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Hedging catastrophe risks using index-based instruments CAS reinsurance seminar New York Feb. 28, 2002 Lixin Zeng, Ph.D. Willis Re. Outline Introduction / background Defining basis risk Calculating basis risk Optimal hedging strategies. Index-based risk management instrument - PowerPoint PPT Presentation
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11
The basis risk of index-based reinsurance instruments
Hedging catastrophe risks using Hedging catastrophe risks using index-based instrumentsindex-based instruments
CAS reinsurance seminarCAS reinsurance seminar
New YorkNew YorkFeb. 28, 2002Feb. 28, 2002
Lixin Zeng, Ph.D.Lixin Zeng, Ph.D.Willis ReWillis Re
22
The basis risk of index-based reinsurance instruments
OutlineOutline
Introduction / backgroundIntroduction / background
Defining basis riskDefining basis risk
Calculating basis riskCalculating basis risk
Optimal hedging strategiesOptimal hedging strategies
33
The basis risk of index-based reinsurance instruments
Index-based risk management instrumentIndex-based risk management instrument
Index typesIndex types Industry lossesIndustry losses Geophysical parametersGeophysical parameters
InstrumentsInstruments Cat optionsCat options Industry loss warranty (ILW)Industry loss warranty (ILW) Index-linked cat bondsIndex-linked cat bonds Other index-linked instruments (yield guarantee, Other index-linked instruments (yield guarantee,
index-based WC products, etc.)index-based WC products, etc.)
44
The basis risk of index-based reinsurance instruments
General conceptGeneral concept
BuyerBuyer SellerSellerFixed premiumFixed premium
Agree on an indexAgree on an index
Variable payoutVariable payout
Actual lossActual loss
55
The basis risk of index-based reinsurance instruments
ExamplesExamples
Call option on an industry loss indexCall option on an industry loss index
Call spread on an industry loss indexCall spread on an industry loss index
W: index; S: strike; L: limit; P: payout; k: payout ratioW: index; S: strike; L: limit; P: payout; k: payout ratio
S for W 0
S W SLfor S)(Wk
SL for W Lk
P
S for W 0
S for W S)(WkP
66
The basis risk of index-based reinsurance instruments
Examples Examples (continued)(continued)
Industry loss warranty (ILW)Industry loss warranty (ILW)
Sometimes subject to an actual lossSometimes subject to an actual loss
Index-linked cat bondIndex-linked cat bond
PP = Principal payment = Principal payment II = Interest payments = Interest payments XX = Parameters related to natural disaster event(s) = Parameters related to natural disaster event(s)
X)fIP (},{
S for W 0
S for W LP
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The basis risk of index-based reinsurance instruments
Compared to traditional indemnity instruments Compared to traditional indemnity instruments
AdvantagesAdvantages Simpler underwritingSimpler underwriting Lower moral hazardLower moral hazard Potentially lower costPotentially lower cost
ChallengesChallenges Tax/reporting implicationsTax/reporting implications Basis risk: mismatch between payout and actual Basis risk: mismatch between payout and actual
lossloss
88
The basis risk of index-based reinsurance instruments
OutlineOutline
Introduction / backgroundIntroduction / background
Defining basis riskDefining basis risk
Calculating basis riskCalculating basis risk
Optimal hedging strategiesOptimal hedging strategies
99
The basis risk of index-based reinsurance instruments
Example: Example: Mismatching of a cat option payout and the Mismatching of a cat option payout and the actual excess lossactual excess loss
S for W 0
S for W kS -kW S)(WkP
1010
The basis risk of index-based reinsurance instruments
Example: Example: Mismatching of a cat option payout and the Mismatching of a cat option payout and the actual excess lossactual excess loss
Actual loss
50 100 150 200 250 300
01
00
20
03
00
Pa
yo
ut
fac
tor
* In
de
x (K*W
)
retentionretention
Strike Strike (K*S)(K*S)
1111
The basis risk of index-based reinsurance instruments
Actual loss50 100 150 200 250 300
010
020
030
0
Pay
out f
acto
r *
inde
x (K*W
)
retentionretention
strike strike (K*S)(K*S)
Basis “gain”Basis “gain”
Basis riskBasis risk
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The basis risk of index-based reinsurance instruments
What is “basis risk”?What is “basis risk”?
