September 9, 2009 Extreme Mortality Bonds Romain Bridet IAA Life Colloquium, Munich 2009
September 9, 2009
Extreme Mortality BondsRomain Bridet IAA Life Colloquium, Munich 2009
Extreme Mortality BondsSeptember 9, 2009 2
Agenda
Transaction Objectives
Financial Structure
Mechanism Overview
Underlying Risk
Pandemic Modeling
EMB Pricing
2009 influenza A/H1N1
Extreme Mortality BondsSeptember 9, 2009 3
Agenda
Transaction Objectives
Financial Structure
Mechanism Overview
Underlying Risk
Pandemic Modeling
EMB Pricing
2009 influenza A/H1N1
Extreme Mortality BondsSeptember 9, 2009 4
Transaction Objectives
For issuersProtection against extreme mortality risk
Systemic riskExclusion from traditional reinsuranceCover duration
For InvestorsNew class of securities
Higher spreadsNon-correlation
Extreme Mortality BondsSeptember 9, 2009 5
Agenda
Transaction Objectives
Financial Structure
Mechanism Overview
Underlying Risk
Pandemic Modeling
EMB Pricing
2009 influenza A/H1N1
Extreme Mortality BondsSeptember 9, 2009 6
Financial Structure
Swap Counterparty
(Re)insurer SPV Debt investors
floating interest rate fixed interest rate
premiums + floating interest rate
option Payoff
premiums
Cash proceeds
Extreme Mortality BondsSeptember 9, 2009 7
Agenda
Transaction Objectives
Financial Structure
Mechanism Overview
Underlying Risk
Pandemic Modeling
EMB Pricing
2009 influenza A/H1N1
Extreme Mortality BondsSeptember 9, 2009 8
Mechanism Overview
Mortality IndexBased on age and gender weighted death ratesBased on national index(es) of mortality
Source: Swiss Re
Extreme Mortality BondsSeptember 9, 2009 9
Mechanism Overview
Reduction in outstanding Principal of the BondIndex < Attachment point Principal repayable in FullIndex > Exhaustion point Principal completely exhaustedLinear Reduction between Attachment point and Exhaustion point
Loss Payment
0
20
40
60
80
100
120
100 110 120 130 140 150
Index
% re
duct
ion
in p
rinci
pal
Exhaustion Point
Attachment Point
Extreme Mortality BondsSeptember 9, 2009 10
Mechanism Overviewn the duration of the bond and 1−= nm the number of measurement periods
tI the value of the mortality index measured at time mt ...2=
A the attachment point
E the exhaustion point
At the end of the measurement period mt ...2= , the reduction in principal is:
⎟⎠⎞
⎜⎝⎛ −
−−
= − 0;max 1tt
t RAEAI
R ( )01 =R
With the constraint that the cumulative principal reduction cannot exceed 100%:
%1002
≤∑=
t
iiR
At time t, the outstanding capital is equal to: ∑=
−t
iiR
2%100
0Start of risk
period 1 2 3
4End of risk
period
Extreme Mortality BondsSeptember 9, 2009 11
Mechanism Overview
Life Catastrophe Excess of Loss vs. EMBEMB Structure close to a stop loss coverIndemnity vs. parametric (ie basis risk for EMB)DurationPandemics completely excluded from Life Cat XL
Extreme Mortality BondsSeptember 9, 2009 12
Agenda
Transaction Objectives
Financial Structure
Mechanism Overview
Underlying Risk
Pandemic Modeling
EMB Pricing
2009 influenza A/H1N1
Extreme Mortality BondsSeptember 9, 2009 13
Underlying Risk
EventsPandemic diseaseTerrorism eventNatural disasterHeat waveIndustrial accidentConventional/Nuclear war
Risk profileIndex based (parametric and not indemnity)Low frequencyHigh severity
Extreme Mortality BondsSeptember 9, 2009 14
Underlying Risk
An Epidemic is a disease that appears as new cases in a given human population, during a given period, at a rate that substantially exceeds what is “expected”, based on recent experience.
A Pandemic is an epidemic that spreads worldwide, or at least across a large region.
Extreme Mortality BondsSeptember 9, 2009 15
Underlying Risk
31 pandemics since 1580 (according to the WHO)
Year Name Deaths Lethality rate
1918-1919 Spanish flu ~ 50 million ~ 10%1957-1958 Asian flu ~ 2 million ~ 0,37% (US)1968-1969 Hong Kong flu ~ 1 million ~ 0,19% (US)1977 Russian flu 10 000 in US ?2003 SARS 299 in HK up to 71% in HK
Extreme Mortality BondsSeptember 9, 2009 16
Agenda
Transaction Objectives
Financial Structure
Mechanism Overview
Underlying Risk
Pandemic Modeling
EMB Pricing
2009 influenza A/H1N1
Extreme Mortality BondsSeptember 9, 2009 17
Pandemic Modeling
Approach: Frequency * Severity
Frequency: 7.4% per annum based on 31 influenzaepidemics over the last 420 years
Severity: exponential curve calibrated with5 historical data points which are the 5 last pandemic events
Extreme Mortality BondsSeptember 9, 2009 18
Pandemic Modeling
( )005,0
exp>
⋅−⋅=rsi
rbaSeverity
0050 180
)90(
,rsi
rcTANSeverity
≤
⋅⋅−=π
( )005,0
exp>
⋅−⋅=rsi
rbaSeverity
0050 180
)90(
,rsi
rcTANSeverity
≤
⋅⋅−=π
Extreme Mortality BondsSeptember 9, 2009 19
Pandemic Modeling
Paul Valéry“What is simple is always wrong, what is complex is unusable.”
