…. an electrifying example pricing multiple triggers larry schober

…. an electrifying example

Pricing Multiple Triggers

Larry Schober

Pricing Multiple Triggers ... an electrifying example

2

Pricing Multiple Triggers

• Make some observations about multiple trigger coverage.

• Highlight some features of multiple trigger coverage through an example.


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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?


4

Pricing Multiple TriggersGeneral Observations

• Various triggers• Feedback or correlation between triggers• Triggers brought together in an integrated model

.

.

.

Trigger 1

Trigger 2

LossCalculation

Feedback Feedback

Trigger n

General Model

FeedbackFeedback


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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


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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 -


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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


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Multiple Trigger ModelForced Outage Example -Revisit Generalized Model

• Trigger 1: outage on a covered plant• Trigger 2: spot price for electricity> strike

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.

.

Trigger 1

Trigger 2

LossCalculation

Feedback Feedback

Trigger n

General Model

FeedbackFeedback

outage

spike


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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.


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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.


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

NERC Regions

WSCC

ERCOT

Texas Interconnect

MAPP

SPP

SERC

FRCC

NPCC

ECAR MAAC

MAIN

Western InterconnectEastern Interconnect


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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


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• 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.


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• 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


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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

Demand vs. Temperature by NERC Region - workdays

-

25,000

50,000

75,000

100,000

125,000

40 50 60 70 80 90 100

Daily High Temperature (F)

Pea

k D

eman

d (

Mw

)

MAPP

Main

ECAR

SPP

WSCC

ERCOT

SERC

FRCC

MAAC

NPCC


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• 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”.


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• 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


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• 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


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• 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)


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

Capacity Shortfalls as an Indicator of Spot Price Jumps(January - December 1998)

$10

$100

$1,000

$10,000

1/1/98 2/1/98 3/1/98 4/1/98 5/1/98 6/1/98 7/1/98 8/1/98 9/1/98 10/1/98 11/1/98 12/1/98

Date

$/M

wh

(lo

g s

cale

)

0

4,000

8,000

12,000

Pea

k D

eman

d (

Mw

)

Control Area Peak Demand

Capacity

Demand


$10

$100

$1,000

$10,000

1/1/98 2/1/98 3/1/98 4/1/98 5/1/98 6/1/98 7/1/98 8/1/98 9/1/98 10/1/98 11/1/98 12/1/98

Date

$/M

wh

(lo

g s

cale

)

0

4,000

8,000

12,000

Pea

k D

eman

d (

Mw

)

Control Area Peak Demand Control Area Capacity (Seasonal)

Capacity

Demand


$10

$100

$1,000

$10,000

1/1/98 2/1/98 3/1/98 4/1/98 5/1/98 6/1/98 7/1/98 8/1/98 9/1/98 10/1/98 11/1/98 12/1/98

Date

$/M

wh

(lo

g s

cale

)

0

4,000

8,000

12,000

Pea

k D

eman

d (

Mw

)


Capacity

Demand


$10

$100

$1,000

$10,000

1/1/98 2/1/98 3/1/98 4/1/98 5/1/98 6/1/98 7/1/98 8/1/98 9/1/98 10/1/98 11/1/98 12/1/98

Date

$/M

wh

(lo

g s

cale

)

0

4,000

8,000

12,000

Pea

k D

eman

d (

Mw

)


Capacity

Demand


$10

$100

$1,000

$10,000

1/1/98 2/1/98 3/1/98 4/1/98 5/1/98 6/1/98 7/1/98 8/1/98 9/1/98 10/1/98 11/1/98 12/1/98

Date

$/M

wh

(lo

g s

cale

)

0

4,000

8,000

12,000

Pea

k D

eman

d (

Mw

)

Control Area Peak Demand Avg Daily Spot Control Area Capacity (Seasonal)

Capacity

Demand


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

Maximum Temperature and Spot Price(January - December 1998)

$10

$100

$1,000

$10,000

1/1/98 2/1/98 3/1/98 4/1/98 5/1/98 6/1/98 7/1/98 8/1/98 9/1/98 10/1/98 11/1/98 12/1/98

Date

$/M

wh

(lo

g s

cale

)

0

20

40

60

80

100

Max

Dai

ly

Tem

per

atu

re (

oF

)

Avg Daily Spot Max. Temp.


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Multiple Trigger ModelRevisit General Model

.

.

.

Trigger 1

Trigger 2

LossCalculation

Trigger nGeneral Model

Feedback

Feedback

Feedback

Feedback...

Supply(capacity)by region

(5b) + (5c)

Demandby region

(5a)

TransmissionOptimizedShortfall

(5d)

Trigger 2Spot PriceJump-diffusion

Model

(5e)

Trigger 1Covered Capacity

(Forced Outages)

(5f)

LossCalculation

applying:o deductibleso coinsuranceo retentions

o limits

(6)

Weather

Trigger 1

Trigger 2

LossCalculation

Temp. Windstorm


Non-covered Capacity(Forced Outages)

Feedback

Feedback

Feedback

Feedback...

Supply(capacity)by region

(5b) + (5c)

Demandby region

(5a)

TransmissionOptimizedShortfall

(5d)

Trigger 2Spot PriceJump-diffusion

Model

(5e)

Trigger 1Covered Capacity

(Forced Outages)

(5f)

LossCalculation

applying:o deductibleso coinsuranceo retentions

o limits

(6)

Weather

Trigger 1

Trigger 2

LossCalculation

Temp. Windstorm


Non-covered Capacity(Forced Outages)

Feedback

Feedback

Feedback

Feedback

Trigger 3Precipitation


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• 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, ...


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• 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.


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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


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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


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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”.


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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.

…. an electrifying example pricing multiple triggers larry schober

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