Actual excess lossActual excess loss
Payout of anPayout of an““comparable” comparable”
reinsurance policyreinsurance policy
Payout of anPayout of anindex-based instrumentindex-based instrument
Basis risk Basis risk Basis risk Basis risk
Basis risk Basis risk
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The basis risk of index-based reinsurance instruments
Why do we care about basis risk? Why do we care about basis risk?
Type Type How effective is the index-based instrument in How effective is the index-based instrument in
reducing the risk of the underlying portfolioreducing the risk of the underlying portfolio
Type Type How does the index-based instrument compare How does the index-based instrument compare
to the traditional reinsurance policyto the traditional reinsurance policy
Type Type Probability of exhausting the limit, counter-Probability of exhausting the limit, counter-
party credit risk, contract dispute, etc.party credit risk, contract dispute, etc.
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The basis risk of index-based reinsurance instruments
DefinitionsDefinitions
SymbolsSymbols LLgg = actual gross loss = actual gross loss rrtt = retention = retention L = max(0, LL = max(0, Lgg - r - rtt) (excess loss)) (excess loss) PPii = payout of the index-based instrument A = payout of the index-based instrument A PPrr = payout of a “ = payout of a “comparable”comparable” traditional traditional
reinsurance policy Breinsurance policy B
1515
The basis risk of index-based reinsurance instruments
Definitions Definitions (continued)(continued)
An index-based instrument A and a An index-based instrument A and a traditional reinsurance policy B are traditional reinsurance policy B are comparable ifcomparable if The strike of A and the attachment of B have The strike of A and the attachment of B have
similar probabilities of attachingsimilar probabilities of attaching A and B have similar payout limitA and B have similar payout limit The costs of A and B are similarThe costs of A and B are similar
1616
The basis risk of index-based reinsurance instruments
Quantification of basis risk Quantification of basis risk
Measures based on covariance and/or linear Measures based on covariance and/or linear correlation between excess loss and payoutcorrelation between excess loss and payout Easy to calculateEasy to calculate Commonly usedCommonly used Actuarial meaning not clearActuarial meaning not clear Can be misleadingCan be misleading
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The basis risk of index-based reinsurance instruments
0.0 0.5 1.0 1.5 2.0 2.5 3.0
0.0
0.5
1.0
1.5
2.0
2.5
3.0
actual excess loss
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Example 1: payout vs. actual excess lossExample 1: payout vs. actual excess loss
Actual excess loss ($100M)Actual excess loss ($100M)
Payo
ut ($
100M
)Pa
yout
($10
0M)
1818
The basis risk of index-based reinsurance instruments
Example 2: payout vs. actual excess lossExample 2: payout vs. actual excess loss
0.0 0.5 1.0 1.5 2.0 2.5 3.0
0.0
0.5
1.0
1.5
2.0
2.5
3.0
actual excess loss
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Actual excess loss ($100M)Actual excess loss ($100M)
Payo
ut ($
100M
)Pa
yout
($10
0M)
1919
The basis risk of index-based reinsurance instruments
How to differentiate the two structures?How to differentiate the two structures?
actual excess loss structure 1 structure 2
$80M $73M $88M100% 98% 98%
0 $14M $14M
expected valuecorrelation
root mean square
2020
The basis risk of index-based reinsurance instruments
How to differentiate the two structures?How to differentiate the two structures?
actual excess loss structure 1 structure 2
$80M $73M $88M100% 98% 98%
0 $14M $14M
99% 0 $32M $37M99.60% 0 $37M $43M99.80% 0 $39M $50M
Quantiles of payout shortfall
expected valuecorrelation
root mean square
2121
The basis risk of index-based reinsurance instruments
Better quantification of basis risk Better quantification of basis risk
Conditional probability-based measuresConditional probability-based measures Probability distribution of payout shortfall given Probability distribution of payout shortfall given
an excess lossan excess loss Explicit actuarial implicationsExplicit actuarial implications
2222
The basis risk of index-based reinsurance instruments
Basis risk for reinsurance instrumentsBasis risk for reinsurance instruments
Basis risk type Basis risk type the mismatch between the mismatch between actual excess loss and payout when L > 0actual excess loss and payout when L > 0 Focus on how the Focus on how the netnet loss probability will loss probability will
change with different reinsurance strategieschange with different reinsurance strategies
Basis risk type Basis risk type the mismatch between the mismatch between index and indemnity instruments when L > 0index and indemnity instruments when L > 0 Probability distribution of Probability distribution of = P = Prr - P - Pii Focus on probability of “regret”Focus on probability of “regret”
2323
The basis risk of index-based reinsurance instruments
Basis risk for reinsurance instrumentsBasis risk for reinsurance instruments
Which measure to focus on?Which measure to focus on?
