Plagues of the 21st Century

Emile Elefteriadis, FCIA, FSACIA November 17, 2004

Agenda

Possible Mortality Catastrophes Vita Capital’s Principal-At-Risk Variable-Rate

Mortality Catastrophe Indexed Note – aka Swiss Re’s Mortality Catastrophe Bond

Modeling Approaches

Possible Mortality Catastrophes

Terrorist Attack – Profound difference in ideology – September 11, 2001– Biological, nuclear threats

War Middle East North Korea India and Pakistan Intervention and escalation Wars have been relatively frequent

Possible Mortality Catastrophes

Meteorite Crash– 1908 Tunguska River, 55 meter meteorite

15,000 Kiloton (kT) explosion Hiroshima 12.5 kT a 1:1900 year event

– 1972 a 10 meter object bounced off earth’s atmosphere.

Energy release could have been over 20kT a 1:35 year event

Possible Mortality Catastrophes

Influenza Epidemics 20th Century

Year Name Geographical Spread

Impact

1918 – 20 Spanish Flu

Originated in USA, spread to Europe

Estimated 40 million deaths (675,000 USA)

1957 – 58 Asian Flu Originated in Singapore, Hongkong, spread to USA, Europe

Estimated 1-2 million deaths (70,000 in USA)

1968 – 72 Hong Kong Flu

Originated in Hong Kong, spread to US, Europe

Estimated 1 million deaths (34,000 in USA)

Other major infectious diseases

Smallpox and threat of biological weapons Newly emerging diseases - SARS Other diseases - CJD, Plague, West Nile

virus and other water borne / vector borne diseases (like Malaria),Yellow Fever

Mortality Catastrophe Bond

In December 2003, Swiss Re sponsored a $400 million securitization of mortality risk

The purpose was to get protection against extreme mortality events, without relying upon the credit-worthiness of a retrocessionaire

A catastrophe bond structure was used, with loss measurement based on a parametric index

Mortality Risk Transfer - Structure

Insurer

FinancialContract

Premium

Up to Original Principal Amount at Redemption

Principal At-Risk Variable

Rate Notes

Total Return Swap

Counterparty

SPV

CollateralAccount

Investment Income

LIBOR - [ ]

Original Principal Amount

Interest: LIBOR + [ ]%

(1)

(2)

(3)

0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

100 100+X 100+Y

Index Results (% of Base Index Value)

% R

ed

uc

tio

n i

n P

rin

cip

al

Mortality Risk Transfer - Payout

Attachment Point: [100+x]%

Exhaustion Point: [100 + y ]%

Mortality Risk Transfer - Trigger Definition

The index value for a given year is defined to be the average death rate per 100,000 for pre-defined coverage area

The average death rate is calculated using a parametric index formula, which applies pre-determined weights to gender, age, and country, and draws on publicly-available mortality data as the inputs:

Attachment Point = x% of Index Value in baseline year Exhaustion Point = y% of Index Value in baseline year % Loss = 100 x (Index Value - Attachment Point) / (Exhaust Point -

Attachment Point)

1i

,,1

)( fjii

fmjii

m

jj qagqagcIndex =

Historical Analysis

Historical Index

200

400

600

800

1,000

1,200

1,400

1,600

1,800

2,000

1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000

Year

Dea

ths

per 10

0,00

0

W W

II 1

940-

1945

AID

S 1

990-

1995

W W

I 19

14-1

918

Influ

enza

191

8

Influ

enza

195

7

Influ

enza

196

8

Modeling Approaches

Perspective:– interest is in acute events– near term (1-5 years)

Mathematical/Stochastic Epidemiologic Models

These models are useful for understanding how certain factors can influence the severity of an influenza epidemic/pandemic

The SEIR model (Susceptibles, Incubating, Infecting, Recovered) is a well known simple model.

Reality is more complex– uncertainty surrounding the true process– parameter uncertainty

Not any better than predictions based on analysis of epidemiologic data from previous pandemics

Age Standardized Mortality

US Age Standardized Mortality*

0

500

1000

1500

2000

Dea

ths

Per

100

,000

*weights by age and sex based on Canadian individual life insured distribtuions and not those used in the Mortality Bond

Epidemiologic Transition

Changes in the relative importance of causes of death – Orman’s three-stage theory:– Famine and Pestilence, prior to 19th century– Infectious diseases and pandemics , middle of 20th

century– Chronic diseases (cardiovascular, cancer)

Fourth stage? death due to longer-term degenerative diseases (Olshansky & Ault (1983), Rogers & Hackenburg ( 1987)

US Age Standardized Mortality

Period Average annual rate of Change in Index

Standard deviation of rate of change in Index

1901-1925 -0.44% 12.2%

1926-1950 -1.64% 3.4%

1950-1975 -0.88% 2.0%

1976-2000 -1.34% 1.5%

1901-2000 -1.08% 6%

Annual Change in Mortality

Annual Changes in Mortality

0.0%

10.0%

20.0%

30.0%

40.0%

-0.36 -0.16 0.04 0.24 0.44 0.64 0.84

% Change

Fre

quecy

Future Value of Index

Approach 1– Index(t)=Index(t-1)*(1+annual change)– annual change is the random variable– “annual change” is not normally distributed: e.g..

