© Brammertz Consulting, 2009 1Date: 21.04.23

Unified Financial AnalysisRisk & Finance Lab

Chapter 15: Life insurance

Willi Brammertz / Ioannis Akkizidis

© Brammertz Consulting, 2009 2Date: 21.04.23

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: 21.04.23

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 4Date: 21.04.23

Chart of account

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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: 21.04.23

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

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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)

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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: 21.04.23

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)

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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 11Date: 21.04.23

Life annuity and maturity

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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: 21.04.23

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: 21.04.23

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

© Brammertz Consulting, 2009 15Date: 21.04.23

AnalysisBalance sheet forecast

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AnalysisP&L

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Monte Carlo simulation on equity

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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)