To develop an optimal reinsurance program, To develop an optimal reinsurance program, should be usedshould be used
To address existing bias towards traditional To address existing bias towards traditional reinsurance, reinsurance, should be used should be used
2424
The basis risk of index-based reinsurance instruments
Example 3Example 3
Reinsurer in a natural disaster areaReinsurer in a natural disaster area 15% market share15% market share Geographically diversified within the regionGeographically diversified within the region
Goal:Goal: Reduce probability of default from 1% to 0.4% Reduce probability of default from 1% to 0.4% Enhance risk/return profileEnhance risk/return profile Reduce earning volatilityReduce earning volatility
2525
The basis risk of index-based reinsurance instruments
Example 3 Example 3 (continued)(continued)
Measure of riskMeasure of risk
Probability of defaultProbability of default Probable maximum loss or Value at Risk with a Probable maximum loss or Value at Risk with a
0.4% exceeding probability: a proxy of risk 0.4% exceeding probability: a proxy of risk capitalcapital
Tail Value at Risk (TVaR): a coherent risk Tail Value at Risk (TVaR): a coherent risk measuremeasure
Semi-deviation of underwriting profit (i.e. Semi-deviation of underwriting profit (i.e. standard deviation of negative underwriting standard deviation of negative underwriting profit): related to earning volatilityprofit): related to earning volatility
2626
The basis risk of index-based reinsurance instruments
Example 3 Example 3 (continued)(continued)
Measure of successMeasure of success
Return on equity (ROE)Return on equity (ROE)
expected profit / company equityexpected profit / company equity
Return on Risk Capital (RORC)Return on Risk Capital (RORC)
expected profit / PMLexpected profit / PML
Modified Sharpe ratioModified Sharpe ratio
expected profit / semi-deviationexpected profit / semi-deviation
2727
The basis risk of index-based reinsurance instruments
Example 3 Example 3 (continued)(continued)
Evaluate competing strategiesEvaluate competing strategies Traditional retro policyTraditional retro policy
retention: 100-year PMLretention: 100-year PML limit: 250-year PML - 100-year PMLlimit: 250-year PML - 100-year PML
ILW (i.e. a binary call option)ILW (i.e. a binary call option) trigger: 100-year industry losstrigger: 100-year industry loss limit: same as abovelimit: same as above
Industry loss index call option (ICO) Industry loss index call option (ICO) strike: 90% of 100-year industry lossstrike: 90% of 100-year industry loss limit: same as abovelimit: same as above
2828
The basis risk of index-based reinsurance instruments
company loss ($M)
Pro
b N
on
Exc
1000 2000 3000 4000 5000 6000
0.9
00
.92
0.9
40
.96
0.9
81
.00
Pro
bab
ilit
y of
non
exc
eed
ance
Pro
bab
ilit
y of
non
exc
eed
ance
2929
The basis risk of index-based reinsurance instruments
company loss ($M)
Pro
b N
on
Exc
1000 2000 3000 4000 5000 6000
0.9
00
.92
0.9
40
.96
0.9
81
.00
Gross lossGross loss
Net after retroNet after retro Attached at 100-year lossAttached at 100-year loss Cover up to 250-year lossCover up to 250-year loss
Pro
bab
ilit
y of
non
exc
eed
ance
Pro
bab
ilit
y of
non
exc
eed
ance
3030
The basis risk of index-based reinsurance instruments
company loss ($M)
Pro
b N
on
Exc
1000 2000 3000 4000 5000 6000
0.9
00
.92
0.9
40
.96
0.9
81
.00
Gross lossGross loss
Net after retroNet after retro
Net after ILWNet after ILW Attached at industry 100-year Attached at industry 100-year
lossloss Same limit as the indemnity Same limit as the indemnity
contract abovecontract abovePro
bab
ilit
y of
non
exc
eed
ance
Pro
bab
ilit
y of
non
exc
eed
ance
3131
The basis risk of index-based reinsurance instruments
company loss ($M)
Pro
b N
on
Exc
1000 2000 3000 4000 5000 6000
0.9
00
.92
0.9
40
.96
0.9
81
.00
Gross lossGross loss
Net after retroNet after retro
