Vose SoftwareModelRisk example · Oil and gas
Major Accident and Operational Loss Exposure
What could our operations lose in a year, and which insurance programme is worth its premium?
From the model’s saved run
Annual loss before insurance
A 1-in-100-year loss is exceeded with a 1% chance in any year (the 99th percentile).
| Measure | Unit | Value |
|---|---|---|
| Mean annual loss | US$m | 30.7 |
| Median annual loss (a typical year) | US$m | 8.5 |
| 1-in-10-year loss | US$m | 36.7 |
| 1-in-100-year loss | US$m | 534 |
| 1-in-200-year loss | US$m | 988 |
| Chance of a major accident in a year | probability | 2.0% |
Probability of at least each value of Chance of a larger annual loss, 10th / 50th / 90th percentile from the saved simulation.
The business question
An offshore operator suffers a steady stream of minor incidents every year — equipment damage, small leaks, short shutdowns — a significant incident such as a fire or a large spill every year or two, and faces the small chance of a major accident that could cost billions.
The board asks two questions: how bad could a year be, and what insurance should the company buy? Insurance pays per occurrence above a deductible and up to a limit, so it does little for the stream of small losses but can transform the tail.
The model simulates each class of loss with a frequency and a severity: the many minor incidents as an aggregate distribution, the rarer significant incidents and major accidents event by event, so that the deductible and the limit can be applied to every occurrence.
It then compares no insurance with two programmes, priced from their expected recoveries plus the insurers' loading, by mean cost and by the cost of a bad year.
- Who it is for
- Risk and insurance managers, HSE and asset integrity teams, CFOs and boards.
- Main outputs
- Annual loss before insurance: mean, median, 1-in-10, 1-in-100 and 1-in-200-year values, chance of a major accident · for each insurance programme: premium, mean annual cost, cost by return period, average of the worst 1% · what insurance costs.
How the model works
Three sheets after this one, read from left to right. Each one feeds the next.
Inputs sheet
For each class of loss, the expected number of events per year and the mean and spread of an event's cost (Lognormal). For each insurance programme, the deductible and limit per occurrence, and the insurers' loading.
Losses sheet
Minor incidents: VoseAggregateFFT adds a Poisson number of Lognormal losses in one function. Significant incidents and major accidents: a Poisson number of events, each simulated in its own row, so that each occurrence can be split between the company and the insurer. The premium is the loading times the expected recoveries, calculated with VoseMean of a VoseDeductObject.
Results sheet
Percentiles of the annual loss read as return periods (the 99th percentile is the 1-in-100-year loss), the mean and tail cost of each programme, the average of the worst 1% of years, and what each programme costs and buys.
ModelRisk techniques
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The results in detail
The insurance programmes compared
Annual cost to the company: retained losses plus the premium.
S-curve (cumulative probability) of A No insurance, Programme B, Programme C from the saved simulation.
| Programme | Premium US$m | Mean cost US$m | 1-in-20 year, US$m | 1-in-100 year, US$m | Worst 1% average |
|---|---|---|---|---|---|
| A No insurance | – | 30.7 | 55.5 | 534 | 1,359 |
| B US$10m deductible, US$500m limit | 16.7 | 35.5 | 42.6 | 64 | 861 |
| C US$25m deductible, US$1,500m limit | 20.3 | 36.5 | 58.4 | 77 | 357 |
What the premium buys
Each programme's annual cost minus the cost with no insurance (A): what the cover adds on average and saves in bad years.
| Programme | Mean cost change, US$m | 1-in-20 change | 1-in-100 change | Worst 1% change |
|---|---|---|---|---|
| B US$10m deductible, US$500m limit | +4.7 | −12.9 | −470.5 | −497.7 |
| C US$25m deductible, US$1,500m limit | +5.7 | +2.9 | −457.9 | −1,001.9 |
Rows of the table above minus row A: a positive change costs more than no insurance, a negative one saves.
Cost by return period
The annual cost that is exceeded once in so many years, with each programme.
| Return period | Percentile 1 − 1 ÷ years | A US$m | B US$m | C US$m |
|---|---|---|---|---|
| 1 in 2 years | 50.0% | 9 | 25 | 29 |
| 1 in 10 years | 90.0% | 37 | 38 | 51 |
| 1 in 20 years | 95.0% | 55 | 43 | 58 |
| 1 in 50 years | 98.0% | 148 | 49 | 69 |
| 1 in 100 years | 99.0% | 534 | 64 | 77 |
| 1 in 200 years | 99.5% | 988 | 501 | 84 |
1 in 2 years is the median, a typical year. Change a return period and the row follows: the percentile is 1 − 1 ÷ the years.
What the insurance costs and buys
The premium buys the expected recoveries plus the insurers' loading; what it buys is a smaller tail.
| Measure | Unit | Value |
|---|---|---|
| Programme B: expected recoveries per year | US$m | 11.95 |
| Programme B: premium | US$m | 16.73 |
| Programme B: premium − expected recoveries | US$m | 4.78 |
| Programme C: expected recoveries per year | US$m | 14.50 |
| Programme C: premium | US$m | 20.29 |
| Programme C: premium − expected recoveries | US$m | 5.80 |
| Simulated mean recoveries, B (check) | US$m | 12.00 |
| Simulated mean recoveries, C (check) | US$m | 14.59 |
How to read these results
- A typical year costs much less than the average year: the average is pulled up by rare large losses. Insurance decisions are about those rare years, so compare the programmes by their 1-in-100 and 1-in-200-year costs and by the worst 1%, not by the mean.
