Introduction to reinsurance Flashcards
Reinsurance <> Coinsurance
In coinsurance, insured share the risks between several insurer. In reinsurance, the insured share the risk to his insurance that share the risk to a reinsurer
Family of reinsurance contracts
- Facultative
- Proportional
- Non proportional
- Excess of loss
- Stop Loss/Aggregate excess of loss
- Treaty
- Proportional
- Quota-share
- Surplus
- Facultative/Obligatory - Non proportional
- Excess of loss
- Per risk
- Per cat
- Stop Loss/Aggregate excess of loss
- Proportional
Main objectives of reinsurance (7)
- Insurer’s capital protection
- Stability of the insurer’s results -> reinsurance reduces the volatility of final result
- Increase underwriting capacity of the insurer
- Financing the growth of young companies
- Reducing the minimum solvency margin
- Spreading of risks
- Technical support
Facultative vs treaty insurance
FAC : Part of the risks in excess of the treaty
capacity
* Reinsurance risk per risk
* Applies for high risks
* May be proportional or non-proportional
* No contract in general: just a cover note
with copy of original contract
* Heavy administrative costs
TREATY : Reinsurance of entire portfolios
* All the risks of a portfolio are ceded to
the reinsurer
– The cedent is obliged to cede
– The reinsurer is obliged to accept.
* Administrative costs far lower
Fac/oblig. reinsurance
* Cedant is not obliged to cede. Reinsurer is
obliged to accept
* This form of reinsurance is disappearing
Proportional reinsurance
- A predetermined part of each and every risk alpha(i) is transferred to the reinsurer.
- The same proportion of risk alpha(i) in premium is ceded
- The reinsurer pays same proportion of risk alpha(i) in losses
Quota share reinsurance
- alpha, ex and graph
- expliquer un exemple
- avantages et inconvénients (4+, 7-)
alpha(i)=alpha for all risks ex : QS 40/60
graph : sum insured in Y, Risks in X, all risks reinsured by alpha%
Example : le réassureur assure tous les risques à 60% (QS 40/60), s’il y’a une perte, peu importe son montant, 60% de celle-ci est remboursée
+ : Simple administration, (Limited) decrease of the total exposure, (Limited) increase of underwriting capacity, Solvency relief
- : Underwriting capacity remains limited, Inadequate against large claims, Inadequate against accumulation of small claims, Limited increase of underwriting capacity, High level of premiums ceded, Small risks are reinsured to, Homogeneity of the portfolio is not better
Surplus reinsurance :
- alpha, ex and graph
- develop and example
- 4+, 6-
alpha(i)=max(0;1-R/Sli) ex: Surplus 3 lines of 2
graph : Sum insured en Y et risks en X, reassureur assure tous les risques > R
Example : Surplus 1 : 4 lines of 1 (8M of 2M), surplus 2 : 8 lines of 5 (16M of 10M), underwriting max 26M. Risk of 25M, loss of 100.000 for this risk -> 8% insured -> 32% surplus 1 -> 60% surplus 2
+ : * Maximum exposure per risk is limited
* Increase of the underwriting capacity
* The net portfolio of the cedent is more
homogeneous
* With a table of lines, the cedent is able
to retain more of the “good” risk
- : * Administration cost
- Still a large proportion of the premium
ceded - Possible anti selection against the
reinsured - Small losses hitting large risks are also
reinsured - Inadequate protection against
accumulation of (small) claims - Not applicable for unlimited liabilities
Excess of loss reinsurance
- ex, graph
- 2 types
- example
- per risk : 5+, 3-
- per event : 2+, 4-
L xs P, intervention for each CLAIM > P limited to L.
Graph : Loss in Y, claim in X.
XS Loss : per risk : loss insurer = loss reinsurer
per event : loss “” not eq. “” “”
Example : 10M XS 2M and 26M XS 10 (2 layers) : loss of 3M -> 1M reinsured by layer 1
Per risk :
+ :
* Limitation of the maximal exposure per
risk
* More homogeneous retention
* Simple administration
* Smaller reinsurance premium than in
surplus
* Applicable even if there is no sum
insured
- : * Fixing the reinsurance premium
- Inadequate against accumulation of
(small) claims - Reinsurance result is unstable => price
can be volatile
Per event :
+ :
* Limitation of the maximal exposure per
event
* Simple administration
- : * Fixing the reinsurance premium
- Reinsurance result is very unstable and
worldwide market => price is highly
volatile - MPL difficult to estimate
- Definition of event can be subject to
discussions/difficult
Stop loss reinsurance
- ex, graph, develop example
- 2+, 4-
Intervention for aggregate loss amounts ex : SL 30% XS 80%
graph : loss ratio (loss/premium) Y and year in X
ex : loss ratio 95% -> 15% of the premiums reinsured
+ : * Ideal coverage
* Simple administration
- : * Fixing the reinsurance premium
- The market is “stop-loss averse”
- Risk of moral hasard
- MPL difficult to estimate
How reinsurers diversifies the underwriting risks
Reinsurers diversify the underwriting risk per geographical area and type of risk
XL : Collective risk model
- S, E(S) ?
