Plagues of the 21 st Century

1. Plagues of the 21st Century Emile Elefteriadis, FCIA, FSA CIA November 17, 2004

2. 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

3. 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

4. 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

5. Possible Mortality Catastrophes • Influenza Epidemics 20th Century

6. 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

7. 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

8. Mortality Risk Transfer - Structure Insurer Financial Contract Premium (1) (2) Up to Original Principal Amount at Redemption (3) Principal At-Risk Variable Rate Notes SPV Total Return Swap Counterparty Investment Income Interest: LIBOR + [ ]% LIBOR - [ ] Collateral Account Original Principal Amount

9. Mortality Risk Transfer - Payout Attachment Point: [100+x]% Exhaustion Point: [100 + y ]% 100% 90% 80% 70% 60% % Reduction in Principal 50% 40% 30% 20% 10% 0% 100 100+Y 100+X Index Results (% of Base Index Value)

10. 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) Index =

11. Historical Analysis

12. Modeling Approaches • Perspective: • interest is in acute events • near term (1-5 years)

13. 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

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

15. 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)

16. US Age Standardized Mortality

17. Annual Change in Mortality

18. 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

19. Annual Change in Age Standardized Index

20. 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.

21. Approach 2 • Index(t)=Index(0)(1-Imp)^t*(1+EM) • EM is extreme mortality distribution

22. Age Standardized Pandemic Mortality

23. Frequency of Pandemics since 1800 source: Gust et al. (2001)

24. Frequency Model • Time between pandemics • Modeled by exponential with mean of about 30 years • Or is there a cycle?

25. Severity -Excess Mortality • Influenza Epidemics 20th Century

26. Influenza - Excess mortality (US Experience)

27. Infectious diseases mostly affects the young and the elderly

28. 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

29. FluAid • Excess mortality modeled as triangular or uniform for age segments

30. 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

31. FluAid Results