1. Non-Life Best Estimate
6 March 2017

2. Agenda 1.) Overview of Solvency II 2.) Focus on Assumptions
3.) Focus on Premium reserve
4.) Focus on Claim reserve

3. Overview of Solvency II1

4. Objective of Solvency
The Solvency is the capacity for an insurer to face its obligations towards beneficiaries of insurance contracts.
The aim is the protection of the insured.
The solvency requirements must be translated at 2 levels:
An adequate level of technical provision in order to cover the business as usual.
A minimum amount of capital in order to protect the viability of the insurer.
Assets
Liabilities
Assets
Capital
Szolvencia célja:
megfelelő tartalék állomány a jövőbeli kötelezettségek fedezésére
Tőkemegfelelés biztosítása a biztosító működése céljából.
Korábbi Szolvencia I és a mostani Szolvencia 2 összehasonlítása:
Büntette a prudens biztosítót
Most: kockázatalapú megközelítés
Technical provisions
7 December 2016

5. Solvency II overview Solvency I framework
Solvency I distinguishes between Life and Non-Life Insurers
Required Capital depends on:
Life
Level of technical reserves, sum at risk, reinsurance cessions
4% of non-linked reserves and 1% of linked reserves and 0.1% to 0.3% of the sum at risk (including also 16-18% of rider premiums or 23-26% of claims incurred basis if higher for accident and health complementary to life contracts), reduced by the quota ceded to reinsurers (up to a maximum of 50%)
Non Life
Level of premiums, claims, reinsurance cessions
Maximum between 16-18% of net written premium or % of incurred claims, reduced by the quota ceded to reinsurers (up to a maximum of 50%)
Overview Solvency II

6. Solvency II overview Reasons to develop new Solvency supervision 1 2 3
Insufficient Risk sensitivity 1
Economic valuation framework vs. Accounting framework 2
Best Practice Risk measurement and management 3
European harmonisation 4
Measuring and managing more than the known risks 5
Credit crisis: more awareness and urgency 6
Overview Solvency II

7. Solvency II Balance Sheet
Solvency II overview
Solvency II – A dynamic model
Fair Value
Of assets
Free Surplus
Solvency
Capital
Requirement
Min Capital
Probability of default of 0,5% over 1 year period
VaR al 99,5%
Risk Margin
Best
estimate
SCR
Risk
Margin
Metodo del
Costo del Capitale
Best
Estimate
of technical
provisions
Solvency II Balance Sheet
Overview Solvency II

8. Best Estimate Liability
Focus on Technical provisions
Best estimate Liabilities
Solvency II
Balance Sheet
Assets
Xs Own Funds
Own Funds
SCR
MCR
The best estimate shall correspond to the
probability-weighted average of future cash-flows, taking account of the time value of money (expected present value of future cash-flows), using the relevant risk-free interest rate term structure.
Risk Margin
Best Estimate Liability
Technical Provisions
Overview Solvency II

9. Focus on Technical provisions
Best estimate Liabilities
The best estimate shall correspond to the probability-weighted average of future cash-flows, taking account of the time value of money (expected present value of future cash-flows), using the relevant risk-free interest rate term structure.
Methodology
Probability weighted average of future cash flows
Using the relevant risk-free rate term structures
Realistic assumptions
Adequate actuarial and statistical methods
Assumptions
Consistent with information provided by financial markets
Consistent with generally available data on insurance risks
Policyholder behaviour
Future management actions
Overview Solvency II

10. Focus on Technical provisions
Best estimate Liabilities
The best estimate shall correspond to the probability-weighted average of future cash-flows, taking account of the time value of money (expected present value of future cash-flows), using the relevant risk-free interest rate term structure.
Flows
Non-life policies
Inflow
Future premiums
Recoveries
No investment return
Outflow – claims
Claims incurred
Future claims (for future premiums)
Outflow - expenses
Administration expenses
Claim handling expenses
Acquisition costs
Premium taxes
Overview Solvency II