- example
S = X1+…+Xn
E(S) = E(N)*E(X)
P=5M, E(X)=20M, E(Y)=15M, E(N)=1/20, E(S)=0,05*15M=750000
XL : Burning cost
- example
- 4+, 4-
XL loss year t /premium year t
if estimated premium income = 140000, pure premium = 6,3% (total BC) * 140000
+ : * Easy to calculate
* No distribution function to be estimated
* Good proxy for working layers
* Takes evolution of exposure into account
- : * Does not use all data (data < threshold)
- Distortion caused by potential extreme
losses - Does not take into account
– The portfolio profile (evolution)
– The (evolution of) underwriting policy of the
cedent - Does not allow to price layers that
have never been hit
XL : mathematical model ; why collective ?
Why collective : E(Scoll)=E(Sind) but Var(Sind)<Var(Scoll) so it’s conservative
XL : mathematical model ; example projet (sans les formules) , 5+ and 4-
Pareto : 2000xs1500, cumulated paid loss et outstand. reserves
- premium indexation : claim index 100->102,44->… indexed=non indexed(last year index/year index)
- Loss index : paid loss->increm->indexed->cumulated+indexex reserves = indexed incurred loss
- # loss>Amin -> extrapol -> Ultimate #loss , lambda poisson=#policies last year*(ultimate #loss/#policies sans last year)
- alpha(hat)=(#ultimate loss>Amin)/sum(ln(Xi/Amin))
- E(X) = Amin*(alpha/(alpha-1))
- P(X>Priority)=(Priority/lambda)^-alpha
- P(lambda>Priority)= lambda *P(X>Priority)
- E(YP)=Priority*(alpha/(alpha-1))
- XL Pure premium = E(YP)*P(lambda>priority)
- On recalcule ensuite XL pure premium en remplacant P par P+L et E(Y)=XLpp(P)-XLpp(P+L)
+ : * Uses all data
* Allow to price all layers
* v d d XL ’
loss distribution
* Allows to price XL specific clauses (see
later)
* Can be combined with market
parameters/distributions
- : * Model choices
- Model = simplification
- Parameters estimation
- Does not take into account
– The portfolio profile (evolution)
– The (evolution of) underwriting policy of the
cedent
XL : Aad 10M xs 5M , Aad 10M
S : 10 20 3 10 tot 43
XL : 5 10 / 5 tot 20
Ret. 5 10 3 5 tot 23
Aad : XL 10 Ret 33
XL : Aal 10M xs 5M, Aal 15M
Aad et Aal ?
S : 10 20 3 10 tot 43
XL : 5 10 / 5 tot 20
Ret. 5 10 3 5 tot 23
Aal : 5M (20M-15M) -> XL 15 Ret 28
combined : Sclau=min(max(0,S-Aad);Aal)
Pure premium=E(Sclau)
XL : Reinstatements
Limitation of the XL aggregate loss
Free or prepaid reinst. (no diff with Aal if prepaid) (paid reinst ; pro rata capita or pro rata temporis)
Ex : 10M xs 5m, premium 100M, premium rate 1%, no reinst. -> Annual XL aggregate loss=10M, 1reinst -> AnnXLagg= 10M+10M , 2 reinst -> 10M+210M
Prepaid or free : XL premium = 1%100M
1 paid reinst. pro rata capita 100% : 1st claim 31/03/2023 : 11M , ret. 5M, XL=6M, reinst. 6M (60% of 10M) , XLpremium=1M+600000 (60%1%100M) 2nd claim : 15/09/23 : 15M XL10M, reinst. 4M (40% of 10M) because only one reinst. XLPREM total : 1M+600000+400000
1 paid reinst. pro rata temporis : 1st claim 31/03/23=11M, Reinst. 9/12 of 10M, premium= 75%1%100M total premium = 1M+750000
-> Sliding scale premium
-> Profit sharing
-> Risk classes
-> Loss indexation
-> Stability clause
-> P is function of S with a max and a min, often xith a loading
-> PC=alphamax(0,BetaPinit-S), 1-Beta = % of admin costs, alpha=fraction of profit paid back
-> short tail : fire, motorown damage large tail ; MTPL, workmen compensation
-> X*Index arrivée/index origine
-> Priority*(sum actual payments/sum deflated payments) -> limite les variations de primes trop busques
Proportional reinsurance :
-> Reinsurance commision
-> Overriding commision
-> Loss participation
-> Collaterals
-> percentage of the written premium (profit sharing)
-> same function but in retrocession contracts
-> participation of the insurer in the loss of the treaty
-> guarantee fir the insurer that the reinsurer wil fullfill his obligaitons (cash/deposits)
Proportional reinsurance : technical accounting
Occurence year basis :
Written premium = earned premium
ERP
Incurred loss = INC
Accounting year basis :
Written premium = ERP
Incurred loss = Accounted loss (AL)
Insurance Linked Securities ; schéma , définition , why ?
