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CMA Final · Strategic Financial Management

Options in CMA Final Strategic Financial Management

An option gives the holder the right, not the obligation, to buy (call) or sell (put) an asset at a fixed strike price on or before expiry. To solve questions, draw the payoff first, then apply the right tool: strategy profit, put-call parity, binomial or Black-Scholes pricing, or a hedge.

What this chapter covers

This chapter in Paper 14 covers how options work and how they are valued. You start with calls, puts and terms like strike, premium, intrinsic value and time value. Then you move to payoffs, combinations such as spreads, straddles and strangles, and the pricing models: put-call parity, the binomial model and Black-Scholes. You finish with the Greeks and with using options to hedge.

The chapter is mostly numerical. Each topic builds on the one before it. Payoffs feed strategies. Strategies and parity feed the pricing logic. Binomial pricing leads naturally to Black-Scholes, and the Greeks measure how Black-Scholes values move.

It connects to the rest of Paper 14 through derivatives, risk management and foreign exchange and interest rate hedging. The same ideas of hedging, arbitrage and risk-neutral thinking appear there. If you are strong here, those chapters become easier.

Options is a calculation-heavy chapter, and numerical questions reward method. Section A of Paper 14 has 15 standalone MCQs of 2 marks each, and many options points can be tested quickly there, such as payoff at expiry, parity, or the sign of a Greek. In the written section, a pricing or strategy problem can be answered step by step with clear working, so you can earn marks even if the final figure slips. The effort is worth it because the same formulas repeat with only the inputs changing.

Options: topics in the order to study them

  1. 1Option Basics: Calls, Puts and TerminologyEvery later topic uses these terms, so learn strike, premium, moneyness, and European versus American first.
  2. 2Option Payoffs and Profit DiagramsPayoffs for buyers and writers are the building blocks of every strategy and hedge.
  3. 3Option Trading StrategiesStrategies are just payoffs added together, so this follows directly from the payoffs.
  4. 4Put-Call ParityIt links call, put, share and bond values, and gives you a check on prices before the pricing models.
  5. 5Binomial Option Pricing ModelIt teaches valuation by replication and risk-neutral probabilities in simple steps, before the continuous model.
  6. 6Black-Scholes Option Pricing ModelIt is the continuous-time counterpart of the binomial idea, and needs the ideas you have just built.
  7. 7Option Greeks and SensitivityThe Greeks show how the Black-Scholes value changes with each input, so you learn them after the model.
  8. 8Hedging with Options and Real-Life ApplicationsIt brings payoffs, pricing and Greeks together in practical cases, so it works best last.

How to prepare Options

Treat this chapter as a set of methods you practise, not a set of notes you read. Aim for a repeatable layout for each type of problem.

  1. Learn the terms and write the payoff formulas for long and short calls and puts from memory: call = max(S − X, 0), put = max(X − S, 0).
  2. Draw a payoff and profit diagram for every strategy. Mark the break-even points, maximum profit and maximum loss.
  3. Practise strategies by building a table of final share prices against payoff, then subtract or add the net premium.
  4. Use put-call parity for European options on non-dividend shares: C + X × e^(−rT) = P + S. Practise with both continuous and simple discounting, as the question states.
  5. Solve binomial problems in a fixed order: up and down prices, option payoffs, hedge ratio or risk-neutral probability, then discount.
  6. Do Black-Scholes by listing d1, d2, N(d1), N(d2), and the discount factor in a neat layout. Check the normal table readings carefully.
  7. Finish with mixed questions on Greeks and hedging, and write a one-line recommendation at the end of each answer.

Common mistakes in Options

  • Ignoring the premium when finding profit or break-even.

    Fix: Always compute payoff first, then adjust for premium on a separate line. Break-even for a long call is strike + premium.

  • Mixing up the buyer's and the writer's position.

    Fix: Label each leg as long or short before you calculate, and state whether the cash flow is paid or received.

  • Using put-call parity where its conditions do not hold.

    Fix: Check that options are European, on the same asset, strike and expiry. If dividends are paid, adjust the share price for them as the question directs.

  • Discounting wrongly in binomial and Black-Scholes problems.

    Fix: Read whether the rate is continuously compounded or simple, and use e^(−rT) or 1 ÷ (1 + r) accordingly. Write the time period beside each step.

  • Reading the normal distribution table incorrectly for N(d1) and N(d2).

    Fix: For negative d, use N(−d) = 1 − N(d). Round d to two decimals as the table needs, and show the table values you used.

  • Stating Greeks without explaining what they mean.

    Fix: Write each Greek as a sentence: delta is the change in option value for a small change in the share price. Then give its sign and use.

Last-day revision: Options

  • A call gives the right to buy and a put gives the right to sell; the writer has the obligation.
  • Call payoff at expiry for the holder = max(S − X, 0); put payoff = max(X − S, 0).
  • Profit = payoff − premium paid for a buyer; for a writer, premium received − payoff paid.
  • Intrinsic value of a call = max(S − X, 0); time value = premium − intrinsic value.
  • A long straddle is a call and a put at the same strike; it gains from large moves either way.
  • A bull call spread buys a lower-strike call and sells a higher-strike call; both profit and loss are limited.
  • Put-call parity (European, no dividends): C + X × e^(−rT) = P + S.
  • Binomial risk-neutral probability: p = (e^(rT) − d) ÷ (u − d), or with simple interest, (1 + r − d) ÷ (u − d).
  • Binomial option value = [p × payoff up + (1 − p) × payoff down] ÷ (1 + r), for one period.
  • Black-Scholes call: C = S × N(d1) − X × e^(−rT) × N(d2).
  • d1 = [ln(S ÷ X) + (r + σ²÷2) × T] ÷ (σ × √T); d2 = d1 − σ × √T.
  • Delta of a call lies between 0 and 1; gamma and vega are positive for long options; theta is usually negative.

Options practice questions

Options in other exams

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

Options: frequently asked questions

Is the Options chapter difficult in CMA Final SFM?

It feels hard at first because it has many formulas. It becomes manageable once you master payoffs and follow a fixed layout for each model. Regular practice of numericals matters more than reading theory.

Do I need to memorise the Black-Scholes formula?

Yes, you should know it well, along with d1 and d2. Questions usually give the inputs and the normal distribution values or ask you to look them up, so your task is to apply the steps accurately.

Which topics should I do first if I have little time?

Do payoffs and strategies, put-call parity and the binomial model first. They are quicker to master and give reliable marks. Then add Black-Scholes and the Greeks.

How do options questions appear in the exam?

Paper 14 starts with 15 compulsory MCQs of 2 marks each, where a quick payoff or parity check can be tested. The written section can include a full numerical on strategies, pricing or hedging, and you need to show working and a clear conclusion.