C2. Basics of Reinsurance Pricing

Question 1

Surplus Share

Surplus %, how much does reinsurer cover

Answer 1

Reinsured Portion = (Insured Value - Retained Line) up to a max of (# of lines) * (retained line)

Surplus % = Reinsured Portion / Insured Value

Reinsurer covers = (Surplus %) * (Loss + ALAE)

Question 2

Proportional Reinsurance Experience Rating Steps

Answer 2

1. Gather historical experience and exclude cat losses
2. Develop and trend losses + onlevel and trend premiums
3. Select expected non-cat LR and cat LR
4. Estimate other expenses such as ceding commission, reinsurer expense ratio, combined ratio

Question 3

Sliding Scale Commission / Expected Technical Ratio

What is it? Formula

Answer 3

Feature that allows the commission paid by reinsurer to ceding company varies with the actual LR

Expected LR * Expected Commission

Question 4

Profit Commission

What is it? Formula for % and $ amount

Answer 4

Returns some of reinsurer’s profit to the ceding company as additional commission

Reinsurer Profit (%) = 1 - Actual LR - Ceding Commission - Reinsurer Expense Margin

Profit Commission (%) = Reinsurer Profit (%) * % returned

Profit Commission ($) = % * Actual ceded premium

Question 5

Loss Corridors

What is it?

Answer 5

Allows the ceding company (primary insurer) to reassume some liability if the LR exceeds a certain amount

Question 6

Property Per Risk Exposure Rating

Exposure Factor P(p) / Expected Loss

Formula, specific layer

Answer 6

P(p) = E[X;pIV]/E[X]
Exposure factor for layer:
* P(Retention+Limit / IV) - P(Retention / IV)

Expected Loss:
* Subject Prem * ELR * Exposure Factor

Question 7

Casualty XOL Exposure

Exposure Factor P(p) / Expected Loss

Answer 7

Exposure factor for layer:
* E[X;AP+Lim] - E[X;AP] / E[X;PL]
* ILF[X;AP+Lim] - ILF[X;AP] / ILF[X;PL]
* AP+Lim and AP are capped at the policy limit (PL)

Expected Loss:
* Subject Prem * ELR * Exposure Factor

Question 8

Casualty XOL Umbrella Exposure

Exposure Factor P(p) / Expected Loss

Answer 8

Exposure factor for layer:
* E[X;AP+Lim+UL] - E[X;AP+UL] / E[X;PL+UL] - E[X;UL]
* AP+Lim+UL and AP+UL are capped at the policy limit (PL) + underlying limit (UL)

Expected Loss:

Question 9

Assumptions of Exposure Rating

2 assumptions

Answer 9

1. Scale Independance - the same exposure curve applies regardless of insured value size
2. All risks are written on the midpoint of the insured value range

Question 10

Exposure Rating

Reinsurance Loss Cost

Formula

Answer 10

Subject Prem * ELR * Exposure Factor
* Similar to a loss ratio

Question 11

Casualty XOL Experience Rating

Given Accident Date, Untrended Loss, ALAE, Underlying Limit –> Calculate Final Loss/ALAE

ALAE Included with loss or Pro-rata

Answer 11

1. Accident Date
2. Untrended Loss (UL)
3. ALAE
4. Underlying Limit
5. Trended Loss
6. Trended ALAE
7. Capped Trended Loss by UL

ALAE Included with Loss
1. Capped Trended Loss (7) + Trended ALAE (6)
2. Calculate Loss/ALAE in Layer

ALAE Pro-rata with Loss
1. Capped Trended Loss (7)
2. Calculate Loss in Layer
3. ALAE = (6) / (7) * Loss in Layer
4. (2) + (3)