Net after ILWNet after ILW
Net after Index Call OptionNet after Index Call Option Attached at 90% of industry 100-year Attached at 90% of industry 100-year
lossloss Same limit as the indemnity contract Same limit as the indemnity contract
aboveabove
Pro
bab
ilit
y of
non
exc
eed
ance
Pro
bab
ilit
y of
non
exc
eed
ance
3232
The basis risk of index-based reinsurance instruments
company loss ($M)
Pro
b N
on
Exc
1000 2000 3000 4000 5000 6000
0.9
00
.92
0.9
40
.96
0.9
81
.00
gross Net after Reins Net after ILW Net after ICOpremium 798 757 757 758 expected loss 399 392 388 388 semi-deviation 1,028 895 839 838 modified Sharpe ratio 38.8% 40.8% 43.9% 44.1%PML(VaR) 3,933 2,869 3,055 2,925 TVaR 5,693 4,628 4,658 4,635 RORC 10.1% 12.7% 12.1% 12.6%ROE 13.9% 12.7% 12.8% 12.9%Prob default 1.0% 0.4% 0.6% 0.5%
3333
The basis risk of index-based reinsurance instruments
-1000 -500 0 500
0.0
0.00
10.
002
0.00
30.
004
Probability density of Probability density of (ILW - retro payout) given L > 0(ILW - retro payout) given L > 0
Basis riskBasis riskBasis “gain”Basis “gain”
3434
The basis risk of index-based reinsurance instruments
Cumulative probability distribution of Cumulative probability distribution of (ILW - retro payout) given L > 0(ILW - retro payout) given L > 0
Alfa_r
Pro
b N
on
Exc
200 300 400 500
0.9
00
.92
0.9
40
.96
0.9
81
.00
““worst case” worst case” ~ 50% ~ 50% of cover limitof cover limit
Pro
bab
ilit
y of
non
exc
eed
ance
Pro
bab
ilit
y of
non
exc
eed
ance
3535
The basis risk of index-based reinsurance instruments
Example 4Example 4
Reinsurer in a natural disaster areaReinsurer in a natural disaster area 10% market share10% market share Not geographically diversified within the regionNot geographically diversified within the region
Goal:Goal: same as Example 3same as Example 3
Evaluate competing strategiesEvaluate competing strategies same as Example 3same as Example 3
3636
The basis risk of index-based reinsurance instruments
company loss ($M)
Pro
b N
on
Exc
500 1000 1500 2000 2500 3000
0.9
00
.92
0.9
40
.96
0.9
81
.00
Initial Net after Reins Net after ILW Net after ICOpremium 331 305 304 305 expected loss 166 161 159 159 semi-deviation 585 724 493 492
modified Sharpe ratio 28.3% 19.9% 29.6% 29.8%PML(VaR) 2,262 1,559 1,909 1,860 TVaR 3,308 2,605 2,708 2,678
RORC 7.3% 9.2% 7.6% 7.9%ROE 10.6% 9.2% 9.3% 9.4%Prob default 1.0% 0.4% 0.9% 0.9%
3737
The basis risk of index-based reinsurance instruments
-500 0 500 1000
0.0
0.0
02
0.0
04
0.0
06
0.0
08
beta
Mean= 138.47 ; Standard deviation= 250.77 Median= 0Probability density of Probability density of given L > 0given L > 0
Basis riskBasis riskBasis “gain”Basis “gain”
3838
The basis risk of index-based reinsurance instruments
beta
Pro
b N
on
Exc
600 700 800 900
0.9
00
.92
0.9
40
.96
0.9
81
.00
Probability distribution of Probability distribution of given L > 0given L > 0
worst case worst case = 100% = 100% of cover limitof cover limit
Pro
bab
ilit
y of
non
exc
eed
ance
Pro
bab
ilit
y of
non
exc
eed
ance
3939
The basis risk of index-based reinsurance instruments
Evaluating pros and cons of using index-based Evaluating pros and cons of using index-based instruments: Factors to considerinstruments: Factors to consider
Lower margin than a comparable retroLower margin than a comparable retro At the same premium, it offers greater At the same premium, it offers greater
reduction of expected lossreduction of expected loss
Basis riskBasis risk Reasonably small for geographically diversified Reasonably small for geographically diversified
exposuresexposures Potential for negative surprise for concentrated Potential for negative surprise for concentrated
portfolioportfolio Don’t count on the “basis gain”Don’t count on the “basis gain”
4040
The basis risk of index-based reinsurance instruments
Index-based or indemnity: which one to use?Index-based or indemnity: which one to use?
