Brief introduction toInsurance and Credit risk
Agenda
► Who we are► Example of use of simulation techniques in insurance► Brief introduction to credit risk modeling
Who we are
Who are we?
Side 4
► Marius is working asan actuary in ourFinancial Services.
► He has longexperience as anactuary in theNordic market
► Lars is a newlygraduated actuarywho joined ourpractice in August2013
Marius FredheimSenior Manager
Lars ØsthasselConsultant
Side 5
Ernst & Young Advisory Services is one of the largest Nordicconsulting firms
Stockholm
Gothenburg
MalmöCopenhagen
Helsinki
OsloStavanger
Bergen
Trondheim
Reykjavik
Advisory services► Ernst & Young Advisory Services is one of the largest
Nordic consulting firms, with over 600 consultantsFinancial services► Financial Services deliver a global perspective. Aligned
to key industry groups including asset management,banking and capital markets, insurance and privateequity
Actuarial services► Actuaries supports the audit function, profitability
improvement projects, pricing, reserving and capitalmodeling. Often related to Solvency II
We leverage our global size… ... Together with our local knowledge
We work with the leading nordicfinancial institutions:
SwedbankNordeaHandelsbankenSEBDanske BankDnB NorVitalCarnegie
OP-PohjolaFolksamSkandiaGjensidigeSpareBank 1LänsförsäkringarIf..
Page 6
• Advice on riskaggregation and design ofsimulation models
• Capital modelling
• Validation on the IRB-system
• P&L attribution
• Standard formulaimplementation
• Capital modelling
• Validation
• IRB
Credit Risk
Solvency II / Basel III
• Provide formal sign offof liability calculations
• Advice on pricing andproduct development
• Advise on regulatory andmarket movements
• Burning costcalculations
• Review existing pricingmechanisms
• Risk factor coverage• Cost of capital –
economic vs. regulatory
• Review reservingmethodologies againstmarket practice
• Accuracy ofimplementation
• Use of reservingnumbers through thebusiness “single versionof truth”
Actuarial function
Pricing
Reserving/reserving reviews
Quantitative services - EY
► TechnicalProvisions
► MCRMinimumCapitalRequirement
► SCRSolvencyCapitalRequirement
► ModelApproval
Pillar 1
► RiskManagement
► Own RiskandSolvencyAssessment(ORSA)
► Supervisory powersandprocesses
Pillar 2
► RiskManagement
► Own RiskandSolvencyAssessment(ORSA)
► Supervisorypowersandprocesses
Pillar 3
Our quantitative resources are working on a wide range of services, including:
Simulation techniques ininsurance
Introduction to risk and capital
The economics of an insurance company
Side 9
UW resultat = Premium – Claims – Costs + InvestementsUW resultat = Premium – Claims – Costs + Investements
Premium Claims
Financial Costs
Reinsurance
Reserves
Resultat
The economics of an insurance company
Side 10
P&L Account for 2014
Net Premium Earned
-/- Net Claims Incurred
-/- Net AcqCost Incurred
-/- Expenses Incurred
+ Investment Income
-/- Tax Incurred
-/- Dividends
= Net Retained Earnings
BS as at31/12/2013
BS as at31/12/2014
P&L for2014
Assets
Liabilities
Equity
Assets
Liabilities
Equity
Risk profile at policy levelCompany’s need to assess different types of scenarios and always define “worst case” scenario
Pro
babi
lity
Worst case scenario- 90 000 loss
Moderate loss scenario- 30 000 loss
Break even scenario- 10 000 loss
Profit
Policy Premium = 10 000 NOK
Potential loss and capital requirementCompany’s need to set aside capital to cover potential loss with 99,5 % probability
Pro
babi
lity
Result
Potential losswith 99,5 %probability
Mean
Potential loss
Capital requirements under Solvency II
Side 13
Starting BOFat T=0
SCR:Change in BOF over
the year in thestressed scenario
(99,5th percentile BOFat time T=1 less the
starging BOF at T=0)
Expected profit inyear
Average change ineconomic capitalfrom T=0 to T=1
T=0 T=1 Mean
ExpectedBOF
at T=1
Modelled stressto the 99.5th
percentile
T=1 99.5th
99.5th percentileBOF
at T=1
Potential lossAverage change ineconomic capitalfrom T=0 to T=1
Different risk categories and aggregation
Some risk categories for insurers
Premium risk Risk related to future claims beinghigher than expected
Reserving risk Risk related to incurred claimsbeing higher than expected
Market riskThe risk of economic losses
resulting from deviations in thevalue of assets
Counterparty riskThe risk to each party of a contract
that the counterparty will not live upto its contractual obligations
Top financial risks insurers are facing
Side 16
Categories of Risk:► Insurance Risk
▬ Underwriting Risk▬ Reserving Risk
► Market Risk► Credit Risk► Liquidity Risk► Group Risk► Operational Risk
InsuranceRisk, 68%
Credit Risk,8%
Market Risk,13%
OperationalRisk, 10%
LiquidityRisk, 0%
Group Risk,1%
Side 17
Definition of Risks in Non-Life insurance
Premium &Reserve
Lapse
Cat
Equity
Property
Spread
Currency
Concentration
CCP
Interest rate NL annuitiesPersonalaccident
Many risk modules from the Solvency II standard formula areaddressing risks that need to be covered within Non-Life riskmodels
Non-lifeLife
Deferredtaxes Op. Risk
Health Default Intangibles
Overall SCR (Non-Life)
Base SCR
Market
17
Total risk profile for the corporate
Side 18
UW risk Credit risk Market riskReserving risk
Corporate Risk Profile
Operational
Pynte på denne?
