…. an electrifying example

1. Pricing Multiple Triggers Larry Schober …. an electrifying example

2. Pricing Multiple Triggers • Make some observations about multiple trigger coverage. • Highlight some features of multiple trigger coverage through an example. Pricing Multiple Triggers ... an electrifying example

3. Pricing Multiple TriggersGeneral Observations • Multiple triggers customize coverage. • Triggers need not be (and usually are not) the typical insurance triggers. • Laser in on revenue drivers = enterprise risk mgt. • Examples of multiple triggers for an: • Insurance company • Electric utility • How do we proceed? Pricing Multiple Triggers ... an electrifying example

4. Pricing Multiple TriggersGeneral Observations • Various triggers • Feedback or correlation between triggers • Triggers brought together in an integrated model Pricing Multiple Triggers ... an electrifying example

5. Multiple Trigger ModelForced Outage Example • In our example, we will focus on • A real life situation where triggers might interact • How do we model the triggers • How we can integrate the triggers in an overall loss model • Data sources and nature of data used to construct the model • A structural model for the triggers, which has the virtue of a flexible framework. • Techniques (bootstrapping, weather) • Hedging alternatives Pricing Multiple Triggers ... an electrifying example

6. Multiple Trigger ModelForced Outage Example - What Are Triggers? • The example we’re going to look at has 2 triggers (combination of events that work together to cause a loss): 1. Power plants fail to produce power, or are “forced out” 2. Cost of purchasing the replacement power on the open (spot) market is high. - AND - Pricing Multiple Triggers ... an electrifying example

7. Multiple Trigger ModelForced Outage Example - How Can We Model the Triggers? • Forced outages, the first trigger, is part of the boiler and machinery coverage. • Utilities try to estimate outages in predicting system reliability • Spot prices, the second trigger, have been deregulated since 4/1/98. • Only a two year history - not a whole lot of historical data - and it’s extremely volatile. • Historical range of $40-60/mwh spiked briefly in 1998-99 to $5-10,000/mwh Pricing Multiple Triggers ... an electrifying example

8. Multiple Trigger ModelForced Outage Example -Revisit Generalized Model outage spike • Trigger 1: outage on a covered plant • Trigger 2: spot price for electricity> strike Pricing Multiple Triggers ... an electrifying example

9. Report: New Risks Challenge Actuarial Models - P/C BestWeek 4/17/2000 • Actuaries should develop simulated models when pricing newly emerging risks. • Without historical data, actuaries must find new ways to price emerging markets. Pricing Multiple Triggers ... an electrifying example

10. Multiple Trigger ModelForced Outage Example - How Can We Model the Triggers? • A structural simulation of the power system for the spot price. • Bootstrapped from past data • Spikes not bootstrapped, conditions are • Historical data collected by national and federal agencies - much of it publicly available. • A parametric simulation for the generator outage trigger. Pricing Multiple Triggers ... an electrifying example

11. U.S. Power SystemBackground - North American Electric Reliability Council (Nerc) Pricing Multiple Triggers ... an electrifying example

12. U.S. Power System • Data sources • Federal energy regulatory commission (FERC) • North american electric reliability council (NERC) • Nuclear regulatory commission (NRC) • Utility’s own data Pricing Multiple Triggers ... an electrifying example

13. Multiple Trigger ModelForced Outage Example • Investigations into the causes of the price spikes in the summer of 1998 focused on: • demand: unusually warm weather early in the cooling season. • supply: abnormally large number of nuclear plants down. • transmission system: impaired by storms. • At the least, we should address these issues. Pricing Multiple Triggers ... an electrifying example

14. Multiple Trigger ModelForced Outage Example • A structural simulation of the power system for the spot price. • Supply-demand model for how much electricity costs. • Supply = available generating capacity • Demand = ƒ (temperature by region of the U.S) • Region’s demand > region’s supply  “spike” on the region • Needs to be a national model - balancing transfers (transmission) from other regions stabilize prices - also potentially not just one region as trigger. • Transmission system capacity constraints • Weather: temperature and windstorm Pricing Multiple Triggers ... an electrifying example

