Catastrophe bonds

Poisson events with Pareto or lognormal losses cutting the principal per occurrence or on annual aggregates between attachment and exhaustion, coupons on the outstanding principal, price from a discount margin or margin from a price, expected loss, attachment and exhaustion probabilities and the spread multiple.

Inputs

Notional

Maturity

Spread over 3M%

Trigger

Attachment loss

Exhaustion loss

Events a year

Event loss

Smallest event loss

Tail index α

Value at

Discount margin%

Paths

CurrencyCurve

Curve: flat rate% cc

Results

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Methodology

Conventions

Events arrive Poisson; each event's loss (or each year's aggregate) cuts the principal by its share of the layer.
Coupons, the forward plus the spread, are paid quarterly on the principal outstanding.
Expected cash flows are discounted at the forward plus a discount margin.

References

Lane (2000)
Cummins (2008)

Formulas

Principal cut: min(max(L − A, 0), E − A) / (E − A)