Pricing Multiple Triggers
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Pricing Multiple Triggers Larry Schober. …. an electrifying example. Pricing Multiple Triggers. Make some observations about multiple trigger coverage. Highlight some features of multiple trigger coverage through an example. Pricing Multiple Triggers General Observations.

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An electrifying example

Pricing Multiple Triggers

Larry Schober

…. an electrifying example


Pricing multiple triggers

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


Pricing multiple triggers general observations

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


An electrifying example

Pricing Multiple TriggersGeneral Observations

  • Various triggers

  • Feedback or correlation between triggers

  • Triggers brought together in an integrated model

Pricing Multiple Triggers ... an electrifying example


Multiple trigger model forced outage example

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


Multiple trigger model forced outage example what are triggers

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


Multiple trigger model forced outage example how can we model the triggers

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


An electrifying example

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


An electrifying example

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


Multiple trigger model forced outage example how can we model the triggers1

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


U s power system background north american electric reliability council nerc

U.S. Power SystemBackground - North American Electric Reliability Council (Nerc)

Pricing Multiple Triggers ... an electrifying example


U s power system

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


An electrifying example

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


Multiple trigger model forced outage example1

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


An electrifying example

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


An electrifying example

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


An electrifying example

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


An electrifying example

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


Multiple trigger model forced outage example2

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


Multiple trigger model forced outage example motivation behind supply demand model

Multiple Trigger ModelForced Outage Example - Motivation Behind Supply-demand Model

Pricing Multiple Triggers ... an electrifying example


Multiple trigger model forced outage example motivation behind supply demand model1

Multiple Trigger ModelForced Outage Example - Motivation Behind Supply-demand Model

Pricing Multiple Triggers ... an electrifying example


Multiple trigger model revisit general model

Multiple Trigger ModelRevisit General Model

Pricing Multiple Triggers ... an electrifying example


Multiple trigger model forced outage example3

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


An electrifying example

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


Multiple trigger model techniques bootstrap

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


Multiple trigger model techniques weather

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


    Multiple trigger model hedging multiple trigger coverage

    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


    Multiple trigger model conclusions

    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


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