15. Multiple Trigger ModelForced Outage Example - Structural simulation of Power System • Demand - varies largely by temperature • as temperatures rise, demand for cooling • as temperatures fall, demand for heating • differs by region • not the same by day • weekday vs. weekend Pricing Multiple Triggers ... an electrifying example

16. Multiple Trigger ModelForced Outage Example - Structural simulation of Power System • Supply - outages (reductions in capacity) are applied by individual generator • using average by class of generator for uncovered capacity. • by generator, all across the U.S. and tied back to region. • same concept applied to covered plants - don’t use average, use generator’s own “experience”. Pricing Multiple Triggers ... an electrifying example

17. Multiple Trigger ModelForced Outage Example - Structural simulation of Power System • Availability of each generator is simulated by day for a whole year • Capacity = sum of all available generators • Nuclear capacity is separately simulated • different durations than fossil (coal/gas) plants Pricing Multiple Triggers ... an electrifying example

18. Multiple Trigger ModelForced Outage Example - Structural simulation of Power System • Need to perform any balancing transfers to surrounding regions • optimize capacity subject to shortfalls. • transmission capacity is an additional constraint. • transmission capacity is reduced for: • line load: reduced for temperature • windstorm: even localized, will impair transmission balancing capability Pricing Multiple Triggers ... an electrifying example

19. Multiple Trigger ModelForced Outage Example • A parametric simulation for the generator outage trigger. • Top-down approach: forced outage rates from previously mentioned data resources applied uniformly • Structural approach (bottom-up) could be applied: • Model each component of the generating plant • More of an engineering approach - not as good a predictor of availability as forced outage rate (NERC) Pricing Multiple Triggers ... an electrifying example

20. Multiple Trigger ModelForced Outage Example - Motivation Behind Supply-demand Model Pricing Multiple Triggers ... an electrifying example

21. Multiple Trigger ModelForced Outage Example - Motivation Behind Supply-demand Model Pricing Multiple Triggers ... an electrifying example

22. Multiple Trigger ModelRevisit General Model Pricing Multiple Triggers ... an electrifying example

23. Multiple Trigger ModelForced Outage Example • Spot price model • Jump-diffusion = frequency severity model • The frequency of a jump or spike is defined by the frequency of shortfall • The severity of the spike or “diffusion” is a function of the magnitude of shortfall • Not deterministic, but probabilistic around the average. • Pareto, lognormal, ... Pricing Multiple Triggers ... an electrifying example

24. Multiple Trigger ModelForced Outage Example • Loss Calculation • simulation in a spreadsheet - keeps it accessible • apply limit, deductible, other policy terms • Iterations • typically convergence at 10-20,000; higher for more “customization” • Loss Cost • loss cost = sample mean + % sample std. dev. Pricing Multiple Triggers ... an electrifying example

25. Multiple Trigger ModelTechniques - Bootstrap • Bootstrapping • Resampling from past data (empirical distribution) • Conditions leading up to a spike are sampled from past actual data. • Spike amounts are NOT sampled from past data • Only 2 years of spikes Pricing Multiple Triggers ... an electrifying example

26. Multiple Trigger ModelTechniques- Weather • You can incorporate: • Southern oscillation: sample la niña (el niño) years • (N) year cycles: sample every N years • Multi (k) year policy: sample (k) consecutive years; not (k) independent years • Adjust past temperatures upward before resampling to reflect warming trend • Warming trend not disputed, but cause is disputed • Possibly sample only latest (adjusted) years Pricing Multiple Triggers ... an electrifying example

27. Multiple Trigger ModelHedging Multiple Trigger Coverage • By their very nature, these are customized covers and fairly unique. • Hard to find perfect match for your exposure. • If the buyer could find it, why buy insurance? • “Basis risk” in trying to hedge one exposure. • Risk of a difference between the performance of a hedge and the losses sustained from the hedged exposure. • Customization can make insurance “solution” preferable to capital market “solution”. Pricing Multiple Triggers ... an electrifying example

28. Multiple Trigger ModelConclusions 1. More variables in multiple trigger coverage. • Simpler is still better. 2. Dependence between triggers is problematic. 3. Framework should allow for expansion of variables. 4. Wake-up call: pricing of risks with little data is not new, but there is more of it as pressure is applied from competing markets looking for involvement in risk management. Pricing Multiple Triggers ... an electrifying example