Extreme Mortality Bonds. Romain Bridet IAA Life Colloquium, Munich 2009

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1 Romai Bridet IAA Life Colloquium, Muich 2009 September 9, 2009

2 September 9, Ageda Trasactio Objectives Fiacial Structure Mechaism Overview Uderlyig Risk Pademic Modelig EMB Pricig 2009 iflueza A/H1N1

3 September 9, Ageda Trasactio Objectives Fiacial Structure Mechaism Overview Uderlyig Risk Pademic Modelig EMB Pricig 2009 iflueza A/H1N1

4 September 9, Trasactio Objectives For issuers Protectio agaist extreme mortality risk Systemic risk Exclusio from traditioal reisurace Cover duratio For Ivestors New class of securities Higher spreads No-correlatio

5 September 9, Ageda Trasactio Objectives Fiacial Structure Mechaism Overview Uderlyig Risk Pademic Modelig EMB Pricig 2009 iflueza A/H1N1

6 September 9, Fiacial Structure Swap Couterparty floatig iterest rate fixed iterest rate premiums premiums + floatig iterest rate (Re)isurer SPV Debt ivestors optio Payoff Cash proceeds

7 September 9, Ageda Trasactio Objectives Fiacial Structure Mechaism Overview Uderlyig Risk Pademic Modelig EMB Pricig 2009 iflueza A/H1N1

September 9, 2009 8 Mechaism Overview Mortality Idex Based o age ad geder

8 September 9, Mechaism Overview Mortality Idex Based o age ad geder weighted death rates Based o atioal idex(es) of mortality Source: Swiss Re

9 September 9, Mechaism Overview Reductio i outstadig Pricipal of the Bod Idex < Attachmet poit Pricipal repayable i Full Idex > Exhaustio poit Pricipal completely exhausted Liear Reductio betwee Attachmet poit ad Exhaustio poit Loss Paymet 120 Attachmet Poit Exhaustio Poit 100 % reductio i pricipal Idex

10 September 9, Mechaism Overview the duratio of the bod ad m = 1 the umber of measuremet periods I t the value of the mortality idex measured at time A the attachmet poit t = 2... m E the exhaustio poit At the ed of the measuremet period t = 2... m, the reductio i pricipal is: t I t A = max Rt 1; 0 E A R ( R ) 1 = 0 With the costrait that the cumulative pricipal reductio caot exceed 100%: t i= 2 R i 100% At time t, the outstadig capital is equal to: 0 Start of risk period 100 % t i= 2 R i 4 Ed of risk period

11 September 9, Mechaism Overview Life Catastrophe Excess of Loss vs. EMB EMB Structure close to a stop loss cover Idemity vs. parametric (ie basis risk for EMB) Duratio Pademics completely excluded from Life Cat XL

12 September 9, Ageda Trasactio Objectives Fiacial Structure Mechaism Overview Uderlyig Risk Pademic Modelig EMB Pricig 2009 iflueza A/H1N1

13 September 9, Uderlyig Risk Evets Pademic disease Terrorism evet Natural disaster Heat wave Idustrial accidet Covetioal/Nuclear war Risk profile Idex based (parametric ad ot idemity) Low frequecy High severity

14 September 9, Uderlyig Risk A Epidemic is a disease that appears as ew cases i a give huma populatio, durig a give period, at a rate that substatially exceeds what is expected, based o recet experiece. A Pademic is a epidemic that spreads worldwide, or at least across a large regio.

15 September 9, Uderlyig Risk 31 pademics sice 1580 (accordig to the WHO) Year Name Deaths Lethality rate Spaish flu ~ 50 millio ~ 10% Asia flu ~ 2 millio ~ 0,37% (US) Hog Kog flu ~ 1 millio ~ 0,19% (US) 1977 Russia flu i US? 2003 SARS 299 i HK up to 71% i HK

16 September 9, Ageda Trasactio Objectives Fiacial Structure Mechaism Overview Uderlyig Risk Pademic Modelig EMB Pricig 2009 iflueza A/H1N1

17 September 9, Pademic Modelig Approach: Frequecy * Severity Frequecy: 7.4% per aum based o 31 iflueza epidemics over the last 420 years Severity: expoetial curve calibrated with 5 historical data poits which are the 5 last pademic evets

