1. Insurance and Financial Risk 1 Discussion: Insurance and Financial Risk M. Pilar Muñoz Statistical and Operations Research Dept. (UPC) pilar.munyoz@upc.edu SAMSI Program on Risk Analysis, Extreme Events and Decision Theory September 16-19, 2007

2. Insurance and Financial Risk 2 Three topics IMPACT Managing Expectations of the Analysis of Extreme – The Policy Markers Story Dougal Goodman (The Foundation for Science and Technology, UK) FINANCE Heavy Tails and Financial Time Series Richard Davis (Columbia University) TECHNICAL APPROACH Approach to Financial Risk for Extreme Events Yacov Haimes (University of Virginia)

3. Insurance and Financial Risk 3 Some observations The common lessons from financial disasters is that billions dollars can be lost because of poor supervision and management of financial risks (Gençay et al, 2003) Companies and organizations should reflect on whether they are properly assessing and planning for low probability/high severity loss events (Goodman) In order to develop guidelines in the area of risk management in financial institutions, among others: Basel Committee (1974) (Bank for International Settlements): established by the central-bank Governors Members come from Belgium, Canada, France, Germany, Italy, Japan, Luxembourg, the Netherlands, Spain, Sweden, Switzerland, the United Kingdom and the United States provides a forum for regular cooperation on banking supervisory matters.

4. Insurance and Financial Risk 4 Some observations Basel II is the second of the Basel Accords (2006) (www.bis.org/publ/bcbs107.pdf ): They recommended in the final version (2006), among others: Separate operational risk from credit risk, and quantify both !

5. Insurance and Financial Risk 5 Some observations More guidelines similar to BASEL II are needed in the areas of Public Health, Computer Science, … Statisticians (Scientists) have to motivate financial institutions, banks, health care services, …to use risk procedures for losses prevention

6. Insurance and Financial Risk 6 Some observations Estimation of the probability of a extreme value in a portfolio is important for risk management Financial returns series are characterized by heavy tails of the distribution, which correspond with extreme events. Extremal index is of utility in the detection of clustering in the data Extremal index can be interpreted as the inverse of the mean number of extremes in a cluster. Independent data: Extremal index =1 Extreme events in clustering: Extremal index < 1

7. Insurance and Financial Risk 7 Some observations Davis & Mikosch: Stochastic volatility models, extremal index =1 GARCH models, extremal index <1 Stochastic volatility and GARCH processes exhibit volatility clustering Only GARCH presents clustering of extremes

8. Insurance and Financial Risk 8 Some observations Partitioned Multiobjective Risk Method (PMRM, Santos & Haimes, 2002) has been applied to Portfolio Selection In liberalized Electricity Markets, companies have to optimize the generation of electricity using nuclear, natural gas, coal, hydro and renewable energies Could be applied PMRM in order to minimize risk management?

9. Insurance and Financial Risk 9 From my experience My empirical experience in the Electricity Market (Muñoz & Bunn, 2007) is that: Electricity prices are more volatile than that other goods affected by extreme values Electricity prices vary seasonally in association with demand (related with weather patterns): oThey exhibit Daily, Weekly and Yearly Seasonality Imperfect nature of power markets: regulatory interventions, agent learning, repeated game opportunities, … Electricity behave as a good but it is consumed as an instantaneous service. Supply factors influence price levels How does all of this affect volatility clustering?

10. Insurance and Financial Risk 10 From my experience Influential Variables (1/4) Demand: 12 p.m. day-ahead Demand Forecast was used as Demand variable (published by the system operator, REE in Spain). Relationship between Price and Demand is quadratic: Demand, Squared Demand. Transformed into orthonormal components to resolve the collinearity: Demand.Linear and Demand.Quadratic. Demand Slope and Curvature: To capture intraday aspects of plant dynamics and its cost / strategic (*): See Karakatsani and Bunn (2006) for a more detailed explanation

11. Insurance and Financial Risk 11 From my experience Influential Variables (2/4) Demand Volatility: Seasonality in Demand variation associated with weather patterns may affect plant scheduling, therefore changes into balancing cost. Defined as the coefficient of variation (standard deviation/mean) of Demand in a weekly (7 day) moving window. Margin: Measure of excess generation capacity. Defined as the maximum declared available output aggregated across all generating units minus the Demand Forecast. Lag-1 Margin: Introduced to capture inter-day concerns about scarcity.

12. Insurance and Financial Risk 12 From my experience Influential Variables (3/4) Scarcity: To capture the steep impact of capacity surplus on price above a threshold. Defined as max{Lower Quartile of Ratio - Ratio, 0} Ratio=Margin/Demand lower quartile of Ratio is calculated from its sampling distribution in each load period. Imbalance: indicator of activity in balancing mechanisms Defined as Indicated Generation – Predicted Demand

13. Insurance and Financial Risk 13 From my experience Influential Variables (4/4) Learning: Three past values of spot price: Pt-1: Price in the same trading period on the previous day Pt-7: Price in the same trading period and day in the previous week MPt-1: Daily Average Price on the previous day. Price Volatility defined similarly to Demand Volatility Seasonality: sinusoidal function with winter peak is used Trend

14. Insurance and Financial Risk 14 From my experience Empirical results for the Spanish market confirm the previous ones published by Karakatsani & Bunn (2006) for UK Electricity Market: Spikes of volatility in electricity prices may be caused by market conditions as for example the scarcity of electricity generation capacity, among others. Temporal market anomalies caused by scarcity or other factors associated with it may be explained by nonlinear switching time series models, flexible to capture asymmetries in the price behavior. Further research on extreme values, time varying models, regime switching and non-parametric models is needed to better understand the spot prices behavior in energy markets