Limitspandemic risk is very uncertain and unpredictablemany parameters not taken into account (like location of outbreak, vaccine production, pandemic lifecycle,…)
Extreme Mortality BondsSeptember 9, 2009 20
Agenda
Transaction Objectives
Financial Structure
Mechanism Overview
Underlying Risk
Pandemic Modeling
EMB Pricing
2009 influenza A/H1N1
Extreme Mortality BondsSeptember 9, 2009 21
EMB Pricing
Pricing a priori with Monte Carlo Simulations
Estimation for each class of Notes n :the Expected Lossthe Probability of First Lossthe Probability of Exhaustion
the Conditional Expected Loss
nPFLnEL
nPE
nn
ntnt AE
AIR−−
=, ( )⎩⎨⎧
>−=
=− 1
1
,1,
,, tsiCRMax
tsiRC
ntnt
ntnt
{ }
XPFL x
C
n
nt∑ >
=0,
δ
{ }⎩⎨⎧
=>
=> 0001
,
,0,
nt
ntC Csi
Csint
δX
CEL x t
ntx
n
∑∑=
,,{ }
XPE x
C
n
nt∑ =
=1,
ζ{ }
⎩⎨⎧
==
== 0011
,
,1,
nt
ntC Csi
Csint
ζ
No Simulation1...X x = time1...T t = No class 1...N n =
n
nn PFL
ELCEL =
Extreme Mortality BondsSeptember 9, 2009 22
EMB Pricing
EMB at issuance (unwrapped)
VITA IVITA II B
VITA II CVITA II D
VITA III AVITA III B
TARTAN B
OSIRIS B
OSIRIS C
OSIRIS D
NATHAN A
0
100
200
300
400
500
600
0.0 5.0 10.0 15.0 20.0 25.0 30.0 35.0 40.0
E(L) (bps)
Spre
ad a
t iss
uanc
e (b
ps) Expensive
(for Issuer)
Economical(for Issuer)
Frontier
Spread and E(L) dependence measured a posteriori
Extreme Mortality BondsSeptember 9, 2009 23
EMB Pricing
Spread
0%
10%
VITA II B VITA II C VITA II D VITA III A VITA III B OSIRIS B OSIRIS C OSIRIS D
Spread at issuance
Spread at December 31, 2007
Spread at July, 31, 2009
Financial crisis
Spread Variations
Extreme Mortality BondsSeptember 9, 2009 24
Agenda
Transaction Objectives
Financial Structure
Mechanism Overview
Underlying Risk
Pandemic Modeling
EMB Pricing
2009 influenza A/H1N1
Extreme Mortality BondsSeptember 9, 2009 25
2009 influenza A/H1N1
Low excess mortality but possible future evolutionMutationDrug Resistance
Source: WHO, CDC
Extreme Mortality BondsSeptember 9, 2009 26
2009 influenza A/H1N1
OSIRIS Index
Fatality rate / Infection rate 5% 10% 30%
0.05% 100% 101% 102%
0.10% 101% 101% 104%
0.50% 104% 107% 122%
1.00% 107% 115% 145%
Mortality Bond OSIRISMortality Holder Axa
Issue date - Maturity January 2006 - January 2010Index of Mortality 60% France, 25% Japan, 15% US
Weighted by age and genderClass B C D
Attachment Point 114% 110% 106%Exhaustion Point 119% 114% 110%
Spread at issuance 120 bp 285 bp 500 bpRating at issuance (S&P) A- BBB BB+
Seasonal flu
Attachment reached
Extreme Mortality BondsSeptember 9, 2009 27September 8, 2009 27
Extreme Mortality BondsSeptember 9, 2009 28
Pandemic Modeling
Age shape depending on Pandemic’s virulence
Low virulence High virulence
U shaped Distribution
-100%
0%
100%
200%
300%
400%
500%
600%
700%
800%
0 10 20 30 40 50 60 70 80 90
Age
% E
xces
s M
orta
lity
Rate
W shaped Distribution
0%
50%
100%
150%
200%
250%
300%
350%
400%
0 10 20 30 40 50 60 70 80 90
Age
% E
xces
s M
orta
lity
Rat
e
Extreme Mortality BondsSeptember 9, 2009 29
EMB Pricing
Spread at issuance & risk parameters
}
{turnxcess Expected E
LossExpected
EERLESpreadRe
)( +=
( ) ( )βαγ CELPFLEER .= (NatCat Bonds Approach)
5.10
68.0
===
γβα
0.00%
1.00%
2.00%
3.00%
4.00%
5.00%
6.00%
VITA IVITA II
BVITA II
CVITA II
DVITA III
AVITA III
BTart
an B
OSIRIS B
OSIRIS
COSIR
IS D
NATHAN A
Real SpreadEstimated spread