Claim Liabilities

September 22, 2018 0 By c.boersma


CSOP 1120 Definitions:

Claim liabilities are the portion of insurance contract liabilities in respect of claims incurred on or before the calculation date.

CIA: Discounting 3.1

Cash Flow Associated with Claim Liabilities: The first step in deriving the actuarial present value is to estimate the cash flow associated with the claim liabilities in order to derive the present value of expected claim and claim adjustment expense payments. Expected claim payments are calculated by applying an expected payment pattern to the undiscounted unpaid claims.

Summary

Claim Liabilities typically represent the largest and riskiest liability for insurance companies.  Correct estimations is critical for the longer term success and viability of insurance companies.  Claims occur during a coverage period, but may or may not be reported during that period.  Even when claims are reported the final cost may not be known for many years.

Companies typically estimate payment patterns for each loss year.  These can be applied to the subsequent development for unpaid claims that are 12-months old as of the year end:

Age
Months
Payment
Pattern
12 25%
24 50%
36 75%
48 100%

Unpaid claim liabilities would generally span many years:

Accident
Year
Paid Future
Unpaid
2019
Paid
2020
Paid
2021
Paid
2015 $100,000 $0 $0 $0 $0
2016 $75,000 $25,000 $25,000 $0 $0
2017 $50,000 $50,000 $25,000 $25,000 $0
2018 $25,000 $75,000 $25,000 $25,000 $25,000
Totals $250,000 $150,000 $75,000 $50,000 $25,000

We can discount these cash flows to 0 by using the mid-point of each of the above years as an approximate average loss date (close enough).  First year (2019) would have $75,000 paid, second year (2020) would have $50,000 paid etc.

Simplification

The exam has periodically used a simplification by using just one loss year (new company start on Jan 1, 2018):

Accident
Year
Paid  @
Dec 31, 2018
Unpaid @
Dec 31, 2018
Age
Months
2019
Paid
2020
Paid
2021
Paid
2018 $25,000 $75,000 12 $25,000 $25,000 $25,000

.

Incremental Payment(x) = unpaid \times \frac{Age_{x}-Age_{12}}{100\% - Age_{12}}

Present value = \sum_{year=2019}^{N} (1+i)^{year-2018.5}\times paid_{year}