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PITFALLS IN REINSURANCE PRICING

REINSURANCE SEMINAR 2000. PITFALLS IN REINSURANCE PRICING. The Potential Minefield. Trend, Development Beyond Policy Limits Trending vs Detrending Cessions-rated Treaties Bornhuetter-Ferguson Data Issues Using Simulation. Trend, Development Beyond Policy Limits.

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PITFALLS IN REINSURANCE PRICING

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  1. REINSURANCE SEMINAR 2000 PITFALLS IN REINSURANCE PRICING

  2. The Potential Minefield • Trend, Development Beyond Policy Limits • Trending vs Detrending • Cessions-rated Treaties • Bornhuetter-Ferguson • Data Issues • Using Simulation

  3. Trend, Development Beyond Policy Limits • 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

  4. Trend, Development Beyond Policy Limits Cont’d • 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?

  5. Trending vs Detrending • 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.

  6. Cessions-rated Treaties What to Look For • “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.

  7. Cessions-rated Treaties Cont’d • 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.

  8. Cessions-rated Treaties Cont’d • Same cessions factors regardless of SIR • Solutions: • Factors varying by SIR (rare) • Factors applying to ground-up premium prior to SIR credit

  9. Cessions-rated Treaties Cont’d • Example • Policy Limit = 5M, Layer =$4Mxs1M • ILFs are as follows: • LimitILF • 1M 1.00 • 2M 1.15 • 5M 1.33 • 6M 1.36 • Rate, no SIR = (1.33-1)/1.33 = 25% • Rate, $1M SIR = (1.36-1.15)/(1.36-1) = 58% • Reinsurer LR would be 2.3 times the cedant’s LR if SIR is not accounted for.

  10. Cessions-rated Treaties 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)

  11. Bornhuetter-Ferguson • 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.

  12. Data Issues • Policy Limit Profiles • Available only by policy counts, not premium • To fix, multiply by ILFs • Example • Pol Limit Policy Count ILF • $250K 1000 1.00 • 1M 500 2.00 • 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

  13. More Data Issues • 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

  14. More Data Issues • Small volume of claims in the layer may cause distortion in the triangle development. • Negative development in gross triangle is tricky. • e.g.12241224 Ground-up: clm#a 1,000 900 or 500 900 clm#b 0 0 500 0 ATA= 0.90 0.90 Excess of 400:clm#a 600 500 or 100 500 clm#b 0 0 100 0 ATA= 0.833 2.50

  15. Simulation Cont’d • 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

  16. Simulation • 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

  17. ANTI-STRESS KIT BANG HEAD HERE Instructions 1. Place on firm surface. 2. Follow direction provided in circle. 3. Repeat until you are anti-stressed or become unconscious.

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