Nolan E. Asch details the Insurance Services Office Inc systems for pricing risks in the US.

Approximately one third of the premium volume in the Lloyd's market comes from risks located within the US. Accurate pricing of US excess-of-loss risks can be a daunting task even for a US-based organisation, expected to be intimately familiar with the US market. It is, therefore, especially important for global reinsurers to use the best possible tools, techniques and data available for excess-of-loss ratings in the US.

To understand excess-of-loss reinsurance pricing, an overview of the pricing techniques commonly employed by US reinsurance practitioners today is essential. In this context, I will explore the application of the two major categories of experience rating and exposure rating to both property and casualty risks, and discuss recent advances in state-of-the-art tools for getting the job done. Throughout this article I will refer to Foundations of Casualty Actuarial Science, 4th Edition, published by the Casualty Actuarial Society (chapter 7 is devoted to reinsurance), which is considered the standard textbook by US actuaries.

Experience rating
Experience rating, as its name implies, uses the actual experience generated by a book of business to price an excess-of-loss contract. This method applies actuarial techniques such as trending and loss development to historical reported losses in order to determine the distribution of total losses across various layers of risk. The use of actual account data is generally considered the analytical method of choice, but there are so many considerations that the process is often difficult and sometimes unreliable. The credibility of an experience rate is a central issue because there is a scarcity of claims large enough to attach the reinsurance. Even in cases where a great deal of account-specific information is available, such analysis only proves useful when it is assumed that the underlying portfolio has not changed materially over time. Further, the availability (or lack) of appropriate loss development or trend factors for a specific layer of loss or class of business reduces the selection of such factors to sheer guesswork.

Because the application of the experience rating technique is a daunting, data- intensive process, exposure rating is the most prevalent method in the US for excess-of-loss reinsurance pricing exercises.

Property excess reinsurance rating
In property reinsurance, exposure rating is the most prevalent rating technique. The historical tools used for property reinsurance rating have been less than scientific. The so-called `Lloyd's scales' have existed for many decades and are still in use today. Underwriters bring these tables with them from job to job; the parentage of the Lloyd's Scales floating around the industry seems to be highly questionable. So, be careful."1

Sometimes these scales can exhibit what are known as `reversals'. A reversal is an indication that a loss of a larger size actually carries a higher probability than a loss of a smaller size. Simply put, it would be more illogical to pay more for $1m of reinsurance excess of $21m than it would be to pay for $1m excess of $20m for the same risk at the same time. The probability of a loss to the higher layer is clearly lower.

"Some underwriters also use tables of factors from a 1960 PCAS [Proceedings of the Casualty Actuarial Society] paper by Ruth Salzmann. But these factors were developed for homeowners insurance [based on only one company's data]. So even if they were adjusted for inflation over the last 40 years, they are of questionable use for the typical commercial property facultative [or treaty reinsurance] exposure."2 It is indeed incredible that in 2002 some major reinsurers are still using tables based on 1960s personal property data from only one firm for pricing commercial property reinsurance treaty transactions.

In 1991, PCAS published a breakthrough article by Steven Ludwig of the Hartford Group, who used data from his company on commercial property business to establish excess-of-loss property reinsurance tables. These `Ludwig Tables' broke ratings into four rating groups: retail/wholesale; service/office; apartment/condominium; and restaurants. For most of the 1990s, the consensus among most sophisticated US reinsurance actuaries was that the `Ludwig Tables', although limited to only one insurer's aging data, were state-of-the-art for property excess reinsurance pricing.

In 1998, Insurance Services Office (ISO) developed the first property reinsurance excess-of-loss pricing model based on current industry-wide data. ISO operates the largest property/casualty insurance database in the US comprising 7.7 billion records for commercial and personal lines combined. ISO premium data represents 70% of the US property/casualty industry's commercial premium volume.

The use of commercial property data reported to ISO for 1991-98 allows ratings to be tailored to any one or combination of 23 rating groups (Figure 1 p.40). Furthermore, the rating exercise can be tailored to any state or combination of states (figure 2). It also contains loss curves on a ground up basis or net of underlying deductibles.

Every pricing exercise is performed with customised, user-supplied information combining occupancy, geography and deductible treatment. Each and every rating exercise contains information regarding the number of occurrences on which the rating is based, allowing the user to draw inferences regarding the credibility of the rating versus usage of industry averages.

The model is updated and refreshed every two years. Later this year, the model will be updated to allow ratings based upon non-catastrophe occurrences only, or upon catastrophe and non-catastrophe losses combined. It will also include access to the Ludwig Model for comparison purposes.