No universally applicable answerNo universally applicable answer Depends on financial objective and risk Depends on financial objective and risk
tolerancetolerance A combination of subjective judgment and A combination of subjective judgment and
objective analysis objective analysis
Quantitative analyses facilitate consistent Quantitative analyses facilitate consistent decision makingdecision making Consistent objectiveConsistent objective Optimal position at the risk/return curveOptimal position at the risk/return curve Explicit monitoring of portfolio riskExplicit monitoring of portfolio risk
4141
The basis risk of index-based reinsurance instruments
OutlineOutline
Introduction / backgroundIntroduction / background
Defining basis riskDefining basis risk
Calculating basis riskCalculating basis risk
Optimal hedging strategiesOptimal hedging strategies
4242
The basis risk of index-based reinsurance instruments
How to calculate conditional loss distributionsHow to calculate conditional loss distributions
Representation of probability distributions in Representation of probability distributions in cat modelscat models
Cat model provides loss distributions of Cat model provides loss distributions of gross and net lossesgross and net losses
For basis risk type For basis risk type : calculate probability : calculate probability distribution of annual aggregate lossdistribution of annual aggregate loss
For basis risk type For basis risk type derive derive F F based on cat based on cat model outputmodel output
4343
The basis risk of index-based reinsurance instruments
Event-based representation of loss probability Event-based representation of loss probability in a cat modelin a cat model
Cat model output Cat model output
Loss due to simulated event #Loss due to simulated event #kk
Rate of event #Rate of event #k k (average number per year)(average number per year)
kX
kr
4444
The basis risk of index-based reinsurance instruments
Event-based representation of loss probability Event-based representation of loss probability in a cat modelin a cat model
AssumptionsAssumptions
nn is is large enough for the set to contain nearly large enough for the set to contain nearly all possible natural disaster eventsall possible natural disaster events
NNkk Number of occurrences of event #Number of occurrences of event #k ~ k ~ Poisson Process withPoisson Process with
?? Events are independentEvents are independent
},...,2,1 ,{ , nkNX kk
),(~ XkXkk NX kk rNE )(
4545
The basis risk of index-based reinsurance instruments
For basis risk type For basis risk type
Probability distribution of annual aggregate Probability distribution of annual aggregate loss after reinsurance or index-based loss after reinsurance or index-based instrumentinstrument
Available approachesAvailable approaches Simulation based on per event lossesSimulation based on per event losses FFT (e.g. Wang, 1998)FFT (e.g. Wang, 1998)
4646
The basis risk of index-based reinsurance instruments
For basis risk type For basis risk type
Probability distribution of per event loss Probability distribution of per event loss XX may be any losses e.g. Pmay be any losses e.g. Prr, P, Pii, , , L, etc., L, etc.
)()(1
xXPxXP k
n
k
4747
The basis risk of index-based reinsurance instruments
)](1[
0
0
0 1,
,10
!
