How to Calculate Burning Cost method in XOL Reinsurance Treaties

The burning cost method is a commonly used approach in reinsurance to calculate the premium for excess of loss (XOL) treaties. This method estimates the cost of future claims based on the historical loss experience of the cedant (the insurance company purchasing reinsurance). Here’s an in-depth look at how the burning cost method works:

Overview of the Burning Cost Method

1. Historical Data Collection:
• Gather historical loss data over a specified period, typically 5-10 years. This data includes all losses that fall within the layers covered by the XOL treaty.
• Adjust the losses for inflation and any changes in exposure or underwriting practices to ensure consistency and relevance.
2. Calculating the Burning Cost:
• Sum of Losses: Calculate the total incurred losses that fall within the reinsurance layer for each year.
• Average Annual Losses: Determine the average annual losses by summing the total losses over the period and dividing by the number of years.
• Exposure Adjustment: Adjust the average annual losses to reflect any changes in exposure (e.g., changes in premium volume, policy count, or sums insured).
3. Loading for Expenses and Profit:
• Add a loading factor to the burning cost to cover the reinsurer’s administrative expenses, profit margin, and any contingencies. This is typically expressed as a percentage of the burning cost.
4. Final Premium Calculation:
• The final premium for the XOL treaty is the sum of the burning cost and the loading factor.

Formula

Burning Cost = Total Losses in the reinsurance Layer / Number of Years

Reinsurance Premium = Burning Cost + (Burning Cost *Loading Factor)                                          

Example

Suppose an insurance company has the following historical loss data for a reinsurance layer of Kes 1 million in excess of Kes 1 million over a five-year period;

Year	Loss in Layer
2019	200,000.00
2020	500,000.00
2021	300,000.00
2022	100,000.00
2023	400,000.00

• ·         Sum of Losses: 200,000 + 500,000 + 300,000 + 100,000 + 400,000 = 1,500,000
• ·         Average Annual Losses (Burning Cost): 1,500,000 / 5 = 300,000
• ·         Loading Factor: Suppose the loading factor for expenses and profit is 20%.

Therefore, reinsurance premiums will be calculated as follows;

Reinsurance premium = 300,000 + (300,000 * 0.20) = (300,0000 + 60,000) 

Key Considerations

• Accuracy of Historical Data: The reliability of the burning cost method heavily depends on the accuracy and relevance of historical loss data.
• Adjustment for Inflation and Exposure: Proper adjustments for inflation and changes in exposure ensure that the calculated burning cost accurately reflects the current risk environment.
• Catastrophic Events: This method may need adjustments for catastrophic events, as they can skew historical loss data and may not be fully indicative of future risk.

Advantages and Disadvantages

Advantages:

• Data-Driven: Relies on actual historical loss data, making it a realistic basis for premium calculation.
• Simplicity: Relatively straightforward and easy to understand.
• Transparency: Clear and transparent process for both ceda nts and reinsurers.

Disadvantages:

• Historical Limitations: May not accurately predict future losses if the historical period is not representative of future risk.
• Sensitivity to Outliers: Significant losses in the historical period can disproportionately affect the burning cost.
• Exposure Changes: Requires accurate adjustments for changes in exposure and inflation.

In conclusion, the burning cost method provides a structured approach to pricing XOL reinsurance treaties, leveraging historical loss data to predict future losses and determine appropriate premiums. Its effectiveness depends on the quality of historical data and appropriate adjustments for current risk factors.