Stop Loss Premium Calculator

Work out stop loss premium instantly with clear inputs, formula shown and shareable results.

About Stop Loss Premium Calculator

Stop-loss cover pays whenever aggregate claims exceed an attachment point. Under a normal approximation the expected excess is (μ − d)·P(S > d) + σ·φ(z), and loading that expected recovery gives the premium.

Formula

Normal stop-loss

E[(S-d)₊] = (μ-d)·(1-Φ(z)) + σ·φ(z), z = (d-μ)/σ

μ: Expected loss
σ: Aggregate SD
d: Attachment

Worked example

With the default values below, Stop Loss Premium Calculator returns Stop-Loss Premium of $163,159.11. Change any input above and every figure here is recalculated in your browser.

Inputs used

Expected Aggregate Lossminimum 0: 5,000,000
Aggregate Standard Deviationminimum 0: 1,200,000
Attachment Pointminimum 0: 6,000,000
Reinsurer Loadingaccepts 0–200 %: 20 %

Results

Stop-Loss Premium: $163,159.11
Expected Loss Above Attachment: $135,965.93
Probability Of Attaching: 20.2328%
Premium As % Of Expected Loss: 3.263%

Step by step

1Values used
2Normal stop-loss
3Stop-Loss Premium= 163,159.11
4Expected Loss Above Attachment= 135,965.93
5Probability Of Attaching= 20.2328
6Premium As % Of Expected Loss= 3.263

Assumptions and limits

The result is derived only from the 4 inputs listed above. Anything not among them is not part of the calculation.
In particular, this calculator does not take inflation, tax or compounding frequency into account.
Figures are rounded for display to 4 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

Why does the premium stay positive above the mean?

Because aggregate losses are random. Even an attachment well above expected losses is reached in bad years, and that tail has value.

Is a normal approximation adequate?

It is a reasonable first pass for large books. Skewed portfolios attach further into the tail than the normal curve suggests.