plagues of the 21 st century emile elefteriadis, fcia, fsa cia november 17, 2004
TRANSCRIPT
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