UW riskmodels
Page 20
Attritional claimsHigh frequency/low severity claims
Large ClaimsLow frequency/high severityclaims, that exceed a certain
threshold
Catastrophic ClaimsAccumulation claims caused by ancatastrophe (natural or man made)
A common approach across different markets - dividing claims into three different types:
2. Calibration/Design – Premium Risk
20
Page 21
2. Calibration/Design – Premium Risk
21
Attritional claims� Modelled as aggregate claims
� Separate parameterisation offrequency and severity or
� Parameterisation ofaggregate loss distribution
Large Claims� Modelled as single large
claims via frequency/severityapproach
� Exposureadjustments/Indexation
Catastrophic Claims� Scientific models often used
from external sources, butparametric approaches alsoused
� Impact of catastrophic eventsis modelled on currentexposure set
Attritional claims� Adjustment of trends and inflation� Excluding annuities for
parameterisation (life risk)� Excluding cat. claims data
sometimes leads to issues due tomissing cat. classification atsingle data level.
Large Claims� Threshold for large claims has to
be smaller than the priority ofnon-proportional reinsurancetreaty relevant for the modelledline of business
Catastrophic Claims� Careful usage of external data
needed as sometimes externaldata do not fit to the writtenbusiness of the insurancecompany (e.g. due tounreasonable model assumptions)→
� Validation strongly required, e.g.comparison of average of externaland internal data or internaldiscussion of size of tail events� Often missing internal
acceptance of model results ifunreasonable tails are used
Side 22
2. Calibration/Design – Premium RiskG
ross
Res
ult
com
pone
nts
Earnedpremium
Costs SimulatedClaims
Underwriting risk
Side 23
► Attritional claims: everyday claims
► Large claims: claims that are largeenough to get individual attention
► Catastrophic claims: claims thatare extremely large and usuallycaused by a single very severeevent
0,0%
0,5%
1,0%
1,5%
2,0%
2,5%
3,0%
3,5%
4,0%
4,5%-4
80
-420
-360
-300
-240
-180
-120 -60 0 60 120
180
240
300
360
420
480
540
600
660
720
780
Side 24
ResultPr
obab
ility
ofO
utco
me
Business Plan LevelCapitalLevel
Side 25
Recap – Insurance Risk inc UnderwritingRisk
► Insurance risk is the risk of loss arisingfrom the occurrence, timing and amount ofinsurance claims.
► It includes current and prospectiveunderwriting and the development of prioryear reserves.► Underwriting Risk ≈ what you will write
► Attritional and large claims► Catastrophe Risks► Underwriting Cycle
► Reserving Risk ≈ what you have written► Possibility that prior year reserves are inadequate► Earned and unearned reserves
30 July 2014 Introduction to CapitalPage 25
P&L Account
Net Premium Earned
-/- Net Claims Incurred
-/- Net AcqCost Incurred
-/- Expenses Incurred
+ Investment Income
-/- Tax Incurred
-/- Dividends
= Net Retained Earnings
Assets Liabilities
Equities, Bonds,Cash
TechnicalProvisions
Property UPR
DAC Provision Other Provisions
Debtors Creditors
Shareholder’sCapital
Total Total
Brief introduction to creditrisk modeling
Page 27
Assets Liabilities
Assets Debt
Equity
Assets Liabilities
Assets Debt
Equity
Setting the SceneWhy is credit important?
Assets LiabilitiesLoans Deposits
Equity
The Firm(s) The Bank
Assets LiabilitiesAssets Debt
Equity
Credit
Leve
rage
*
*Basel III leverage ratio requirement of more than 3 %
Page 28
What is Credit Risk?
Definition of Credit RiskCredit risk is most simply defined as the potential that a borrower willfail to meet his obligations in accordance with agreed terms.
Definition of DefaultThe failure to pay interest orprincipal when due.
A contract is said to be in default90 days after due.The bank hasto report and establish the loss.
Page 29
How can we assess the losses associatedwith Credit Risk?
Unexpected Loss (UL)� The risk that losses exceed EL within a year
Time
EL
UL
Individual losses Expected Loss (EL)The average value of losses
over a year
Unexpected Loss (UL)The risk that losses exceed EL
within a year
Stochasticsimulation
Historical Data Models
Page 30
How to cover the losses associated withCredit Risk?
