An insurer wanting to know what its portfolio can lose in a year faces a simple temptation: take the events that have occurred over forty years, run them across today's portfolio, and look. That method has a name, historical replay, it is useful and it is insufficient. Insufficient for a reason that fits in one sentence: forty years of history contain forty draws, which allows nothing to be said beyond the forty-year return period, that is, exactly where decisions are taken.
The remedy is to manufacture events that did not occur but could have. The parameters governing a peril are fitted on history, track, intensity, duration, season, then tens of thousands of events consistent with those parameters are drawn at random. The set is called a stochastic event catalog, each event carries an annual frequency, and stacking all of it returns a full distribution of annual loss. That is what a catastrophe model produces, and it is the only known way of holding a view on what has not happened.
One must be precise about what this procedure adds and what it does not. It adds RESOLUTION: where history offered one storm in 1999, the catalog offers three thousand neighboring storms, some of which pass fifty kilometers further south, where the portfolio happens to be. It adds no new INFORMATION about the physics: everything in it was inferred from the same observation series. A hundred-thousand-year catalog built on forty years of measurement remains a catalog that knows what forty years knew, expressed more finely.
From this comes the property that most disconcerts non-specialists: the length of the catalog is not a measure of its quality. A hundred thousand simulated years are no better than ten thousand if the underlying laws are the same; they only reduce simulation noise, that is, the difference one would get by rerunning the draw. A figure that moves by five percent when the same model is rerun on the same portfolio is not a difference of view on risk, it is noise, and it must be told apart from a genuine disagreement.
The catalog also carries the spatial structure of events, and that is its most valuable contribution for an insurer. An event in the catalog is not an intensity at a point: it is a field, touching hundreds of communes at once with different intensities that are consistent with one another. That consistency is what allows one to say what the portfolio loses AT THE SAME TIME, therefore to size whatever is handled per event. A sum of risks each assessed in its own corner would never say it, however carefully each was done.
One must finally know what the catalog takes for granted, because that is where serious disagreement lives. It assumes stationarity: the laws fitted on the past hold for the year to come. It assumes an independence between successive events that is not always true, one storm season often bringing several. And it assumes that the parameters retained describe the peril, which is poorly verifiable for rare and poorly observed perils. None of these assumptions is hidden: they are written in the documentation, which few people open.
The conduct to adopt is then the same as before any measuring instrument. One asks for the catalog length and the associated simulation noise, so as to know above what gap a difference deserves discussion. One asks over which observation period the laws were fitted, which bounds the rarity beyond which the figure is extrapolation. And one never presents a model output as a forecast: it answers the question of what could happen in any given year, never that of what will happen next year.
A regional mutual compares two technical notes on the same householders portfolio. The first, produced in-house by historical replay over the last forty years, reports a two-hundred-year loss of 62 million euros for windstorm. The second, produced by a market model on a fifty-thousand-year catalog, reports 104 million. The technical director rules: the gap is too large, the market model is plainly calibrated to sell reinsurance, and the in-house note will be retained, since it rests on real facts rather than simulations. What must be put to him?
The real-facts argument turns squarely against the conclusion it serves. A replay over forty years contains forty annual draws: it contains no information beyond the forty-year return period, and the two-hundred-year figure it displays is therefore not an observation but an extrapolation made on very little material, which is precisely the reproach aimed at the other note. The second objection is that historical replay contains only one track per storm, the one that occurred: it knows nothing of the same storm passing fifty kilometers further south, over the area where this mutual holds half its contracts. That absence is not corrected by lengthening the series, it belongs to the method, and it biases systematically downward a portfolio geographically concentrated beside the historical tracks. It does not follow that the 104 million figure is the right one, and the technical director is right on one point: it must not be accepted on its authority. What has to be asked is verifiable in one meeting. What is the model's simulation noise at that return period, so as to know whether a gap of this order is draw randomness or a genuine divergence. Over which observation period were the laws fitted, and does that period contain the region's reference storms. And what share of the gap comes from the vulnerability functions rather than the hazard, which is tested by running the model's portfolio over the historical events alone. If the gap survives those three questions, it becomes a difference of view on risk, and a difference of view is documented and owned rather than settled by picking the more comfortable number.
- 01Forty years of history contain forty draws: historical replay says nothing beyond the forty-year return period.
- 02A stochastic catalog adds resolution, never information: it knows what the observed series knew, expressed more finely.
- 03Catalog length measures simulation noise, not quality: a hundred thousand years are no better than ten thousand under the same laws.
- 04A catalog event is a coherent field across hundreds of communes: that is what allows one to say what the portfolio loses at the same time.
- 05Stationarity, independence of events and choice of parameters are assumptions written in the documentation, and that is where serious disagreement lives.