Industries / Insurance and reinsurance
Model loss distributions, price premiums and reinsurance, and hold capital for a 1-in-200-year loss.
ModelRisk
ModelChoiceA motor insurer's claims next year
10,000 futures
The premium covers the year's claims in 97% of futures. The 1-in-200 year needs $0.66M of capital on top.
Clients in insurance and reinsurance
Across the business
From pricing a policy to the 1-in-200 year, each part of the business has its own question. Pick one to jump to it.
Questions we answer
Charts marked with a model code come from a free example model you can open in Excel. The others are marked illustrative.
ModelRiskBoth policies expect $100k of claims a year, but the property claims are far more volatile. Priced on the capital each one ties up, the property policy needs a risk premium 48% higher: $165.7k against $111.8k.
Mean claims $100k · loading 11.8%
ModelRiskThree distributions fit the same 250 claims and disagree fourfold on the 1-in-1,000 claim, from $1.45M to $5.75M. The Pareto fits best, and allowing for the uncertainty in its parameters adds 9% to the 1-in-200 year.
ModelRiskWith 25 years of history the 1-in-200 year lies far beyond the data. A Lognormal fitted to every event puts it at $85.6M; extreme value theory on the large events gives $149.3M, and $161.1M with the uncertainty in the fitted tail.
ModelRiskCompare programmes on the same simulated claims. Excess of loss and quota share together lift the 1-in-200 result from −$43.2M to −$15.4M for $2.12M a year, and free $27.8M of capital.
Mean $3.59M · 1 in 200 −$43.2M
ModelRiskThe broker's programme loses $14.4M in a 1-in-200 year, more than the $10M of capital the insurer holds. The ModelRisk Optimizer chose the retention, the cover and the quota share together; its programme loses $9.8M in that year, for about the same expected cost.
ModelRiskCapital depends on how the risks go wrong together. With a t copula, which lets bad years coincide, the insurer needs $128.6M: 43% less than adding up each risk's own capital, and $25.4M more than if the risks were independent.
ModelRiskOn its best-estimate mortality, lapse and disability rates the block loses money in 0.5% of futures. Let those rates be as uncertain as the limited experience behind them, and the chance of a loss is 8.4%.
Mean $10.20M · chance of a loss 0.5%
ModelChoiceA mid-size insurer weighs entering cyber insurance, where one ransomware event can wipe out years of profit. Piloting in three states has the best expected value, $3.2M; a nationwide launch comes out at −$7.8M.
How it fits together
Built in ModelRisk, in Excel. Each step has a free example model you can open.
ModelRiskFit the claimsFrequency and severity fitted to the history, with parameter uncertainty.IN-02 ModelRiskAdd them upA year's claims summed claim by claim.IN-01 ModelRiskPrice the policiesPremiums that reflect the capital each policy ties up.IN-06 ModelRiskReinsureExcess of loss and quota share on the same claims.IN-03 ModelRiskCapitalRisks combined with copulas for the 1-in-200 capital.IN-07 Free example models
Claims, pricing, catastrophe, reinsurance, capital and life models, and a decision tree for a new product. Each one opens in Excel.
Aggregate Claims: Frequency × SeverityWhat will a year's claims cost?Fitting Claim Frequency and Severity to DataWhich distributions fit the claims history — and how much does the shortness of that history add to the risk?Reinsurance Programme: Excess of Loss and Quota ShareWhat does reinsurance cost, and what does it buy?Catastrophe and Large-Loss TailHow large is the 1-in-200 year loss when the history covers only 25 years?Pricing a Policy: Premium PrinciplesTwo policies cost the same on average — should they cost the same to insure?Capital Requirement and DiversificationHow much capital does an insurer need, and how much does diversification save?Life Portfolio and LapseWhat is a block of life policies worth, and what makes it uncertain — chance, or not knowing the rates?Insurance Product LaunchA mid-size property & casualty insurer is evaluating whether to enter the rapidly growing cyber insurance market.Training
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See consultingFAQ
Because that is not the sum of every claim. In the free aggregate claims example the shortcut puts the 1-in-200 year at $72.4M; adding up every claim gives $8.2M.
With a model of the tail rather than of the average event. In the free catastrophe example, extreme value theory on the large events puts the 1-in-200 year at $149.3M, where a Lognormal fitted to every event says $85.6M.
Yes. ModelRisk has 14 copulas, including the t copula, which lets risks go wrong together in the tail. In the free capital example the 1-in-200 capital is $128.6M with a t copula and $103.2M if the risks were independent.
Yes. ModelRisk and ModelChoice each have a free 15-day trial, and our team can go through one of your own models with you.
Free 15-day trials of ModelRisk, ModelChoice and Tamara. For Pelican, we'll show it to you on risks like yours.
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