Work out stop loss premium instantly with clear inputs, formula shown and shareable results.
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.
Normal stop-loss
E[(S-d)₊] = (μ-d)·(1-Φ(z)) + σ·φ(z), z = (d-μ)/σ
Because aggregate losses are random. Even an attachment well above expected losses is reached in bad years, and that tail has value.
It is a reasonable first pass for large books. Skewed portfolios attach further into the tail than the normal curve suggests.