This course uses the case method to study the fundamentals of financial risk management. The course has two main objectives: the first is to cover techniques to identify measure and manage risk as modern financial market and regulation require. Specifically, topics of discussion will include dynamic hedging and portfolio replication, the development and advances of Value-at-Risk, management and measurement of interest rate risk, option price risk and credit risk. The second main objective of the course is to discuss different aspects of model risks and links to practical aspects of derivative pricing. Additionally, specific risks of financial instruments such as portfolio credit derivatives will be covered.

Class 1 1 Fundamentals and Building Blocks of Risk Management Systems 1.1 Instruments, Futures and Forwards, Swaps, Options 1.2 Hedging Strategies and Portfolio Replication 2 Indentifying, Measuring the Exposure to Financial Price Risk 2.1 Rationale for Risk Management 2.2 Portfolio Risk Management, Introduction to Value-at-Risk Class 2 2.2.2 Advances in Value-at-Risk, Extreme Value Theory and Expected Shortfall, Stress Testing 2.2.3 Application of Value-at-Risk 3 Market Risk 3.2 Interest Rate Risk, Yield Curve Risk 3.2.2 Pricing of Interest Rate Derivatives 3.2.3 Asset Liability Management 3.3 Other Market Risks Class 3 4 Credit Risk 4.2 Credit Risk Measurement, Measuring Exposure 4.2.2 Measuring Probability of Default (PD) and Loss Given Default (LGD) respectively Recovery Rate (RR) 4.2.3 Expected Loss and Unexpected Loss 4.2.4 Credit Value-at-Risk 4.3 Credit Derivatives Pricing (Single Name Instruments) Class 4 4.4 Credit Risk Mitigation 4.4.1 Portfolio Securitization 4.4.1.1 Instruments, Specific Risks 4.4.2 Pricing of Securitized Instruments (CDO s) 4.4.3 Credit Risk and Market Risk Correlation 4.4.3.1 Example of CDO²Pricing and Specific Risks 5 Model Risk 5.1 Definition of Model Risk, General Framework 5.2.1 Efficient Market Theory 5.2.1.1 Fundamentals 5.2.1.2 Advances in the Efficient Market Theory 5.2.1.3 Influence of Behavioral Science 5.2.2 Risk Neutral Pricing Class 5 5.3 Specific Model Risks 5.3.1 Distribution of Returns 5.3.1.1 Normal Distribution and Geometric Brownian Motion 5.3.1.2 Fat Tails and Empirical Distributions 5.3.2 Volatility Smile and Volatility Models 5.3.2.1 Constant/Implied Volatility 5.3.2.2 Dynamic Volatility Models GARCH 5.3.3 Correlation Models 5.3.3.1 Constant/Linear Correlation 5.3.3.2 Local/Stochastic Correlation 5.3.3.3 Single Factor Gauß Copula

Lecture will be held in English. After every class a case covering the topics discussed in class will be handed out and has to be prepared until the subsequent class. Every student has to hand in a maximum two page memorandum covering the main points of the case. Each memorandum has to be typed and double spaced. You can attach as many pages of calculation as you like. The memoranda will be part of the final grade of the course. The students are encouraged, but not required, to meet in groups to work on the cases and hand in group memoranda. However, a maximum of 4 people can be in the same group. After Class 5 there will be a take home case, which has to be prepared by each single student on its own. The deadline for submitting the take home case will be one months after the Class 5. The grading of the course will be based on the final take home case (60% of final grade), the four case memoranda (20% of final grade) and class participation (20% of final grade).

Optional Readings: Jorion P. Value at Risk, 3rd Edition, Mcgraw-Hill Professional, 2006 John C. Hull, Options, Futures and Other Derivatives, 7th Edition, Prentice Hall International, 2008 Darrell Duffie, Kenneth J Singleton, Credit Risk, Princeton University Press, 2003 Salih N. Neftci, An Introduction to the Mathematics of Financial Derviatives, 2nd Edition, Academic Press, 2000 Frank J. Fabozzi, The Handbook of Fixed Income Securities, 6th Edition, Mcgraw Hill, 2000 Philipp J. Schönbucher, Credit Derivatives pricing models, John Wiley & Sons Ltd, 2003 Alexander J. McNeil, Rüdiger Frey, Paul Embrechts, Quantitative Risk Management, Princeton University Press, 2005

Lehrveranstaltung: 105.101 Quantitative Methoden im Risikomanagement 105.155 AKFVM Bewertung von Zinsderivaten