PITFALLS IN REINSURANCE PRICING

Trend, Development Beyond Policy Limits Trending vs Detrending Cessions-rated Treaties Bornhuetter-Ferguson Data Issues Using Simulation

How do you know if there is a problem? –Experience rating >>Exposure rating –Large number of claims at round numbers coinciding with limits profile –Little exposure in covered layer based on limit profile

What to do if you have a problem –Cap trended losses at the policy limit, except... Are policy limits changing over time? –Adjustment necessary only if limits are not changing –Trending beyond limits assumes that policy limits are keeping pace with selected trend What if losses already exceed policy limits? Cont’d

Detrending the loss limits can be used in experience rating, instead of trending the loss forward. What premium do you divide the detrended excess losses by to get the excess layer loss cost? – Actual premium, if rate changes =loss trend –“Detrended” premium, if the rate level is flat –what if the rate level has been decreasing? Be sure to use consistent assumption for the gross expected loss ratio in exposure rating.

“Trust me”. No information provided on cessions factors or ILFs –Why? There are no ILFs. The company is using “market” rates. –Use agreed-on cessions factors. –Check out the underlying premium adequacy.

Good News/Bad News –The “Good”: Base rates have been increased –The “Bad”: Total rates remained the same –The “Ugly”: Guess who gets the short end of the deal? The XOL reinsurer. –Why? ILFs must have decreased. Cont’d

Same cessions factors regardless of SIR –Solutions: Factors varying by SIR (rare) Factors applying to ground-up premium prior to SIR credit Cont’d

Example –Policy Limit = 5M, Layer =$4Mxs1M –ILFs are as follows: »LimitILF »1M1.00 »2M1.15 »5M1.33 »6M1.36 –Rate, no SIR = (1.33-1)/1.33 = 25% –Rate, $1M SIR = ( )/(1.36-1) = 58% –Reinsurer LR would be 2.3 times the cedant’s LR if SIR is not accounted for. Cont’d

Premium Calculation on Policies with Deductibles and ILFs –Deductible credits apply to the Basic Limits –Wrong: Prem = Base Rate x Ded Credit x ILF –Correct: Prem = Base Rate x (ILF - Ded Cr) Cont’d

When is it reasonable to use B-F for pricing? –Other than for Loss Portfolio Transfers, which are essentially reserving analyses B-F on top of B-F –using last year’s selected ultimate as this year’s expected –for pricing - what does B-F add? Never credibility weight the B-F ULR with the Last year ULR.

Policy Limit Profiles –Available only by policy counts, not premium –To fix, multiply by ILFs –Example –Pol Limit Policy CountILF – $250K – 1M –Using policy counts, 1/3 of the exposure is at $1M –Taking the ILFs into account, 1/2 of the total exposure is at $1M

Deductible Limit Profiles not available Trend analysis may be affected by changing limit profile Rate Change History –Does not include changes in credits/debits –Changes in Exposure vs rate levels Loss Development Triangle –only ground-up triangles –only net triangles available

Small volume of claims in the layer may cause distortion in the triangle development. Negative development in gross triangle is tricky. e.g Ground-up: clm#a 1, or clm#b ATA= Excess of 400:clm#a or clm#b ATA=

Simulation does not necessarily add value –Simulating directly off a large claim sample –Simulating per occurrence XOL from a fitted loss distribution –You get the same answer with a direct calculation Simulation can be the best option –for example, contracts with drop down clauses, loss corridor, Annual Aggregate Ded Cont’d

How many iterations are necessary? –If the answers is not stable, more iterations are needed Garbage in- Garbage Out –Make sure inputs are reasonable contract terms, frequency distribution, severity distributions

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