Risk transfer between reinsurer and investors
A speciale purpose reinsurance vehicle invest in Cat bond investors (3-4yrs), Cat bond sponsors (cedant), collateral account (stable value asset)
Diversify, certainty, flexibility, competition
ILS product : CAT bonds
Fully collateralized securitization, alternative to traditional
reinsurance
Issued by (re)insurers or other corporate sponsors
Generally, of 1–5-year term
Active secondary market
Average risk spreads between 5% - 15%
cash flow : ▪ Premium from cedant to SPV -> Paid at issuance and on each subsequent quarterly payment date during the Risk Period (some alternatives are also available)
▪ Transaction (at issuance and ongoing) expenses from investor to service providers -> Paid at issuance and on each payment date until maturity
▪ Issuance proceeds from cat bond investors to SPV (and then Collateral Account) -> Paid only once, at inception of the transaction
▪ If any, claims paid from SPV (Collateral Account) to cedant -> following an event, paid on each quarterly payment date during the risk period and, if needed, during the
extension period until the earlier of (i) all claims are paid or (ii) commutation
▪ If any, return on collateral from SPV (Collateral Account) to cat bond investors -> Paid on each quarterly payment date during the risk period and the extension period until
the earlier of (i) all claims are paid or (ii) commutation
S2 and reinsurance :
-> Reinsurance in the balance sheet
ASSETS : Part of reinsurance in the technical provisions + Investments matching deposits
LIABILITIES : Gross technical provisions + Deposits from reinsurers
Distinct technical provisions in the balance sheet for claims that already occured and claim that could occur in the future during coverage periode
S2 separate : Premium provisions (future claim events) and claims provisions (events already occured)
S2 and reinsurance :
-> Gross best estimate
-> Reinsurance best estimate
-> Premium vs claims provisions
-> When the contract does not exist anymore
-> Capital requirement definition
-> proba weighted average of future CF
-> Reinsurance Best Estimate calculation should follow similar principles
than gross Best Estimate (CF, discount rates, …) BUT Recoverables have to be adjusted due to expected default
-> future claim events vs claim events that have already occurred
-> The contract does not exist anymore from the moment where insurer or
reinsurer:
– have the unilateral right to terminate the contract
– have the unilateral right to reject premiums payable under the contract
– have the unilateral right to amend premiums or future benefits under the
contract
-> “The loss of basic own funds of insurance or reinsurance
undertakings that would result from an instantaneous loss equal to
the prescribed scenario.”
S2 and reinsurance :
-> 2 approach of capital requirements
-> SCR calculation
-> Impact of reinsurance on SCR
-> Requirements
-> Optimal reinsurance
-> Counterparty default risk
-> SCR (standard approach or internal) or MinimumCR
-> SCR should be calculated net of Reinsurance, SCR for counterparty risk should be taken into account
-> Risk mitigation effect
of reinsurance diminue le SCR, Additional capital to cover
reinsurer’s default risk le réaugmente un peu
-> Qualitative criteria, Only risk mitigation techniques that are in force for at least the next 12
months
-> biggest RORAC = E(profit)/SCR ou biggest Economic Value Added = cost sans reins. -cost with reins.
-> « Risk of default of a counterparty to risk mitigating contracts like reinsurance arrangements (…) »
2 options to go further:
1. USP for s
2. XL adjustment factor (standard or USP)
- Set of standard parameters that may be replaced in the Non-Life
premium and reserve risk sub-module
i. Standard deviation for premium risk
ii. Standard deviation for gross premium risk
iii. Adjustment factor for non-proportional reinsurance
iv. Standard deviation for reserve risk
* Data requirements
– Internal and external data
* Method requirements
– Standardised methods to be used - Only for premium risk
* Standard values defined in the delegated acts:
– 80% for MTPL, GTPL and Fire
– 100% for other lines of business
* Possibility to use USP → Only for “recognisable” XL contracts
-> Loss given default
-> Risk mitigating effect (RM)
-> Moddeling
-> Loss of basic own funds which the insurer would incur if the counterparty
defaulted
-> Extra capital to be allocated in case of default
-> * Large individual losses need to be modelled separately
* Event losses need to be modelled separately
* Small (attritional losses) may be modelled on an aggregate
basis
* Surplus: link with original risk needed (to determine the
cession rate)
