IAI CM2 study plan
IAI CM2 · Give each week a clear focus.
8 weeks · About 7 hours per week
Survival models and life table functions & Mortality estimation and graduation
Derive survival probabilities from a force of mortality and reconstruct life table columns (l_x, d_x, q_x, p_x, e_x) from any two given columns
Compute curtate and complete expectation of life using both summation and integral forms, and explain the difference
Apply fractional age assumptions (UDD, constant force, Balducci) to interpolate between integer ages and quantify the error each introduces
Estimate mortality from exposed-to-risk data using exact and actuarial exposure, and construct a crude q_x series from a small synthetic dataset
Your checkpoint
A one-page worked solution set: build a 5-age life table from a stated mu(x), compute e_x two ways, and show the same q_x under all three fractional age assumptions
Mortality estimation and graduation & Survival models and life table functions
Graduate a crude mortality series using at least two methods (e.g. Gompertz/Makeham curve fit and a weighted moving-average or spline smoother)
Test goodness of fit of a graduated series against crude rates and interpret the results
Explain the trade-off between smoothness and adherence to data, and justify a chosen graduation
Identify standard mortality tables and selection effects, and adjust a table for a simple select period
Your checkpoint
A graduation report of 400-600 words plus a table comparing crude and graduated q_x with a stated test statistic and a defended choice of method
Life insurance and annuity contracts & Premium and policy value calculations
Derive present values for term, whole life, endowment and annuity contracts under both discrete and continuous payment patterns
Relate insurance and annuity functions through commutation-style identities and verify them numerically
Compute gross and net premiums allowing for expenses, and state the equivalence principle explicitly
Calculate net premium reserves prospectively and retrospectively and confirm the two agree for a simple policy
Your checkpoint
A spreadsheet or script valuing one whole life and one endowment policy: premium, reserve at three durations by both methods, and a reconciliation of the difference
Premium and policy value calculations & Pension and other benefit schemes
Compute reserves on a non-unit-linked and a unit-linked contract, explaining how the unit fund changes the reserve logic
Analyse a defined benefit pension scheme: project a member's final salary benefit, value it, and compute the normal cost
Distinguish defined benefit from defined contribution outcomes and describe how actuarial assumptions drive scheme cost
Explain the roles of the trustee, sponsor and actuary in a benefit scheme
Your checkpoint
A closed-book 90-minute mock on Domains 1-5 scored against a marking scheme, with every lost mark traced to a named concept
Principles of actuarial modelling & Brownian motion and stochastic calculus
State the properties of standard Brownian motion and verify them for a simulated path
Apply Ito's lemma to functions of Brownian motion and of an Ito process, including the quadratic variation term
Classify stochastic processes as Markov, martingale or neither, with justification
Critique a simple actuarial model for parsimony, transparency and sensitivity to assumptions
Your checkpoint
A worked sheet of ten Ito's lemma applications (including f(t,x)=x^2, e^{ax}, and t*x) with each drift and diffusion term identified
Martingales and stochastic integration & Option pricing and Black-Scholes framework
Show that a discounted asset price is a martingale under the risk-neutral measure for a simple binomial and a Black-Scholes setting
Derive the Black-Scholes partial differential equation from a replicating portfolio and state the boundary conditions
Price European calls and puts with the Black-Scholes formula and check put-call parity numerically
Compute and interpret the Greeks, and explain how delta hedging is maintained in discrete time
Your checkpoint
A derivation of the Black-Scholes PDE from first principles, plus a fully worked pricing and hedging example with all five Greeks tabulated
Option pricing and Black-Scholes framework & Interest rate models and term structure
Extend the Black-Scholes framework to dividend-paying assets, currencies and futures, adjusting the drift term correctly
Derive or state the term structure implied by a short-rate model and price a zero-coupon bond within it
Compare Vasicek, Cox-Ingersoll-Ross and Hull-White models on tractability, negative rates and calibration
Interpret forward rates, spot rates and the yield curve, and reconcile them for a given curve
Your checkpoint
A comparison table of three short-rate models with bond price formulas, plus a curve-fitting exercise reconciling spot, forward and yield curves
Survival models and life table functions & Life insurance and annuity contracts & Premium and policy value calculations & Brownian motion and stochastic calculus & Option pricing and Black-Scholes framework & Interest rate models and term structure
Sit two full-length timed papers under exam conditions and mark them strictly
Re-derive from memory the core formula sheet: survival identities, annuity/insurance links, Ito's lemma, Black-Scholes PDE and price
Redo every question missed across the eight weeks until each is solved unaided
Build a final one-page cue sheet of the ten highest-risk formulas and concepts
Your checkpoint
Two marked mock papers with a written error log and a final one-page cue sheet covering all ten domains
Milestones
Week 2: Can build and graduate a life table unaided and explain the fractional age assumptions without notes
Week 4: Scores at least 60% on the Domains 1-5 mock, with reserves and pension costs correct on first attempt
Week 6: Derives the Black-Scholes PDE from memory and prices a European option with parity check passing
Week 8: Scores at least 70% on both full mocks and has cleared every item in the error log