Designing Parametric Risk Contracts

Using Catastrophe Risk Models

Dennis E. Kuzak

Sr.Vice President, EQECAT, Inc.

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Agenda

• Introduction to Parametric “Insurance Contracts” – Description– Advantages and disadvantages– Parametric Triggers and Parametric Index Triggers– Example-Australis Ltd.

• Reporting Agencies for Caribbean Contracts• Hypothetical Country Contract

– Country Map– Designing a parametric index– Post –event determination of loss

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Parametric “Insurance” Contracts

• Financial contracts vs. traditional indemnity insurance

• Physical measurement of the loss parameter• Highly correlated with expected physical damage

(e.g. peak gust wind speed)• Subject to probabilistic analysis• Sufficient historical data to construct statistical or

simulation based risk model• Independent recording of event parameter

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Parametric Triggers

Advantages– Simplicity– No Disclosure/Exposure Data.

– Transparency– Moral Hazard

– Rapid Settlement

Disadvantages– Basis Risk– Regulatory

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Parametric Triggers

• “Quake in a box” – Tokyo Marine-1997 and Concentric Ltd (Tokyo Disneyland) 1999

• Payoff based on earthquake magnitude > Magnitude JMA occurring within a region defined by boxes or circles

• Simple to understand• Rapid settlement- 30 to 60 days max.• Considerable basis risk- poor correlation between loss and loss recovery

Parametric Re Concentric Ltd.

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Parametric Index Triggers

• Why were they created?– Existing parametric triggers have unacceptable basis risk

• How do they reduce basis risk?– Select physical parameter highly correlated with

damage/loss– Multiple measurement (grids) locations in close proximity

to risks– Use weighting factor at each location to recognize

vulnerability and value distribution

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Example- Australis Ltd (2006)

• Securitization of Australian Cyclone (hurricane) and Earthquake Risk for Swiss Re

• Parametric index for cyclone and earthquake risk • Cyclone risk for NE Australia and earthquake risk for entire

country• Cyclone risk uses peak gust wind speed, earthquake uses

intensity scale (0-12) • Earthquake reporting agency: Geosciences Australia• Cyclone reporting agency: Joint Typhoon Warning center

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Australian Earthquake Calculation Locations

Victoria

Tasmania

AustralianCapital Territory

New South Wales

South Australia

Queensland

Northern Territory

Western Australia

Perth 7%

Adelaide 6%

Brisbane 11%

Sydney / Newcastle 27%

Melbourne 17%

Remainderof Australia 32%

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Weight Distribution of Cyclone Calculation Locations

Queensland

New South Wales

South Australia

AustralianCapital Territory

Northern Territory

Tasmania

Victoria

Western Australia

Brisbane 68%

Remainderof Locations 14%

Mackay 2%

Cairns 4%

Gladstone 3%

Maryborough & Bundaberg 5%

Townsville 4%

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Hurricane Reporting Agency

• The National Hurricane Center (NHC) is a branch of the Tropical Prediction Center (TPC), under the National Oceanic and Atmospheric Administration (NOAA). NHC maintains a continuous watch on tropical cyclones over the Atlantic, Caribbean, Gulf of Mexico, and the Eastern Pacific from May 15 through November 30. The Center prepares and distributes hurricane watches and warnings for the general public, and also prepares and distributes marine and military advisories for other users.

• The NHC's Preliminary Reports contain comprehensive information on each storm, including synoptic history, meteorological statistics, casualties and damages, and the post-analysis best track (six hourly positions and intensities).

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NHC Best Track Report

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Earthquake Reporting Agency

• National Earthquake Information Center (“NEIC”) created in 1966 as part of US Geological Survey

• Rapidly determines location and magnitude of significant earthquakes in US and worldwide

• Collects data through operation of national and global seismograph network of over 3000 stations

• Reports locations and magnitude via:– http://www.neic.cr.usgs.gov/neis/bulletin/bulletin.html– Quick Determination of Epicenters (QED) - daily– Preliminary Determination of Epicenters (PDE)

• Weekly and monthly

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Hypothetical Country Contract

* 2 Capital

* 1 Port and manufacturing

* 3 Tourism

* 4 Tourism

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Creating a Parametric Index

1. Compile physical and financial data for the country

2. Aggregate exposures at each calculation location

3. Using hurricane model, calculate physical damage loss exceedance (LEC) curve

4. Estimate catastrophe funding deficit from reduced taxes and emergency response efforts as a % of physical damage.

5. Calculate funding deficit loss exceedance curve

6. Create parametric wind index ( based on gust wind speed) which is “equivalent” to the funding deficit LEC

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Creating a Parametric Index

0%

2%

4%

6%

8%

10%

12%

Loss ($ Billions)

Pro

bab

ility

0 .2 .4 .6 .8 1.0 1.2 1.4 1.6 1.8 2.0 2.2

0%

2%

4%

6%

8%

10%

12%

Loss ($ MiIlions)

Pro

bab

ility

0 20 60 100 140 180 220

Damage LEC

Catastrophe Deficit LEC

Wind Index LEC

1000 3000 5000 7000

Contract Amount: $40 xs $40 M

Index Layer: Attach 2000

Index Layer: Exhaust 4000Wind Index

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Post Event Loss Determination

• Obtain Hurricane parameters from the National Hurricane Center

• Calculate wind speed at each of the four locations• Calculate wind index at each location• Sum the four values to calculate event index• Loss recovery = ((Event Index- attachment)/Layer)

* contract amount

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Hurricane path and calculated wind speeds

* 2 Capital

(130 MPH)

* 1 Port and manufacturing ( 125 MPH)

* 3 Tourism

(95 MPH)

* 4 Tourism

( 145 MPH)

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Wind Index

= 0.00005502 i wi (vi – 30)4

i=1

i=4

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Index Calculation and Loss Payment

Calculation Location

Weight Event Gust Windspeed

V-30 (v-30 )^4 X Weight

1 0.3 125 95 81450625 24,435,188 2 0.2 130 100 100000000 20,000,000 3 0.4 95 65 17850625 7,140,250 4 0.1 145 115 174900625 17,490,063

Sum 69,065,500 x 0.00005502

Event Index 3,800

Event Loss (3,800-2000)/(4,000-2,000) =0.9Contract Amount $40 million

Payment $36 Million