Price Capital
EL
Prob
.Den
sity
Loss
UL
μ
Page 31
Fundementals of Credit Risk
Page 32
Mathematical definition of Expected Losses
Rating Exposure Losspercentage
Expected Loss = PD * EAD * LGD
Customers will always have an Expected Loss –even good customers!
What drives Expected Loss?A statistical methodfor estimating future
losses based onhistorical data
Page 33
PD - Probability at Default
What’s the probability of the customer goingInto default on the loan(s)?
0,00
0,01
0,02
0,03
0,04
A1 A2 A3 A4 A5 A6 A7 B1
PDle
vel
Probability of Default(PD)
Expresses theprobability of the
customer defaultingwithin a year
Page 34
EAD – Exposure at Default
What is ‘at stake’?
Expected utilisationat the time of defaultExposure at Default (EaD)
Increaseddrawing up todefault (CCF)
Unused
Unused
Drawn Drawn
EaD
Time ofestimation
Limit
Time of default
Page 35
LGD – Loss Given Default
How big a proportion do we expect to lose?Expected proportionof exposure that will
be lost in case ofdeault
0% 100%Degree of collateralization
LGD
LGD0%Coll.
LGD100%Coll.Min. LGD
Loss Given Default (LGD):
Page 36
PD-modeling
There are three fundamentally models usedfor PD modeling
Hybrid rating models
Option models
Structural models
Cash flow models
Simulation models
Expert judgement
Structred qualitative approach bylittle data
Rating forms
Purely statistical approach basedon historically data
Regression models
Neural networks
Discrimination analysis
Statistical scoring model Economic models Qualitative model
755 000 000695 000 0002 000 000552 000 000750 00049750 000200 00043200 0000,5120,50
ScoreTilFraWealth
0 1 2 3
D r i f t s a p p a r a t
K o mp l e k s i t e t
S t ø t t e f r a mo r / e i e r
E g e n k a p i t a l a n d e l
F l e k s i b i l i t e t
K v a l i t e t l e d e l s e
P o l i t i s k / j u r i d i s k r i s i k o
N ø k k e l m a n n s r i s i k o
Side 37
Regression analysis of historical data
Today (2013)
“Good”loans
“Bad”loans
Upon credit approval (2012)
Using the customerdata we now have, canwe construct a modelthat would haveenabled us to identifythe bad customers atthe time of initial creditscreening?
Question
Retrospective
Side 38
Page 39
Credit Risk analysis using Logistic Regression Modeling
850 past and prospective customers to execute a Logistic Regression Analysis
Random Sample:
513
Random mix of goodand bad loans
Validation Sample:
204
Random mix of goodand bad loans
Prospective Sample:
133
Unknown
Validate the modelConstruct the model Use the model
Customer information:Age, Sex, Income, Debt-to-income ratio, Change of Address, Education level,
Amount of credit card debt
Page 40
Different predictors are used depending on whether youare a new or existing customer
► New customer will be assigned anaverage PD based on age, sex,residence, income, assets etc
New Customer
► Existing custumer will have ahistory which will be included in thePD estimation (in addition to theusual parameters). Such asoverdrafts days and income-to-consumption ratio.
Existing custumer
Grade 1 (‘AAA’) Grade N (‘D’)
Grade
ScoreGrade n .
Calibration curve
Probabilityof default (PD)
Credit Scoring with Logistic Regression
÷÷÷÷
ø
ö
çççç
è
æ ×+-
+
=
)2ln(20
)50ln()2ln(
20200
1
1)(SCORE
e
ScorePD
Liquidity
Solvency
Behaviour
Factors
0 - 10................
0 - 10
Expert judgement,univariate analysisand regression
Transformation
Weight ofEvidence
w1................
wn
Coefficient
Logisticregression-analysis
X = S Score
0.................
Default
PD
A.................
Default
Rating class
Depends on thedesired ratingscale structure
Backgroundinfo
Side 41
PD accuracy
► The ultimate goal of any rating model is to predict the probability of defaultsfor new applicants
► PDs are either produced by the model or obtained via mapping of internalgrades to external default experience
► The accuracy of these estimates needs to be validated► Realized default rates will deviate
from estimated ones. Validationprocedures need to examinewhether the deviation is substantialand should lead to a reviewof the model or can be attributedto statistical noise. Focus:► Significance of deviations► Monotony of PDs with regards to ‘risk’
Def
ault
prob
abili
ty(P
D)
Rating classes
Problem with modelor statistical noise?
Forecast Actual
Binomial test
► The binomial test determines the probability of observing the realizeddefault rate under the hypothesis that the estimated value is correct
► The probability to get n or less defaults given N non-defaultedborrowersand probability of default PD is given by:
► The binomial test with 95% double-sided confidence level amounts to:► P(defaults ≤ n) > 97,5% means that with this PD one should have gotten less
defaults than realized and the PD is underestimated► P(defaults ≤ n) < 2,5% means that with this PD one should have gotten more
defaults than realized and the PD is overestimated► Typically the test is carried out for each risk class
Thank you for your attention!
Feel free to contact us for any and all questions on this material!
Marius Fredheim([email protected]),Lars Østhassel ([email protected])