Premiums versus exposures
It is often important to be able to adjust subject premium to properly reflect true exposures. Figure 3 shows how $1m of premium in a given class in the same year can represent either 100 or 200 true exposure units for the reinsurer.

Likewise, figure 4(see p.42) shows how three years of $10m subject premium can appear to indicate no growth from 1995-1997, but actually represents a 25% increase in true exposure when adjusted for rate level changes. Access to historic industry rate level changes is important. If reinsurers know what the industry average rate increase is in 2001, they can draw conclusions about how conservative or aggressive the primary insurer actually is in the US market.

Casualty excess reinsurance rating
In exposure rating for casualty lines, the total premium received by the reinsurer is the portion of the insurer's total premium exposed to the excess layer in question. The calculation of this portion is usually based on an industry-wide distribution of losses by line of business. "Since most companies use ISO increased limits factors for third party liability pricing [especially for commercial lines], it is very important that the actuaries very closely monitor ISO factors and understand their meaning."3 Increased limits factors are vehicles used by ISO to allocate the relative exposure contained in the premium dollar for any policy limit to different possible layers.

For non-US reinsurers and brokers, access to the detailed analyses underlying such information has been limited until recently. Analyses and software that make use of ISO's extensive database of information have become more common in markets outside the US, particularly in London and Bermuda. Without access to such information, non-US reinsurers and brokers often have had to rely on data where origins range from unknown to questionable. Distributions based on analyses performed in the 1970s and 1980s are still used, despite their age and limitations.

Let's take a casualty example of how the exposure rating technique is actually applied. A package of information, known as a submission, is supplied to the reinsurer by an entity seeking coverage. This information generally includes a limits profile (figure 5), which is simply a listing of the total subject premium broken down by policy limit.

Here's an example of a $500,000 xs $500,000 layer. Clearly, none of the premium written at a $250,000 policy limit is exposed to this excess layer, and therefore the reinsurer should not receive any of it. At the $1m limit, the reinsurer should assess how much of the associated premium should be allocated to the first $500,000 of severity and how much to the reinsurance layer above it. By noting that the increased limits factor at the $1m policy limit is 17.2% greater than the $500,000 factor, the reinsurer can predict that, on average, 17.2% of the losses on $1m policies are expected to be greater than $500,000. Similar calculations would be made for each policy limit in the limits profile.

Figure 6 shows a typical ISO increased limits table analysis. Clearly, severity distributions will vary by class of business. Until 2000, ISO had 25 such tables covering the general liability, commercial auto and medical professional lines of business. Since then, it has been expanded to 69 different casualty classes, each based on data for a unique subset of classes (figure 7).

Vital variables
Allocated Loss Adjustment Expense (ALAE) is a very important variable in casualty excess-of-loss pricing. Reinsurance treaties typically allocate ALAE in one of several different ways, either proportionally to loss or by adding the ALAE to the loss amount before applying the attachment point. Although "increased limits factors published by ISO have no provision for ALAE outside the basic limit,"4 ISO has developed custom software that generates customised increased limits factors, based on a proprietary study of the joint distribution of loss and ALAE.

A portion of the excess premium should be exclusively associated with risk. ISO's increased limits factors include risk loads that vary by limit and are based upon a standard methodology. ISO's reinsurance software can calculate custom risk loads based on several methodologies, or exclude the risk load and seamlessly interact with other software that the reinsurer may have developed for its own use. The reinsurer will then take all this analysis and convert it to a final quoted price for a specific layer of reinsurance.

Pricing excess-of-loss reinsurance coverage is always a challenge. Limited or outdated tools and data have historically hamstrung many global reinsurers without a physical presence in the US. Over the last several years, a growing number of them have begun using the new generation of tools and models that have recently become available, putting them in a more competitive position.

Footnotes:
1 Gary S. Patrik, `Reinsurance', Foundations of Actuarial Science, Fourth Edition (Casualty Actuarial Society, 2001),

2 Gary S. Patrik, `Reinsurance', Foundations of Actuarial Science, Fourth Edition (Casualty Actuarial Society, 2001),

3 Gary S. Patrik, `Reinsurance', Foundations of Actuarial Science, Fourth Edition (Casualty Actuarial Society, 2001),

4 Gary S. Patrik, `Reinsurance', Foundations of Actuarial Science, Fourth Edition (Casualty Actuarial Society, 2001),

By Nolan Asch
Nolan E. Asch is principal, reinsurance, at Insurance Services Office, Inc. (ISO). Before joining ISO, he was chief actuary for SCOR US (Re) for 12 years.