])([
!)]([
)()]([
)(])([
)(
max
xFr
m
mkkr
rmk
m
mk
m
m
iik
ikmim
k
kkk
k
em
rxFe
m
erxF
mMPxXP
mMPxXP
xXP
Number of Number of times event times event k k
occursoccurs
CDF of CDF of XXkk
4848
The basis risk of index-based reinsurance instruments
Event-based representation of loss probability Event-based representation of loss probability in a cat modelin a cat model
Loss probability distribution Loss probability distribution XXkk
)](1[)( xFrk
kkexXP
Frequency for Frequency for event event kk
Probability that the loss Probability that the loss exceeds x given event exceeds x given event k k occurs occurs
4949
The basis risk of index-based reinsurance instruments
Event-based representation of loss probability Event-based representation of loss probability in a cat modelin a cat model
Probability distribution of Probability distribution of XX
n
kkk xFr
exXP 1
)](1[
)(
5050
The basis risk of index-based reinsurance instruments
Event-based representation of loss probability in a cat modelEvent-based representation of loss probability in a cat model
A frequently used simplificationA frequently used simplification Assuming Assuming XXkk is deterministic, i.e.is deterministic, i.e.
ThenThen
xX
xXxF
k
kk ,0
,1)(
xX
r
k
kexXP )(
5151
The basis risk of index-based reinsurance instruments
Validity of the simplificationValidity of the simplification
Loss
Pro
b o
f N
on
Exc
.
0 20 40 60 80 100 120
0.9
90
0.9
92
0.9
94
0.9
96
0.9
98
1.0
00
Per-event loss standard deviation / meanPer-event loss standard deviation / mean
___________ 0___________ 0
___________ 10%___________ 10%
___________ 25%___________ 25%
___________ 50%___________ 50%
___________ 75%___________ 75%
___________ 100%___________ 100%
5252
The basis risk of index-based reinsurance instruments
How to calculateHow to calculate F F
FF( b | L > 0 ) ( b | L > 0 )
= Prob(= Prob( < b | L > 0) < b | L > 0)
= Prob(P= Prob(Prr - P - Pii < b | L > 0) < b | L > 0)
= Prob(P= Prob(Prr - P - Pii < b & L > 0) / Prob(L > 0) < b & L > 0) / Prob(L > 0)
5353
The basis risk of index-based reinsurance instruments
The problem of derivingThe problem of derivingFF( b | L > 0 ) = Prob(P( b | L > 0 ) = Prob(Prr - P - Pii < b & L > 0) / Prob(L > 0) < b & L > 0) / Prob(L > 0)
consists of two components:consists of two components:
(1) Prob(P(1) Prob(Prr - P - Pii < b) < b)
(2) Prob(P(2) Prob(Prr - P - Pii < b & L > 0) < b & L > 0)
5454
The basis risk of index-based reinsurance instruments
Problem 1: Prob(Z < z), where Z = X - YProblem 1: Prob(Z < z), where Z = X - Y
},..2,1 ,{
2;
),(~
),(~);,(~
},..2,1 , ,{
,
22
,
nkrZ
NZ
NYNX
nkrYX
kk
XYkYkXkZkYkXkZk
ZkZkk
YkYkkXkXkk
kkk
5555
The basis risk of index-based reinsurance instruments
Problem 2:Problem 2:
Prob(PProb(Prr - P - Pii <b) - Prob(P <b) - Prob(Prr - P - Pii < b & L < 0) < b & L < 0)
solution is simple only if independent or solution is simple only if independent or bivariate normalbivariate normal
If independent then:If independent then:
y)P(Y x)P(X y)Y &x P(X
5656
The basis risk of index-based reinsurance instruments
Problem 2 Problem 2 (continued)(continued)::
If bivariate normal then:If bivariate normal then:
)1(2
2
121
2
22
2),,(
yyxx zzzz
yx ezzf
yy
xx z ,z
yx
yx
x yz
-
z
-
),,( y)Yx,Prob(X dsdttsf
5757
The basis risk of index-based reinsurance instruments
OutlineOutline
Introduction / backgroundIntroduction / background
Defining basis riskDefining basis risk
Calculating basis riskCalculating basis risk
Optimal hedging strategiesOptimal hedging strategies
5858
The basis risk of index-based reinsurance instruments
Example 3 Example 3 (continued)(continued)
Goal: design an ILW structure such thatGoal: design an ILW structure such that
Probability of default reduced from 1.0% to Probability of default reduced from 1.0% to 0.4%0.4%
