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© Brammertz Consulting, 2009 1Date: 19.04.23
Unified Financial AnalysisRisk & Finance Lab
Chapter 15: Life insurance
Willi Brammertz / Ioannis Akkizidis
© Brammertz Consulting, 2009 2Date: 19.04.23
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, 2009 3Date: 19.04.23
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, 2009 5Date: 19.04.23
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, 2009 6Date: 19.04.23
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, 2009 7Date: 19.04.23
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)
© Brammertz Consulting, 2009 8Date: 19.04.23
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)
© Brammertz Consulting, 2009 9Date: 19.04.23
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, 2009 10Date: 19.04.23
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)
© Brammertz Consulting, 2009 12Date: 19.04.23
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, 2009 13Date: 19.04.23
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, 2009 14Date: 19.04.23
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