“Every model is wrong, but some are useful.”
George E. P. Box, pioneering statistician in modeling
Exam C – Construction and Evaluation of Actuarial Models is most likely the preliminary exam you will take last and will likely do so early in your career. This post will try to shed some new light on the relationship between exam C and one of its real-world applications.
Some people may be under the impression that exam C is purely an extension of exam P with very strong leaning towards property & casualty. However, it is a lot more than that. Knowledge of exam C is useful to all actuaries, not just those in the property & casualty field. Below is a description on how exam C relates to a particular area in actuarial science–catastrophe modeling in agricultural reinsurance–presented in a question-and-answer format.
Q: Why do we discuss catastrophe modeling, especially in agriculture?
A: Catastrophes, by their nature, are events that rarely occur but have the potential to cause large amounts of losses when they do occur. Insurance and reinsurance companies issue some policies or other financial products, which can be referred to as catastrophe-linked securities, that provide loss coverage or financial compensation when catastrophes occur. However, there are great difficulties associated with evaluating catastrophe-linked securities:
- The low frequency of catastrophes means less data, making them hard to model.
- These securities are very risky due to the potential for heavy losses.
- Investors are less familiar with, and therefore less willing to invest in these securities, leading to a small market.
Agriculture is undoubtedly the fundamental industry of the world. But a lot of weather-related catastrophes, such as droughts or excessive rain or snow, may impact production. Agriculture is the perfect field to apply catastrophe models.
Q: How does exam C relate to catastrophe modeling?
A: Exam C trains your ability to analyze data and examine your model assumptions. In a real-world scenario, you need to first have background knowledge of your models. For example, to create a catastrophe security covering corn crop losses due to floods, you need to research, among other things, the corn crop loss function based on the likelihood and severity of floods, how geographic factors influence the loss function, and the reasonable deductibles and loss limits for such a security based on your company’s risk preference and risk management strategy. Analyzing these factors will help you to:
- Quantify your losses, fit past observations into different loss distributions, and estimate the parameters for your assumed loss distributions; and then
- Create a short list of statistically stable loss models from which you choose the “best” distribution after experience after adjustment.
Is that it? No. To get a price for the security and evaluate its risks, you have to consider what kind of product it is. Is it a reinsurance policy, a convertible or a defaultable bond, or a swap? After considering the financial risks, using pricing methods developed in recent years, you can get a price for the product based on its risk evaluation.
After all is said and done, can we expect to find the “right” price to cover the catastrophe losses? No. At the beginning of this article I quoted some wise words from one of the best statisticians in modeling: “Every model is wrong, but some are useful.” Nobody knows for sure if a model is “correct”. Ultimately, it is simply your best attempt at simulating and predicting reality.
Q: What are the opportunities and challenges of choosing catastrophe modeling as a career?
A: The reinsurance market is less known but very profitable; it requires dealing with great risks. Take catastrophe bonds as example. The market in August 2013 was only a little more than 20 billion U.S. dollars globally, but it proved to be an efficient tool in diversifying risk and a profitable investment vent. It is a hidden gold mine, especially with respect to the agricultural reinsurance business, where we constantly deal with food production and global climate changes. So there are so many opportunities for actuaries to use their professional skills to manage risks.
Meanwhile, opportunities = challenges. Let’s briefly consider the great challenges that catastrophe modeling poses:
- Acquiring and understanding background knowledge on the different types of catastrophic losses that pertain to a specific business.
- Applying better statistical methods and tools to create more stable predictive models using limited data.
- Analyzing data to quantify and incorporate financial and catastrophic risks into the pricing formula.
- Accounting for the possible dependence structure of financial and catastrophic risks in pricing formulas. (Catastrophes potentially have great impact on the financial markets, which means financial risks and catastrophic risks may not be independent.)
To take advantage of the opportunities and be able to face the challenges, we must equip ourselves with advanced knowledge, which means studying hard for your exam and keeping up with industry trends.