Unified Financial Analysis Risk & Finance Lab

1. Unified Financial Analysis Risk & Finance Lab Chapter 15: Life insurance Willi Brammertz / Ioannis Akkizidis

2. Comparison life insurance vs banking • General accepted wisdom • Asset side of life insurance and banks are equal • Liability side differs • Challenge: Even the liability side is very similar if seen from a contract centric approach • Only true difference • Life insurance contract is special contract type (but a normal financial product where saving can be enforced) • Payment at death • However the likelihood of death is • Very small • Statistically well predictable (low risk)

3. Differences between life insurance and banking • Payment at death • Annuity payment with uncertain date (until death) • Treatment of cost • Cost deducted from premium • Part of the contract • Relationship between assets and liabilities

4. Chart of account

5. Life insurance contract • ∏α, ∏β and ∏γ are deductible cost parts • ∏α covers acquisition cost (deducted from first premiums) • ∏β covers servicing cost • ∏γ covers funds management cost • ∏Rcovers the mortality risk • ∏Sis the saving part

6. Cost calculation and deduction • ∏α, ∏β and ∏γ are deductible cost parts • Insurances have specific formulas for deduction • Linear write off (for ∏α) • Zillmer reserves (for ∏α) • ... • Formulas must be accepted by regulator

7. Risk premium • Insurance only pays the difference between the sum insured (S) and net reserve (RN) • Premia for year t is calculated using the expected mortality q(t) for the year t • Insurances can „play a bit“ with q(t)

8. Reserve building and interest rate calculation • Reserve (saving part) ∏S(t) • Is a pure residual! • Can be negative in extreme cases (especially if unit linked) • Interest (R(ti)) is paid on reserve and bonus (B(ti)) • Interest rate r is a legally set minimum rate (usually below market rates)

9. Reserve building, acquisition cost and surrender value • Acquisition cost is capitalized and written off over time • Reserve is built over time • Net is surrender value (includes additional deductions)

10. Annuity calculation • At maturity date, reserves are paid out (no further deductions) • Two possibilities • Bullet • Annuity • Speciality about annuity: maturity date not known (formula contains px = survival rate of people aged x • r is again the technical rate (leads to a lower payment)

11. Life annuity and maturity

12. Forecasting volumes, characteristics and pricing • Volumes determined by market expectations • Type determined by market expectation • Endowment • Unit linked • ∏α, ∏β and ∏γ and r are known parameters • Further characteristics a function of clientele • Age • Gender • Etc.

13. Behavior • Surrender: Similar formulas used like in prepayment • Bonus calculation: • Interesting simulation element • Must reflect the market • Choice of retirement age (where contracts allow choice) • Choice between bullet and annuity payment

14. Cost • ∏α, ∏β and ∏γ are deducted according to some formula • Real cost depend on numer of people, premisses etc. • Difference between the two is additional benefit for insurance • Real cost is calculated as already discussed under banks

15. AnalysisBalance sheet forecast

16. AnalysisP&L

17. Monte Carlo simulation on equity

18. Alternative decomposition of embedded value • (PVIF = Present Value in Force: on the basis of continued investment, mortality etc. Needs MC calculation) • (ANAV = Adjusted Net Asset Value: Residual) • (EEV = European Economic Value)