11. Focus on Technical provisions
Best estimate Liabilities
The best estimate shall correspond to the probability-weighted average of future cash-flows, taking account of the time value of money (expected present value of future cash-flows), using the relevant risk-free interest rate term structure.
The premium and claim provisions are closely related in that they both represent a provision to cover the expected cash-flows, in and out, during the lifetime of the insurance and reinsurance obligations. The key distinsctions is that the claims provision covers claim events that have occured at or before the valuation date whilst the premium provision relates to cashflows to future exposure.
Premium reserve:
PV of future premium
PV of future expenses
PV of future claims (not yet occured)
Claim reserve:
PV of future payments for already occured claims
Overview Solvency II

12. Focus on Assumptions 2

13. Focus on Assumptions Discount rate
The risk-free rates shall meet all of the following criteria: they are free of any risk, undertakings are able to earn them in a risk-free manner in practice, they are reliably determined based on financial instruments traded in a market.
Risk Free Interest rate
The rates of the basic risk-free interest rate term structure shall meet the following criteria:
insurance and reinsurance undertakings are able to earn the rates in a risk-free manner in practice;
the rates are reliably determined based on financial instruments traded in a deep, liquid and transparent financial market.
For each currency and maturity, the basic risk-free interest rates shall be derived on the basis of interest rate swap rates for interest rates of that currency, adjusted to take account of credit risk
Published on a monthly basis by EIOPA
technical-information/risk-free-interest-rate-term-structures
Overview Solvency II

14. Focus on Assumptions
Claim ratios are derived from the mixture of historical and expected datasets.
Claim ratio
Claim ratio = Claims incurred / Earned premium
During the derivation costs may be included, but need to avoid double counting!
The ratio may based on historical data or expert judgement if data is not available
Due to the different charactheristics of the separate Line of Businesses, the claim ratio should be calculated for the separate LoBs.
Overview Solvency II

15. Focus on Assumptions
Operating assumptions are derived from the mixture of historical and expected datasets.
Administration expenses
The administration expenses are usually expressed as a percentage derived from the planned or historical expenses.
If data is available the administration expenses may be calculated for the separate Line of Businesses. (LoBs)
The administration expenses are covering the following expenses (the list is not complete):
Overhead expenses
Office rental
Bills
Other operating costs
Administration expenses % = Administration expenses from the P&L / Earned premium
Overview Solvency II

16. Focus on Assumptions
Operating assumptions are derived from the mixture of historical and expected datasets.
Lapse ratio
Lapse assumptions are covering the possibility of future cancellation of the policies.
If no historical dataset is available, the actuaries may consider an expert judgement or apply market benchmarks.
Lapse rate = Cancelled premiums / Earned premium
Overview Solvency II

17. Focus on Assumptions
Operating assumptions are derived from the mixture of historical and expected datasets.
Tax assumption
For certain Line of businesses, the future premiums may have a taxable obligation. (insurance tax).
May be expressed based on the expected payable tax of the forthcoming year or based on historical data
Tax assumption % = Expected payable insurance tax / Earned premium
Overview Solvency II

18. Focus on Premium reserve3

19. Focus on Premium reserve
Best estimate Liabilities
Premium reserve is calculated to over future premiums for the existing business and future claim events
Premium reserve
The premium provision relates to cashflows of future exposure.
Premium reserve covers the following:
Future expenses
Future claims
Premium reserve = PV(cash-out flows - cash-in flows)
It may happen that the premium reserve is negative!
Premium reserve
Expenses
Future claims incurred
Future premium
Cash-in
Cash-out
Overview Solvency II

