extreme mortality bonds - menu · extreme mortality bonds september 9, 2009 10 mechanism overview n...

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


Agenda


Financial Structure

Mechanism Overview

Underlying Risk

Pandemic Modeling

EMB Pricing




For issuersProtection against extreme mortality risk

Systemic riskExclusion from traditional reinsuranceCover duration

For InvestorsNew class of securities

Higher spreadsNon-correlation


Agenda


Financial Structure

Mechanism Overview

Underlying Risk

Pandemic Modeling

EMB Pricing



Financial Structure

Swap Counterparty

(Re)insurer SPV Debt investors

floating interest rate fixed interest rate

premiums + floating interest rate

option Payoff

premiums

Cash proceeds


Agenda


Financial Structure

Mechanism Overview

Underlying Risk

Pandemic Modeling

EMB Pricing



Mechanism Overview

Mortality IndexBased on age and gender weighted death ratesBased on national index(es) of mortality

Source: Swiss Re


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


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


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


Agenda


Financial Structure

Mechanism Overview

Underlying Risk

Pandemic Modeling

EMB Pricing



Underlying Risk

EventsPandemic diseaseTerrorism eventNatural disasterHeat waveIndustrial accidentConventional/Nuclear war

Risk profileIndex based (parametric and not indemnity)Low frequencyHigh severity


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.


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


Agenda


Financial Structure

Mechanism Overview

Underlying Risk

Pandemic Modeling

EMB Pricing



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


Pandemic Modeling

( )005,0

exp>

⋅−⋅=rsi

rbaSeverity

0050 180

)90(

,rsi

rcTANSeverity

≤

⋅⋅−=π

( )005,0

exp>

⋅−⋅=rsi

rbaSeverity

0050 180

)90(

,rsi

rcTANSeverity

≤

⋅⋅−=π


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,…)


Agenda


Financial Structure

Mechanism Overview

Underlying Risk

Pandemic Modeling

EMB Pricing



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 =


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


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


Agenda


Financial Structure

Mechanism Overview

Underlying Risk

Pandemic Modeling

EMB Pricing




Low excess mortality but possible future evolutionMutationDrug Resistance

Source: WHO, CDC



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


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


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

extreme mortality bonds - menu · extreme mortality bonds september 9, 2009 10 mechanism overview n...

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