- Insurance raises the mean annual cost by the insurers' loading — that is its price — and in exchange cuts the tail. Programme B's low deductible absorbs more of the significant incidents, but its limit is too low for a major accident. Programme C keeps more of the small losses and protects the company against the catastrophe.
- The expected recoveries are calculated exactly with VoseMean of a VoseDeductObject, and the simulated mean recoveries agree with them within the sampling error — which is large, because a major accident drives most of the recoveries and happens in only about 200 of the 10,000 samples. For the same reason, simulate more samples before relying on the 1-in-200-year values.
- Minor incidents are frequent but individually small. Together they make up much of the typical year, and no per-occurrence insurance with a meaningful deductible covers them.
See it move. Open the workbook, change an input on the Inputs sheet and run the simulation: every table and chart on this page updates in Excel.
Inputs and assumptions
Every assumption in the model, with its uncertainty and where it comes from. The figures are illustrative.
Minor incidents 3 inputs
Equipment damage, small leaks, short shutdowns: frequent and individually small.
| Assumption | Unit | Value |
|---|---|---|
| Expected number per yearIncident register, last five years. | events | 12.0 |
| Mean cost of an eventRepair, clean-up and lost production. | US$m | 0.40 |
| Standard deviation of the costLognormal: most are small, a few cost a few million. | US$m | 0.60 |
Significant incidents 3 inputs
Fires, large leaks, structural damage, extended shutdowns.
| Assumption | Unit | Value |
|---|---|---|
| Expected number per yearSeven in the last nine years across the company's assets. | events | 0.80 |
| Mean cost of an eventIncluding business interruption. | US$m | 12.0 |
| Standard deviation of the costLognormal, wide. | US$m | 15.0 |
Major accident 3 inputs
Blowout, explosion or major spill: rare, catastrophic.
| Assumption | Unit | Value |
|---|---|---|
| Expected number per yearIndustry frequency for an operator of this size: about 1 in 50 years. | events | 0.020 |
| Mean cost of an eventWell control, clean-up, third-party liability, fines, lost production. | US$m | 800 |
| Standard deviation of the costLognormal: the worst cases cost several billion. | US$m | 900 |
Insurance programmes 5 inputs
Per-occurrence cover for significant incidents and major accidents. Premium = loading × expected recoveries.
| Assumption | Unit | Value |
|---|---|---|
| Programme B: deductible per occurrenceQuote 1. | US$m | 10.0 |
| Programme B: limit per occurrenceQuote 1. | US$m | 500 |
| Programme C: deductible per occurrenceQuote 2: higher retention, much higher limit. | US$m | 25.0 |
| Programme C: limit per occurrenceQuote 2. | US$m | 1,500 |
| Insurers' loadingExpenses, capital cost and profit of the insurers; implied by the quotes. | × expected recoveries | 1.40 |
Units and conventions
- Money
- US$ million (US$m), cost to the company in the year of the loss.
- Return period
- A 1-in-100-year loss is exceeded with a 1% chance in any year: the 99th percentile of the annual loss.
- Per occurrence
- The deductible and the limit apply to each event separately, not to the year's total.
- Worst 1%
- The average annual cost in the worst 1% of years (conditional value at risk, VoseSimCVARp).
Key assumptions and limitations
- Independence
- Events occur independently (Poisson) and their sizes are independent of each other and of their number.
- Minor incidents
- Every minor incident is below every deductible, so all of them are retained.
- Slots
- At most six significant incidents and two major accidents in a year are simulated. The checks show that more is practically impossible with these rates.
- Insurance
- Premiums are the insurers' loading times the expected recoveries; no aggregate limits, reinstatements or credit risk. Data are invented for this example.
How to use it
- Calibrate the frequencies and severities on the Inputs sheet from your incident records and from industry data for major accidents.
- Enter the insurance quotes you are comparing: deductible, limit and the loading implied by the premium.
- Run a simulation from the ModelRisk ribbon (10,000 samples with a fixed seed are set; use more for the 1-in-200-year values).
- Compare the programmes by the return period that matters to the board, and by the cost of the insurance.
ModelRisk functions used
- VoseAggregateFFT, VosePoissonObject, VoseLognormalObject
- The year's total of minor-incident losses, computed by fast Fourier transform.
- VosePoisson, VoseLognormal
- Number of significant incidents and major accidents, and the cost of each.
- VoseDeductObject, VoseMean
- The insurer's payment per event after the deductible and the limit, and its mean, for the premium.
- VoseInput, VoseOutput
- Name the uncertain inputs and the annual outputs.
- VoseSimMean, VoseSimPercentile, VoseSimCVARp
- Statistics of the simulation for the tables and charts on the Results sheet.
Further reading
- Frequency-severity modelling (Vose guide)
- Klugman, S. A., Panjer, H. H. and Willmot, G. E. (2019). Loss Models: From Data to Decisions, 5th edition. Wiley.
- Vose, D. (2008). Risk Analysis: A Quantitative Guide, 3rd edition. Wiley — chapter on aggregate distributions.
Download the workbook and run it yourself. It opens in Excel with ModelRisk. The free trial runs every example model.
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An illustrative example: the figures are invented for teaching and do not describe a real company, project or asset. Last updated 9 October 2026.