1918 pandemic is more than 6 standard deviations– fatter tail distribution more appropriate; – however returns are correlated: large increase

followed by large decrease-negative autocorrelation, reversion to mean

Annual Change in Age Standardized Index

Annual Change-Age Standardized Index

-40.00%

-30.00%

-20.00%

-10.00%

0.00%

10.00%

20.00%

30.00%

40.00%

50.00%

1901

1906

1911

1916

1921

1926

1931

1936

1941

1946

1951

1956

1961

1966

1971

1976

1981

1986

1991

1996

Annual Change-Age Standardized Index

Future Value of Index

Approach 1b– Bootstrap method based on the observed annual

change distribution– resampling is modified to reflect negative correlation

between successive annual changes moving block bootstrap circular bootstrap e.g.: if sample is selected from a block that has a large

positive annual change, the subsequent sample will PROBABLY be drawn from the block that has sample points resulting in a large negative annual change.

Approach 2

Index(t)=Index(0)(1-Imp)^t*(1+EM)– EM is extreme mortality distribution

Age Standardized Pandemic Mortality

Pandemic Percentage Change in Index

Excess Mortality

Per 1000

1918-20 43% 5.54

1957-58 2.2% 0.14

1968-72 2.8% 0.18

Frequency of Pandemics since 1800

Years Virus Subtype Origin

1830-1833 Unknown Russia

1836-1837 Unknown Russia suspected

1889-90 H2 Russia

1889-1900 H3 Unknown

1918-20 H1N1 USA

1957-58 H2N2 China

1968 H3N2 China

source: Gust et al. (2001)

Frequency Model

Time between pandemics Modeled by exponential with mean of about

30 years Or is there a cycle?

Severity -Excess Mortality

Influenza Epidemics 20th Century

Year Name GeographicalSpread

Impact

1918 – 20 Spanish Flu Originated inUSA, spreadto Europe

Estimated 40million deaths

1957 – 58 Asian Flu Originated inSingapore,Hongkong,spread toUSA, Europe

Estimated 1-2million deaths(70,000 inUSA)

1968 – 72 Hong KongFlu

Originated inHong Kong,spread to US,Europe

Estimated 1million deaths(34,000 inUSA)

Influenza - Excess mortality (US Experience)

Excess mortality from pneumonia and influenza during 20th century pandemics

-800-600-400-200

0200400600800

10001200

0 10 20 30 40 50 60 70 80 90

Age

Exce

ss m

orta

lity

per

100,

000

popu

latio

n (1

918)

-20

0

20

40

60

80

100

120

140

160

Exce

ss m

orta

lity

per

100,

000

popu

latio

n (1

957

& 1

968)

1918 A(H1N1)

1957 A(H2N2)

1968 A(H3N2)

Source: Glezen: Emerging infections: Pandemic influenza, 1996

Infectious diseases mostly affects the young and the elderly

Proportion of deaths due to infectious diseases

0%

5%

10%

15%

20%25%

30%

35%

40%

45%

<1 1 to 4 5 to14

15-24

25-34

35-44

45-54

55-64

65-74

75-84

85+

% o

f to

tal d

eath

s

UK (2000) Netherlands (2000) US (1998)

Sources: Office of National Statistics (UK); Centraal Bureau voor Statistiek(Netherlands), Center for Disease Control (US).

CDC’s FluAid –Severity Model

Based on paper “Economic Impact of Pandemic Influenza in the United States: Priorities for Intervention”, Meltzer, et all, 1999

Non-epidemiologic model used to estimate excess deaths, hospitalizations and resulting economic impact under various vaccine based interventions for a potential pandemic in the USA.

Applied FluAid model to Canadian individual inforce

FluAid

Excess mortality modeled as triangular or uniform for age segments

Exposure ('000 in force)

0-18 19-64 65+ Total% of

Total

Non-high risk 90,2071,157,04

8 24,0251,271,28

0 97.8%

High risk 271 20,009 8,440 28,720 2.2%

Totals 90,4781,177,05

7 32,4651,300,00

0 100.0%

FluAid

High-risk group assumed to be fraction of lives in ultimate period of mortality table and a fraction of substandard lives in the select period

Excess mortality use model default values (based on 1957, 1968 pandemic mortality)

– non-high risk group-sample from triangular distribution– high risk group-sample from uniform distribution– Monte carlo

FluAid Results

DEATHS ('000s FACE AMOUNT)

AttackRates

15% 25% 35%

0-18 Most Likely 1 2 2

min 1 1 1

max 5 8 11

19-64 Most Likely 91 152 213

min 39 64 90

max 143 238 333

65+ Most Likely 41 68 95

min 38 63 88

max 48 80 111

TOTAL Most Likely 133 222 310

min 78 128 179

max 196 326 455