© Brammertz Consulting, 20091Date: Unified Financial Analysis Risk & Finance Lab Chapter 15: Life insurance Willi Brammertz / Ioannis Akkizidis

© Brammertz Consulting, 20092Date: 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)

© Brammertz Consulting, 20093Date: 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

© Brammertz Consulting, 20094Date: Chart of account

© Brammertz Consulting, 20095Date: 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 > ∏ R covers the mortality risk > ∏ S is the saving part

© Brammertz Consulting, 20096Date: 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

© Brammertz Consulting, 20097Date: Risk premium > Insurance only pays the difference between the sum insured (S) and net reserve (R N ) > Premia for year t is calculated using the expected mortality q(t) for the year t > Insurances can „play a bit“ with q(t)

© Brammertz Consulting, 20098Date: 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(t i )) is paid on reserve and bonus (B(t i )) > Interest rate r is a legally set minimum rate (usually below market rates)

© Brammertz Consulting, 20099Date: 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)

© Brammertz Consulting, Date: 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 p x = survival rate of people aged x > r is again the technical rate (leads to a lower payment)

© Brammertz Consulting, Date: Life annuity and maturity

© Brammertz Consulting, Date: 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.

© Brammertz Consulting, Date: 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

© Brammertz Consulting, Date: 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

© Brammertz Consulting, Date: Analysis Balance sheet forecast

© Brammertz Consulting, Date: Analysis P&L

© Brammertz Consulting, Date: Monte Carlo simulation on equity

© Brammertz Consulting, Date: 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)