Burning Cost Method for Reinsurance Pricing
Understanding the burning cost method and its application in reinsurance treaty pricing.
Burning Cost Defined
The burning cost method prices reinsurance by analyzing historical losses that would have penetrated the proposed reinsurance layer. It divides layer-specific historical losses by the corresponding subject premium (adjusted for rate changes and exposure growth) to produce a burning cost rate. This experience-based approach works best when there is sufficient historical data and the underlying risk profile has been relatively stable.
The term "burning cost" reflects the idea that the actuary is measuring how much the reinsurance layer has historically "burned through" in losses relative to the premium that supported it. This is one of the most intuitive and widely used reinsurance pricing methods, and understanding it is essential for anyone working in or studying reinsurance pricing.
Step-by-Step Process
The burning cost calculation involves several well-defined steps. First, the actuary gathers individual loss data for the cedant, typically going back 5 to 10 years. Only losses large enough to potentially enter the proposed reinsurance layer are relevant, so a threshold is usually applied to focus on significant claims. Second, each historical loss is developed to its estimated ultimate value using appropriate loss development factors. This accounts for the fact that older claims may still be open and could develop further.
Third, the developed losses are trended from their historical level to the prospective period. Trending adjusts for inflation and other cost changes. For example, if a loss occurred three years ago and the annual severity trend is 5%, the trended loss equals the developed ultimate times (1.05)^3. Fourth, the trended, developed losses are applied to the proposed reinsurance layer structure. Each loss is capped at the layer limit and reduced by the attachment point. Only the portion of each loss that falls within the layer is counted.
Calculating the Rate
The burning cost rate is calculated by dividing the total layer losses by the corresponding subject premium. The subject premium must also be adjusted to a common level, accounting for rate changes and exposure growth. This is called the on-level premium adjustment. If the cedant increased its rates by 10% two years ago and the historical premium for that year was $50 million, the on-level premium would be $50 million times 1.10, or $55 million.
For example, suppose the actuary is pricing a $2 million excess of $3 million reinsurance layer. Over the past five years, the cedant had the following losses that entered this layer (after development and trending): $800,000, $0, $1,200,000, $500,000, and $2,000,000. The total layer losses are $4,500,000. If the total on-level subject premium over the same period is $300 million, the burning cost rate is $4.5 million divided by $300 million, or 1.5%. This rate represents the pure loss cost before loadings.
Practical Application
To apply the method, the actuary collects individual large losses, develops them to ultimate, trends them to the prospective period, and applies them to the proposed treaty structure. Losses are capped at the reinsurance layer limits. The resulting burning cost is then loaded for expenses, profit margin, and a risk load reflecting volatility. Common challenges include limited data credibility (especially for high layers), changes in the underlying portfolio composition, and the need to incorporate catastrophe losses appropriately. The burning cost is typically compared to exposure-rated results.
Loading the Burning Cost
The pure burning cost rate must be loaded to account for the reinsurer's expenses and required profit. Typical loadings include a brokerage commission (often 10% to 15% of the reinsurance premium), the reinsurer's internal expenses (5% to 10%), and a profit and risk load (5% to 15%, depending on the volatility of the layer). The risk load reflects the uncertainty in the estimate and compensates the reinsurer for providing capacity in a layer where losses are infrequent but potentially large.
The loaded rate is calculated as: technical price equals burning cost divided by (1 minus total loading percentage). If the burning cost is 1.5% and the total loading is 30%, the technical price is 1.5% divided by 0.70, or approximately 2.14%.
Credibility Considerations
One of the most important challenges with the burning cost method is data credibility. For excess layers where losses are infrequent, the historical experience may contain only a handful of claims. This means the estimate is highly sensitive to whether a single large loss happened to occur during the experience period. A five-year window with one $2 million layer loss produces a very different burning cost than a five-year window with zero layer losses, even if the underlying risk has not changed.
Actuaries address this by extending the experience period (sometimes to 10 or 15 years), by using credibility weighting with exposure-rated or industry benchmark estimates, or by combining the burning cost approach with a frequency-severity model for the layer. The choice of approach depends on the amount of data available and the stability of the underlying portfolio.
Common Pitfalls
A common mistake is failing to develop historical losses to ultimate before applying them to the layer. Undeveloped losses will understate the burning cost because open claims may eventually exceed the attachment point or develop further within the layer. Another pitfall is neglecting to trend losses to the prospective period, which understates the burning cost in an inflationary environment. Failing to adjust subject premium to an on-level basis can also distort the rate.
Actuaries should be cautious about including catastrophe losses in the burning cost without careful consideration. A single catastrophic event can dominate the experience and may not be representative of the expected annual catastrophe cost. Some practitioners exclude catastrophes from the burning cost and add a separate catastrophe loading based on catastrophe model output.
Study Tips
For exam preparation, practice the full burning cost calculation from data collection through final loaded rate. Be comfortable with loss development, trending, and on-level premium adjustments. Understand how to apply individual losses to a reinsurance layer by capping and reducing for the attachment point. Know how to calculate loadings and when credibility adjustments are appropriate. Finally, be prepared to compare burning cost results with exposure-rated estimates and explain differences between the two approaches.