Actuarium

Formula sheets

Every formula on the syllabus, rendered natively, with the traps examiners set for each. Print one per exam and keep it by your desk.

ILA LAM — Individual Life & Annuities — Life ALM & Modeling

SOA

Macaulay & modified duration   D=∑t vtCFt∑vtCFt,Dmod=D1+i\;D=\dfrac{\sum t\,v^t CF_t}{\sum v^t CF_t},\quad D_{mod}=\dfrac{D}{1+i}

Surplus duration   DS=A DA−L DLA−L\;D_S=\dfrac{A\,D_A-L\,D_L}{A-L}

Immunisation (Redington) PVA=PVL,  DA=DL,  CA>CLPV_A=PV_L,\;D_A=D_L,\;C_A>C_L

CTE   CTEα=E[X∣X>VaRα]\;\mathrm{CTE}_\alpha=E[X\mid X>\mathrm{VaR}_\alpha]

Delta hedge   Δguar=∂V∂S\;\Delta_{guar}=\dfrac{\partial V}{\partial S}; hedge position =−Δguar=-\Delta_{guar} futures notional

Traps to remember

  • Using modified duration on liabilities with rate-sensitive lapses (effective duration is required).

  • Treating a risk-neutral ESG as suitable for real-world capital projections.

  • Forgetting that hedge gains/losses may not match the statutory reserve movement.

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