20. Focus on Premium reserve
Example
Premium reserve is calculated to over future premiums for the existing business and future claim events
Premium reserve
Let’s take a casco policy with Future written premium of in the next year.
The assumptions are the following:
Lapse ratio: 5%
Administration expenses: 6%
Premium tax: 10%
Expected loss ratio: 60%
If the future premium is payable within 1 year, the time value of money may be ignored.
Premium reserve
Probability of premium payment: (1-5%)
Expected cash-out:
Admin: expected future premium * administration expenses
Tax: expected future premium * tax rate
Overview Solvency II

21. Focus on Premium reserve
Example
Premium reserve is calculated to over future premiums for the existing business and future claim events
Premium reserve
Now calculate the future claims for the future exposure!
The expected loss ratio is 60%
The claims are running of for a couple of years, therefore the time value of money should be taken into account
How can we make a cash flow from the expected future losses?
Estimate a run-off pattern for the claims (eg)
Based on the experienced development factors
Expert judgement
Overview Solvency II

22. Focus on Premium reserve
Best estimate Liabilities
Discounting
Premium reserve
Let’s have the risk-free interest rates (RFR) the following:
t_0=0.262%
t_1=0,626%
t_2=0,849%
The discount factor for each t then is calculated as:
(1+ 𝑅𝐹𝑅 𝑡 ) −𝑡
The PV then is calculated as:
- 𝐸𝑥𝑝𝑒𝑐𝑡𝑒𝑑 𝑝𝑟𝑒𝑚𝑖𝑢𝑚 −𝑒𝑥𝑝𝑒𝑛𝑠𝑒𝑠 −𝑐𝑙𝑎𝑖𝑚𝑠 ∗𝑑𝑖𝑠𝑐𝑜𝑢𝑛𝑡 𝑓𝑎𝑐𝑡𝑜𝑟_𝑡 𝐸𝑥𝑝𝑒𝑐𝑡𝑒𝑑 𝑝𝑟𝑒𝑚𝑖𝑢𝑚 −𝑒𝑥𝑝𝑒𝑛𝑠𝑒𝑠 −𝑐𝑙𝑎𝑖𝑚𝑠 ∗𝑑𝑖𝑠𝑐𝑜𝑢𝑛𝑡 𝑓𝑎𝑐𝑡𝑜𝑟_𝑡
What does the result mean?
Premium reserve:
PV(Expenses)
PV(expected claims)
PV(future premiums) =
Cash-in
Cash-out
Overview Solvency II

23. Focus on Claim reserve 4

24. Focus on Claims reserve
Best estimate Liabilities
The claim reserve is the coverage for claims that have already occured
Claim reserve
Recap from Solvency I
Outstanding reserve (reported)
IBNR (not yet reported)
Calculated with usual actuarial techniques (eq Chain ladder)
Cash-flow should be derived based on payment patterns
Overview Solvency II

25. Focus on Premium reserve
Best estimate Liabilities
Run-off triangles
Claim reserve
The reserve can be calculated based on incurred or paid triangles or with other actuarial techniques
Paid triangle:
Estimates the OS and IBNR reserve together
Incurred triangle:
Need to adjust for the OS reserve
May contain some prudency
Overview Solvency II

26. Focus on Claims reserve
Best estimate Liabilities
Producing of the cash flows
Claim reserve
If the use an accident year / payment year triangle we need take into consideration the structure of the triangle:
The blue diagonals are relating to the same payment years
After the filling of the triangle, the payments should be calculated, rather than the cumulative payment up until the corresponding lag period
Overview Solvency II

27. Focus on Claims reserve
Best estimate Liabilities
Producing of the cash flows
Claim reserve
The payments of the future years are in the blude diagonals > produce the payment pattern from them
Overview Solvency II

28. Focus on Claims reserve
Best estimate Liabilities
Producing of the cash flows
Claim reserve
The last step is discounting back the future payment to the valuation date.
Overview Solvency II

29. Focus on Claims reserve
Best estimate Liabilities
Producing of the cash flows
Claim reserve
The last step is discounting back the future payment to the valuation date.
Overview Solvency II

30. Q&A Session

31. 29 May 2018