IAI Actuarial Core Principles · Actuarial Mathematics for Modelling

Financial Instruments and Insurance Contracts as Cashflow Models

A cashflow model lists the amounts, timing and certainty of payments in and out of a contract. To solve a question, you identify who pays what and when, mark which payments are certain or contingent, then value them using the right interest or discount rate. This works for bonds, equities, derivatives, loans and insurance.

What this chapter covers

This chapter teaches you to see every financial contract as a stream of payments. A bond, a share, a forward, a loan and a life policy all look different. Each can be written as a list of cashflows: amount, time, and whether the payment is fixed, uncertain or contingent on an event.

You start with the basic notation and the idea of certain versus uncertain cashflows. Then you move through bonds, equities and property, derivatives, loans and annuities, and finally insurance contracts. Each step adds one new source of uncertainty: fixed payments, then growth and dividends, then payoffs that depend on another asset, then repayment structures, then payments that depend on death, survival or claims.

This chapter feeds the rest of CM1. Theory of interest rates, equation of value, decrement models and pricing and reserving all assume you can write down the cashflows first. It also links to CM2, where the same instruments are valued with economic and option models. If your cashflow set-up is wrong, every later calculation is wrong.

Pricing and reserving carry the largest syllabus weighting in CM1, and theory of interest and equation of value together carry a large share too. Almost every question in those areas starts by building a cashflow model. In the written paper you earn method marks for a correct cashflow set-up even if your arithmetic slips. In the multiple-choice section, a clear cashflow list lets you check an answer quickly. It is also the base for the computer-based Paper B, where you build the same models in a spreadsheet or in R.

Financial instruments and insurance contracts as cashflow models: topics in the order to study them

1Cashflow Models: Basic Concepts and NotationEverything else uses its language: timing, certainty, discounting and the sign convention for inflows and outflows.
2Fixed Interest Securities and BondsBonds have fixed, known cashflows, so they are the simplest case to practise valuation and yield.
3Loans, Annuities and Level Payment CashflowsIt reuses the fixed-payment thinking from bonds and adds repayment structure, interest and capital split.
4Equities, Property and Other Real AssetsCashflows become uncertain and may grow, so you learn how dividends, rent and growth are modelled.
5Derivatives: Forwards, Futures and Options CashflowsPayoffs depend on an underlying asset, so you need the asset cashflow ideas from the previous topic first.
6Insurance Contracts as Cashflow ModelsIt combines premiums, benefits and expenses with contingent timing, and prepares you for decrement models and pricing.

How to prepare Financial instruments and insurance contracts as cashflow models

Treat this chapter as a skill, not a list of definitions. You learn it by writing cashflow lists until it is automatic.

Learn the notation first. Write a one-page sheet of symbols and conventions, and use the same symbols in every answer.
For each instrument, draw a timeline. Mark each payment, its size, its date, and whether it is certain or contingent.
Practise valuing the timeline at a given rate. Do bonds and loans until you can set up the equation of value in under a minute.
Compare instruments side by side. Note which risks each one carries: default, inflation, market, timing or mortality.
For derivatives, write the payoff at maturity for both the buyer and the seller before thinking about price.
Build one insurance contract as a cashflow model: premiums in, benefits and expenses out, with the probability or condition for each payment.
Finish with mixed past-paper questions. Time yourself on MCQs, then write full answers for the longer questions, stating assumptions clearly.

Common mistakes in Financial instruments and insurance contracts as cashflow models

Valuing cashflows before listing them clearly
Fix: Draw the timeline first. Write each amount, date and sign, then choose the formula.
Mixing up inflows and outflows between the investor and the issuer
Fix: Write at the top of your answer whose point of view you are using, and keep to it.
Mismatching the interest rate period and the payment frequency
Fix: Convert to an effective rate per payment period before discounting.
Treating uncertain cashflows as if they were certain
Fix: For equities, property and insurance, state what is uncertain and what assumption you are making.
Confusing a derivative's payoff with its profit
Fix: Write payoff at maturity first, then subtract the premium paid or add the premium received if profit is asked.
Leaving out expenses or timing details in insurance cashflows
Fix: Use a checklist: premiums, benefits, expenses, commission, and the date or condition for each.

Last-day revision: Financial instruments and insurance contracts as cashflow models

A cashflow model lists amount, timing and certainty of each payment.
Fix a sign convention: inflows positive, outflows negative, and stay with it.
Bond cashflows are coupons plus redemption, fixed in advance unless the bond is index-linked or has default risk.
Bond price equals the present value of its cashflows at the investor's required yield.
Loan repayments are interest on the outstanding balance plus capital repaid.
Equity and property cashflows are uncertain, so the model needs assumptions about growth and dividends or rent.
A forward or futures payoff depends on the underlying price at maturity compared with the agreed price.
An option payoff cannot be negative for the holder, because the holder can choose not to exercise.
Insurance premiums are usually certain in amount, while benefits depend on a contingent event.
Always state assumptions on interest rate, timing and contingency in written answers.
Check units and timing: annual rate versus payment frequency is a common slip.
Method marks come from a correct cashflow set-up, so show the timeline.

Financial instruments and insurance contracts as cashflow models practice questions

Financial instruments and insurance contracts as cashflow models in other exams

The same ground in other exams, if you are preparing for more than one or want another angle on it.

Financial instruments and insurance contracts as cashflow models: frequently asked questions

What is a cashflow model in CM1?

It is a representation of a contract as a set of payments with their amounts, dates and conditions. You use it to value the contract, compare instruments or price a product. In CM1 you will build these for bonds, loans, derivatives and insurance policies.

Which topic should I study first in this chapter?

Start with basic concepts and notation. Every later topic uses the same language for timing, certainty and discounting. Then move to bonds, because their cashflows are fixed and easiest to practise on.

Do I need to memorise formulas for this chapter?

Learn the core ones, such as the present value of a stream of payments and the loan balance relationships. More important is knowing how to build the cashflow list. If the set-up is right, the formula is usually straightforward.

How is this chapter tested in Paper A and Paper B?

Paper A tests it through multiple-choice and written questions where you set up and value cashflows. Paper B is computer-based, so you may need to build the same cashflow models in a spreadsheet or in R. Practise both by hand and on the computer.

How does this chapter connect to the rest of the paper?

It is the base for equation of value, decrement and multiple life models, and pricing and reserving. In each of them you first write the cashflows, then apply interest and, where needed, probabilities of the contingent events.