.org/ extremely useful. Moreover we invite you to try the Riskometer under the Financial and Insurance Mathematics home page. This is also the starting point for exploring the finance-related web-sites at the ETH Zürich.
  1. P. Artzner, F. Delbaen, J. Eber and D. Heath (1997): "Thinking Coherently," RISK, 10 (November), 68-71.
  2. P. Artzner, F. Delbaen, J. Eber and D. Heath (1998): "Coherent Measures of Risk," preprint, forthcoming in Mathematical Finance, postscript and pdf-file available from http://www.math.ethz.ch/~delbaen/.
  3. M. Baxter and A. Rennie (1996): Financial Calculus. Cambridge University Press, Cambridge.
  4. N. Bingham and R. Kiesel (1998): Risk-Neutral Valuation. Springer.
  5. T. Björk (1998): Arbitrage Theory in Continuous Time. Oxford University Press, Oxford.
  6. T. Bollerslev, T. Chou and K. Kroner (1992): "ARCH Modelling in Finance: A Selective Review of Theory and Empirical Evidence," Journal of Econometrics, 52, 201-224.
  7. J. Campbell, A. Lo and A. McKinlay (1997): The Econometrics of Financial Markets. Princeton University Press, Princeton, New Jersey.
  8. J. Cox and M. Rubinstein (1985): Options Markets. Prentice Hall, Englewood Cliffs.
  9. J. Danielsson and C. de Vries (1997): "Tail index and quantile estimation with very high frequency data," Journal of Empirical Finance, 4, 241-257.
  10. K. Dowd (1998): Beyond Value at Risk: The New Science of Risk Management, Wiley Series in Financial Engineering. Wiley, New York.
  11. D. Duffie and J. Pan (1997): "An overview of Value at Risk," The Journal of Derivatives, Spring 1997, 7-49.
  12. E. Eberlein, U. Keller and K. Prause (1998): "New insights into smile, mispricing, and value at risk: the hyperbolic model," Journal of Business, 38, 371-405.
  13. P. Embrechts, R. Frey and H. Furrer (1999): "Stochastic Processes in Insurance and Finance," in Handbook of Statistics, vol. 18. North Holland, to appear, postscript-version available from http://www.mathematik.uni-leipzig.de/MI/frey/.
  14. P. Embrechts, C. Klüppelberg and T. Mikosch (1997): Modelling Extremal Events for Insurance and Finance. Springer, Berlin.
  15. P. Embrechts, A. McNeil and D. Straumann (1999): "Correlation and dependency in risk management: properties and pitfalls," preprint, ETH Zürich, postscript and pdf-version available from http://www.math.ethz.ch/~embrechts.
  16. P. Embrechts, S. Resnick and G. Samorodnitsky (1998): "Extreme Value Theory as a Risk Management Tool," preprint, ETH Zürich, forthcoming in North American Actuarial Journal; postscript-version available from http://www.math.ethz.ch/~embrechts.
  17. R. Frey (1997): "Derivative Asset Analysis in Models with Level-Dependent and Stochastic Volatility," CWI Quarterly, Amsterdam, 10, 1-34, postscript-version available from http://www.mathematik.uni-leipzig.de/MI/frey/.
  18. J. Hull (1997): Options, Futures and Other Derivatives, 3rd ed., Prentice Hall Int, Englewood Cliffs.
  19. P. Jorion (1996): Value at Risk: The New Benchmark for Controlling Market Risk. Irwin Professional Publishing.
  20. I. Karatzas and S. Shreve (1998): Methods of Mathematical Finance. Springer, Berlin.
  21. D. Lamberton and B. Lapeyre (1996): Introduction to Stochastic Calculus Applied to Finance. Chapman and Hall, London.
  22. A. McNeil (1998): "Calculating Quantile Risk Measures for Financial Return Series using Extreme Value Theory," preprint, ETH Zürich, postscript and pdf available from http://www.math.ethz.ch/~mcneil.
  23. A. McNeil (1999): "Extreme Value Theory for Risk Managers," preprint, ETH Zürich, soon available from http://www.math.ethz.ch/~mcneil.
  24. A. McNeil and R. Frey (1998): "Estimation of Tail-Related Risk Measures for Heteroscedastic Financial Time Series: an Extreme Value Approach," preprint, ETH Zürich, postscript and pdf-file available from http://www.mathematik.uni-leipzig.de/MI/frey/#publikationen.
  25. M. Musiela and M. Rutkowski (1997): Martingale Methods in Financial Modelling, Applications of Mathematics. Springer, Berlin.
  26. A. Pagan (1996): "The Econometrics of Financial Markets," Journal of Empirical Finance, 3, 15-102.
  27. T. Rolski, H. Schmidli, V. Schmidt and J. Teugels (1999): Stochastic Processes for Insurance and Finance. Wiley, Chichester.
  28. A. Steinherr (1998): Derivatives. The Wild Beast of Finance. Wiley, New York.
Time: Thursday, 13.15-15.00
Location: HG E1.1
First lecture:   October 24, 2002

Previous similar courses:
 Semester  Lecturer(s)
 Winter 2002/03  Prof. Dr. Paul Embrechts
 Winter 2000/01  Prof. Dr. Paul Embrechts
 Summer 1999  Prof. Dr. Paul Embrechts
 Prof. Dr. Rüdiger Frey
 Summer 1998  Prof. Dr. Paul Embrechts

Links to: Courses and Seminars, Finance and Insurance, RiskLab, MAS Finance
Please send comments and suggestions concerning this page to Uwe Schmock, e-mail: schmock@math.ethz.ch
Last update: September 2, 2003