Maintaining highest possible ROEMaintaining highest possible ROE
Select the optimal ILW parametersSelect the optimal ILW parameters TriggerTrigger LimitLimit Exhaustive search of combinationsExhaustive search of combinations
5959
The basis risk of index-based reinsurance instruments
Trigger ($M)
Lim
it ($
M)
6000 8000 10000 12000 14000
050
010
0015
0020
0025
0030
00
0.04 0.05 0.06 0.07 0.08 0.09 0.1 0.11 0.12
0.13
How different trigger / limit combinationsHow different trigger / limit combinationsaffect ROEaffect ROE
6060
The basis risk of index-based reinsurance instruments
Trigger ($M)
Lim
it ($
M)
6000 8000 10000 12000 14000
050
010
0015
0020
0025
0030
00
0.04 0.05 0.06 0.07 0.08 0.09 0.1 0.11 0.12
0.13
0.070.08 0.09 0.1 0.11
0.120.13
How different trigger / limit combinationsHow different trigger / limit combinationsaffect ROE and affect ROE and RORCRORC
6161
The basis risk of index-based reinsurance instruments
Trigger ($M)
Lim
it ($
M)
6000 8000 10000 12000 14000
050
010
0015
0020
0025
0030
00
0.040.05 0.06 0.07 0.08 0.09 0.1 0.11 0.12
0.13
0.070.08 0.09 0.1 0.11
0.120.13
0.002 0.004 0.0060.008
0.01
How different trigger / limit combinationsHow different trigger / limit combinationsaffect ROE, affect ROE, RORC, RORC, andand prob. of defaultprob. of default
**
6262
The basis risk of index-based reinsurance instruments
company loss ($M)
Pro
b N
on E
xc
1000 2000 3000 4000 5000 6000
0.90
0.92
0.94
0.96
0.98
1.00
Initial Net after Reins Net after Optimal ILW Net after ICO
premium 798 757 740 758 expected loss 399 392 384 388 semi-deviation 1,028 895 791 838 modified Sharpe ratio 38.8% 40.8% 45.1% 44.1%PML(VaR) 3,933 2,869 2,857 2,925 TVaR 5,693 4,628 4,469 4,635 RORC 10.1% 12.7% 12.5% 12.6%ROE 13.9% 12.7% 12.4% 12.9%Prob default 1.0% 0.4% 0.4% 0.5%
6363
The basis risk of index-based reinsurance instruments
gross Net after
Reins
Net after ILW (initial
structure)
Net after ILW
(optimal) premium 798 757 757 740 expected loss 399 392 388 384 semi-deviation 1,028 895 839 791 modified Sharpe ratio 38.8% 40.8% 43.9% 45.1%PML(VaR) 3,933 2,869 3,055 2,857 TVaR 5,693 4,628 4,658 4,469 RORC 10.1% 12.7% 12.1% 12.5%ROE 13.9% 12.7% 12.8% 12.4%Prob default 1.0% 0.4% 0.6% 0.4%
How the optimal ILW structure improves the How the optimal ILW structure improves the risk/return profilerisk/return profile
6464
The basis risk of index-based reinsurance instruments
Summary: Index-based instrumentsSummary: Index-based instruments
Are becoming an increasingly important risk Are becoming an increasingly important risk management toolmanagement tool
Change the risk/return profile in a different Change the risk/return profile in a different manner than traditional reinsurancemanner than traditional reinsurance
Require the buyer to thoroughly analyze the Require the buyer to thoroughly analyze the basis risk tobasis risk to Avoid surprise or regretAvoid surprise or regret Take full advantage of index-based instrumentsTake full advantage of index-based instruments
6565
The basis risk of index-based reinsurance instruments
Summary: Basis riskSummary: Basis risk
There is no universally applicable definition of There is no universally applicable definition of basis riskbasis risk Depends on the financial objective and risk Depends on the financial objective and risk
tolerance of the buyertolerance of the buyer
Calculating basis risk is a nontrivial taskCalculating basis risk is a nontrivial task
The goal of this presentationThe goal of this presentation Promote a discussion on this topic among Promote a discussion on this topic among
actuariesactuaries Not intended to provide the “right” answer or Not intended to provide the “right” answer or
demonstrate the “right” methoddemonstrate the “right” method
