1. 1 Modelling of scenarios for credit risk: establishing stress test methodologies European Central Bank Risk Management Division Strategy Unit Ken Nyholm November 20 th, 2006 The views presented here are not necessarily shared by the European Central Bank

2. 2 Outline Consistent, accountable and intuitive stress testing method under migration mode Risks: market and credit A modelling framework for yields, returns and portfolio losses An example

3. 3 Tail events are in focus

4. 4 Historical yield curve evolution in US

5. 5 Historical yield evolution in Japan

6. 6 Historical evolution of credit curves

7. 7 Generic yield curve shapes

8. 8 Framework specifications Design of the calculation “engine” must be: –Comprehensive enough to include all relevant systematic and stochastic components –General enough to allow for frequent re-calculations –Systematic in its treatment of risk factors –Flexible enough to answer stress-testing questions –In accordance with economic/financial theory and intuition

9. 9 A general design

10. 10 A general design Risk sources: –Market and Credit risk Scenario dependant: –Migration and default probabilities –Credit spreads –Asset correlations, recovery rates time horizon –Yield curve evolution: location and shapes –Yield curve and spread innovations (error-term variances) A keyword could be: regime switching

11. 11 The three basic building blocks Bond migration / credit state calculator –Time varying migration and default probabilities Regime switching yield curve model –Underlying yield curve factors are subject to regime switches –Yield for all credit grades are simulated in a consistent fashion Bond pricing module: – Combining the credit state, maturity and yield curve

12. 12 The three basic building blocks Intuition of the credit migration module –Allows for migration and default mode calculations –Relies on initial credit ratings of the assets Applies the following steps: –Generates correlated random numbers based on the assumed correlation structure among the obligors –Translates random numbers into ratings using a time- varying migration matrix to get t+1 rating for each obligor

13. 13 The three basic building blocks Intuition of the yield curve module: –Underlying factors drive yield curves –These factors are allowed to shift regime over time –Different future scenarios can hence be generated where yields and spreads vary according to chosen regimes –How to obtain yield curve factors? –One answer: the Nelson-Siegel model / parametric model How to create a link to the underlying factors? –Regime switches

14. 14 The modelling framework: Yield curve model

15. 15 The modelling framework: Yield curve model

16. 16 The modelling framework: Yield curve model

17. 17 The modelling framework: Yield curve model

18. 18 The modelling framework: Yield curve model

19. 19 The modelling framework: Yield curve model

20. 20 Current tools and techniques One possible scenario where the underlying/exogenous factors are set to be gdp and cpi growth:

21. 21 Current tools and techniques

22. 22 Bond pricing module A standard bond pricing equation is used And, returns are calculated as:

23. 23 Two scenarios: A portfolio of 30 obligors under migration mode Initial credit ratings from AAA to BB (md=2.0) One year horizon Scenario A: –Recovery 40% –Normal yield curve state for all periods –Average asset correlation: 0.20 Scenario B: –Recovery 20% –Averse yield scenario after 3 months –Average asset correlation: 0.40

24. 24 Scenario results

25. 25 Summary A scenario generation framework based on building blocks: –Facilitates extension of individual blocks separately –Straightforward to integration of new elements –Individual blocks can be used in other contexts Allows for inclusion of relevant time varying factors: –Yield curve and spread evolutions –Default and migration rates Intuitive and in accordance with economic theory