18 September 9, Pademic Modelig Severity = a exp ( b r ) si r > 0,005 Severity π = TAN (90 c r ) 180 si r 0, 005

19 September 9, Pademic Modelig Paul Valéry What is simple is always wrog, what is complex is uusable. Limits pademic risk is very ucertai ad upredictable may parameters ot take ito accout (like locatio of outbreak, vaccie productio, pademic lifecycle, )

20 September 9, Ageda Trasactio Objectives Fiacial Structure Mechaism Overview Uderlyig Risk Pademic Modelig EMB Pricig 2009 iflueza A/H1N1

21 September 9, EMB Pricig Pricig a priori with Mote Carlo Simulatios x = 1...X Simulatio No t = 1...T time =1...N class No R I A t, t t = C, t, = E A ( ) Max Rt, Ct 1, si t > 1 R si t = 1 PFL = t, > x δ{ C 0} X δ { C > 0} t, = 1 0 si si C C t, t, > 0 = 0 PE = t, = x ζ { C 1} X ζ { C = 1} t, = 1 0 si si C C t, t, = 1 = 0 EL = x t X C x, t, Estimatio for each class of Notes : EL PFL PE the Expected Loss the Probability of First Loss the Probability of Exhaustio CEL = EL PFL the Coditioal Expected Loss

22 September 9, EMB Pricig Spread ad E(L) depedece measured a posteriori EMB at issuace (uwrapped) Spread at issuace (bps) VITA II B VITA I VITA II C VITA III B VITA III A NATHAN A OSIRIS B Expesive (for Issuer) TARTAN B OSIRIS C VITA II D OSIRIS D E(L) (bps) Ecoomical (for Issuer) Frotier

23 September 9, EMB Pricig Spread Variatios Spread Spread at issuace Spread at December 31, 2007 Spread at July, 31, % Fiacial crisis 0% VITA II B VITA II C VITA II D VITA III A VITA III B OSIRIS B OSIRIS C OSIRIS D

24 September 9, Ageda Trasactio Objectives Fiacial Structure Mechaism Overview Uderlyig Risk Pademic Modelig EMB Pricig 2009 iflueza A/H1N1

25 September 9, iflueza A/H1N1 Low excess mortality but possible future evolutio Mutatio Drug Resistace Source: WHO, CDC

26 September 9, iflueza A/H1N1 Mortality Bod OSIRIS Mortality Holder Axa Issue date - Maturity Jauary Jauary 2010 Idex of Mortality 60% Frace, 25% Japa, 15% US Weighted by age ad geder Class B C D Attachmet Poit 114% 110% 106% Exhaustio Poit 119% 114% 110% Spread at issuace 120 bp 285 bp 500 bp Ratig at issuace (S&P) A- BBB BB+ Seasoal flu OSIRIS Idex Attachmet reached Fatality rate / Ifectio rate 5% 10% 30% 0.05% 100% 101% 102% 0.10% 101% 101% 104% 0.50% 104% 107% 122% 1.00% 107% 115% 145%

27 September 9, 8,

28 September 9, Pademic Modelig Age shape depedig o Pademic s virulece U shaped Distributio W shaped Distributio 800% 400% % Excess Mortality Rate 700% 600% 500% 400% 300% 200% 100% 0% -100% Age % Excess Mortality Rate 350% 300% 250% 200% 150% 100% 50% 0% Age Low virulece High virulece

29 September 9, EMB Pricig Spread at issuace & risk parameters Spread = Loss } E( L) + Expected ( PFL) α ( CEL) β EER γ. { EER Expected Excess Retur = (NatCat Bods Approach) 6.00% 5.00% 4.00% 3.00% 2.00% 1.00% Real Spread Estimated spread α = 0.68 β = 0 γ = % VITA I VITA II B VITA II C VITA II D VITA III A VITA III B Tarta B OSIRIS B OSIRIS C OSIRIS D NATHAN A

Number 26 page 630 The production of Reliable Manufacturing company for 2007 and part of 2008 follows Production (thousands

Assigmet November 9 th Forcastig- Seasoal Idex Number 26, 27, 28,29 page 639-631 Statistical Techiques i Busiess ad Ecoomics Lid/Marchal/ Wathe Number 26 page 630 The productio of Reliable Maufacturig