Risk models tend to be a synthesis of data, expert opinion, and technique: The best thinking and information boiled down to a very educated guess. It is essential to understand how this guess was made and to weave that knowledge into decisions about risk-taking. This can be difficult. Risk models are generally complex — sometimes opaque in their workings — and even models that seem transparent can produce unforeseen results due to the interaction of their many moving parts. The components of a risk model encompass the nature of risk events, including frequency, severity, correlation, and probability. Each component must be sound and interact properly with other components. It is no wonder that P&C insurers are employing ever-increasing numbers of modeling specialists.
Risk models link the present and the past. Most risk models involve some form of “back testing,” which overlays current exposure onto historical patterns of loss (and gain). Historical patterns are almost always adjusted to compensate for changes in economic or physical conditions. The compatibility of the current risk profile and historical risk patterns is very important. Model users must ask themselves if the model accurately recognizes their data and if the assumptions and adjustments that went into the model represent their present situation. The problem is more subtle than simply, “garbage in, garbage out.” Anything from climate change to inflation could make a model an inaccurate descriptor of the contemporary risk environment.
Property catastrophe models (cat models) developed by specialty firms are among the most widely used risk models in the P&C industry. Cat models represent a class of models that attempts to create representations of physical events, such as hurricanes, earthquakes, or even wildfires. Such models rely on scientists and engineers to describe how an event unfolds and its likely effects on exposed objects (buildings, autos, oil platforms, etc.).
Another category of risk model is based on network theory rather than event replication. This approach is more useful in modeling non-recurring events or events caused by interrelationships between entities (usually businesses) that can cause unknown concentrations of risk or cascading chains of loss. The CASUS and Casualty Cat models (both developed jointly by Guy Carpenter and Arium, Ltd.) are examples of network-theory models. CASUS maps concentrations of people that can create unforeseen workers compensation loss potential (such as a convention or concentration of customers).
Casualty Cat maps the loss-causing, relationship-types of business activities and the liability patterns that can flow through an event such as the Enron insolvency.
In some cases companies build their own highly specific models, often based on their own historical data. Such a practice involves actuarial expertise and a healthy dose of business judgment. Technology also plays a part in the form of actuarial toolkits that help analysts adjust data and fit probability distributions to historical data. Risk analysis toolkits (such as Guy Carpenter’s InstratFitTM) contain a consistent advanced-math platform that is specifically tailored to support risk simulation and helps experts estimate the parameters for statistical distributions of loss frequency, severity, and correlation that describe the company’s risk.
As estimates of risk parameters are developed, it is critical to understand the surrounding uncertainties. Platforms such as InstratFit generate “parameter uncertainty” (sometimes called “secondary uncertainty”) with each estimate of a frequency or severity distribution. These uncertainty measures should not only be used to judge the soundness of the parameter estimate, but should also be recognized by the risk model. The concept of building uncertainty into risk models has become more common in recent years, but it is still difficult to explain and is sometimes difficult for risk decision-makers to accept. Recognizing parameter uncertainty will always increase the risk as represented by a model. This translates into increased estimates of the cost of risk or price of risk hedging. There is an inherent discomfort when abstract influences such as parameter risk drive up risk measures (and inevitably, cost derived from them), but recognizing parameter risk is essential in the use of risk models. Uncertainty in the risk parameters might be the most volatile aspect of risk that an insurer faces.
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