# 5 Things About Catastrophe Modeling Every Reinsurer Should Know

Whether you’re new to the field of reinsurance or a veteran in need of a quick refresher, here are five things that reinsurance underwriters, risk managers, and executive teams alike should understand when interpreting catastrophe modeling output.

### 1) How to Interpret Exceedance Probability (EP) vs. Return Period

EP curves tell you the likelihood that a loss of any given size or greater will occur in a given year. They come in two flavors: Aggregate EP curves, which represent losses from all events each year, and Occurrence EP curves, which represent the losses from only the single largest event each year.

A Return Period is another way to express the annual EP probability, and describes an estimated likelihood of a loss of a given size occurring within a given time frame. For example, a 50-year return period is a statement that a given event/scenario will occur, on average, once in repeated samples of 50 year time periods.

Here is how you flip between these two metrics:

Loss Return Period = 1/(Exceedance Probability)

Exceedance Probability = 1/(Loss Return Period)

Figure 1. An EP curve marked to show a 1% probability of having losses of USD 100 million or greater each year

So, let’s say your aggregate EP curve shows that your 1% EP is USD 100 million. The proper way to interpret this point is by saying that:

• You have a 1% probability of having losses of USD 100 million or greater each year.
• As a long-term average, a loss of USD 100 million or greater in a year will occur once every hundred years (the key term here being “long-term average”).
• A loss of USD 100 million has a return period of 100 years (since 1/.01 = 100)

If you’d like to learn more, EP curves, return periods and many other topics are covered in much more depth in the AIR Institute Certified Catastrophe Modeler Program.

### 2) Average Annual Loss (AAL): Aggregate AAL vs. Occurrence AAL

AAL is the mean loss (the “expected value”) that occurs in any given year. AAL represents a long-term average, and it should not be used on its own for pricing or rate making since losses can fluctuate significantly each year.

To calculate the AAL, sum the losses from each year in the catalog / # of years in the catalog.

Aggregate AAL = Sum the losses from all events from each year in the catalog.

Occurrence AAL = Sum the losses from only the largest event from each year in the catalog. It tells you the long term average for the largest loss causing event in each simulated year. This metric may have value in understanding the threshold for a single claim, but unlike the Aggregate AAL, it does not account for the full spectrum of yearly losses.

So Aggregate AAL will always be > = Occurrence AAL.

Thus, Aggregate AAL is a better measure of portfolio risk than Occurrence AAL, because Aggregate AAL provides you with estimates of the full range of your losses.

### 3) Applying Reinsurance Terms to Losses Based on Detailed Exposure Information vs. Aggregate Exposure Information

Let’s say an insurance company sends you aggregate Year Loss Table (YLT) data, but before pricing a reinsurance contract, you ask to get their exposure data and are able run a detailed loss analysis in AIR’s Touchstone® platform, or otherwise you request and receive detailed losses via a Company Loss File (CLF). One thing to keep in mind while you’re looking to do some more analysis on your data to price reinsurance contracts is the following: as you might likely expect, because the aggregate data only takes exposure data only as granular as a sub-region and line of business and is based off some calculation of industry averages, it will never match the detailed YLT output of Touchstone. Also, if you are having to aggregate data from across sites and site collections, you might want to look into this SharePoint linked list rollup (find it at https://bamboosolutions.com/products/list-rollup-classic/). It is designed for powerful data aggregation and will no doubt save you time, so it may be worth a look.

Keep that in mind as you set out to price your reinsurance contracts!

### 4) Tail Value at Risk (TVaR)

TVaR is a calculation of the average losses of all years having an EP less than or equal to p%. Instead of just looking at a single simulation year, such as your 1% EP, this number tells you more about the shape of your curve for the most extreme events, thus providing insight into the overall size of your company’s tail risk.

If you’d like to learn more, we’ve written an in depth blog post walking through an example of how to calculate TVaR.

### 5) Evaluating Portfolio Risk Based Only on Regional Losses Can Overestimate Overall Aggregate Risk

Let’s say you’re looking at your reinsurance portfolio of losses by region so as to ensure that the risks you’re writing are well diversified. A common mistake we’ve seen some of our clients make is to compute the Regional EP metrics, and then sum them up to attempt to understand the risk of the portfolio.

Table 1. Summing regional EP percentages erroneously overestimates the riskiness of your portfolio

The issue with this approach is that it actually overestimates the riskiness of your portfolio. For example, you will errantly get a 1% U.S. EP of approximately USD 3.19 million (Table 1), instead of USD 2.06 million (Table 2). The reason for this is because not all events affect all of the regions-so the sort order to compute each individual region’s EP is different than the sort order of the entire U.S. EP. When you re-sort all the U.S. event results to get an EP curve, you get a different sort order than from the individual region’s sort order.

Note: The only metric that you can sum on a standard EP curve is the Expected Value (EV).

The way Analyze Re helps with this issue is by using CoMetrics, which provides an additive view of regional risk in the context of a portfolio. CoMetrics preserves the sort order of the US down to the regional level, so that you can understand how much each region is actually contributing to the total U.S. risk at each EP point.

Table 2. The sort order of all U.S. events is preserved with a CoMetrics curve, which provides an additive view of regional risk

Notice that in this case, the total sum of the regions is now equal to the EP for the U.S. at all EP points. In the example of the 1% EP with CoMetrics, we can now say that of the USD 2.06 million in losses in the U.S., USD 0.96 million is the result of losses in Florida. In addition, we can also say that for the U.S. portfolio at the 1% EP, Florida is about two times the risk of the Southeast.

One thing to keep in mind with CoMetrics is that you cannot interpret each individual region as you would on a regular EP curve. You cannot say that Florida has a 1% probability of losses being USD 0.96 million or greater in the coming year (per the regular EP curve, it is USD 1.58 million).

So there you have it!

At Analyze Re, we’ve built real-time analytics dashboards that allow you to view insights around all of these metrics and more in seconds, so that you can price even the most complex reinsurance contract structures and manage your portfolios for greater profitability. Keeping these learnings in mind while conducting your analysis will allow to you avoid errors and improve your decision making.

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