Parametric insurance pricing

Parametric insurance pricing is how the premium is built: the expected annual payout of the index, plus loads for model uncertainty, expenses and the cost of the capital tied up behind the limit. It starts with one question: what will the contract pay, on average, per year? Because the payout depends on an index rather than a loss, you can rerun the contract over the index's history. Thirty years of rainfall at a station, a century of earthquake catalog, forty years of hurricane tracks: apply the payout schedule to each year, take the average, and you have a burning cost. When the record is too short to show the tail, a stochastic model generates tens of thousands of simulated years. The mean simulated payout gives the expected loss, along with the attachment and exhaustion probabilities. The market then quotes the price as rate on line, premium over limit, and as a multiple of expected loss. The load covers what the average leaves out. First, model uncertainty: a twenty-year series, a station that moved, a climate trend the record does not yet contain. Second, the cost of the capital the risk taker holds so it can pay the full limit at once, higher when the risk is correlated with the rest of its book. A Florida hurricane layer eats more capital than a Sahel rainfall index. Last come expenses: data, calculation agent, structuring, fronting, premium taxes. Basis risk is not in the seller's price. It sits with the buyer, who can collect without a loss or lose without collecting, and it is measured by comparing the index's payout history with actual losses. An index closer to the loss usually costs more in data and modeling and narrows that gap. Attachment changes the shape of the price. Cover that triggers often carries a high expected loss and a low multiple. Tail cover is cheap in dollars but priced at a high multiple, because the capital sits idle most years.