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Exam Hotspots

Six topic clusters recur across derivatives exams: put-call parity arbitrage, two-step binomial trees, Black-Scholes calculation and interpretation, margin call mechanics, basis risk in cross-hedges, and swap comparative advantage. Mastering these six families covers roughly 70 to 80 percent of typical exam marks. Each cluster has a predictable trap, so revising the traps is as important as revising the formulas.

Why it matters

Exam questions are not random. Examiners draw from a small bank of question patterns that test core mechanics. Put-call parity questions almost always include the four trade legs. Binomial trees almost always include an American check at the second-to-last node. Margin questions almost always require restoring to initial margin, not maintenance. Recognise the pattern and the marks follow.

Formulas

Effective price from a short hedge
Peff=F1+b2P_{\text{eff}} = F_1 + b_2
F1F_1 is the futures price at the time the hedge was opened. b2=S2−F2b_2 = S_2 - F_2 is the basis at close-out. Common exam trap: forgetting to add b2b_2 when basis is nonzero.
Risk-neutral binomial price (one step)
f0=e−rΔt[pfu+(1−p)fd]f_0 = e^{-r \Delta t} \bigl[ p f_u + (1-p) f_d \bigr]
After backward induction at each node, check for early exercise on American options at each node before discounting back.
Comparative advantage swap gain
Total gain=(rAfix−rBfix)−(rAfloat−rBfloat)\text{Total gain} = (r_{A}^{\text{fix}} - r_{B}^{\text{fix}}) - (r_{A}^{\text{float}} - r_{B}^{\text{float}})
Total saving is split between the two counterparties and the intermediary. Hull (2022), §7.4.

Worked examples

Scenario

Effective price trap. A wheat exporter sells November ASX wheat futures at F1=F_1 = A$330 to hedge a November sale. At close-out the futures price is F2=F_2 = A$310 and the spot is S2=S_2 = A$315.

Solution

Basis at close is b2=S2−F2=315−310=+5b_2 = S_2 - F_2 = 315 - 310 = +5. The effective price received from the hedge equals F1+b2=330+5=F_1 + b_2 = 330 + 5 = A$335 per tonne, not A$330. Students who ignore basis post the wrong number. The hedge locks in F1F_1 plus the basis movement, which can be positive or negative.

Scenario

Margin call trap. A trader holds a long ASX SPI 200 futures position. Initial margin is A$8,000, maintenance margin is A$6,000. After two days of losses the margin account balance falls to A$5,200.

Solution

A margin call is triggered because the balance fell below maintenance. The trader must restore the account to the initial margin of A$8,000, requiring a top-up of $8000 - 5200 = $ A$2,800, not the A$800 needed to merely reach maintenance. Restoring to maintenance is the most common exam error.

Scenario

Two-step American put on a binomial tree. S0=100S_0 = 100, u=1.1u = 1.1, d=0.9d = 0.9, r=5%r = 5\%, Δt=0.25\Delta t = 0.25, strike K=100K = 100.

Solution

Risk-neutral probability p=(e0.0125−0.9)/(1.1−0.9)=0.5628p = (e^{0.0125} - 0.9)/(1.1 - 0.9) = 0.5628. At the upper node Su=110S_u = 110, the put intrinsic value is zero. At the lower node Sd=90S_d = 90, intrinsic value is $10$ and continuation value is e−0.0125(p⋅0+(1−p)⋅19)=8.21e^{-0.0125}(p \cdot 0 + (1-p) \cdot 19) = 8.21, so early exercise at SdS_d gives $10$. Roll back to time zero, f0=e−0.0125(0.5628⋅0.527+0.4372⋅10)=4.62f_0 = e^{-0.0125}(0.5628 \cdot 0.527 + 0.4372 \cdot 10) = 4.62. Forgetting the early exercise check at SdS_d understates the put.

Common mistakes

  • ✗After a margin call, top up to the maintenance margin. Wrong. The call requires restoration to the initial margin. This is the single most-tested margin error in exam papers.
  • ✗American and European calls on a non-dividend stock have different prices. They are equal because early exercise of a call on a non-dividend stock is never optimal. With dividends or for puts, early exercise can be optimal and prices differ.
  • ✗The futures price equals the expected future spot price. The futures price equals spot plus cost of carry under no-arbitrage. The expected future spot may be higher or lower depending on whether the asset is in normal backwardation or contango.

Revision bullets

  • •Parity arbitrage: identify which side is cheap, list the four trade legs
  • •Binomial trees: backward induction with early-exercise checks for American
  • •BSM: compute d1d_1, d2d_2, look up N(⋅)N(\cdot), apply formula
  • •Margin calls: restore to initial margin, not maintenance
  • •Basis risk: effective price equals F1+b2F_1 + b_2 at close-out
  • •Swaps: split the comparative advantage gain across both parties
  • •American call on non-dividend stock equals European

Quick check

The most common exam mistake on margin call questions is:

Which statement about American versus European calls is correct?

Connected topics

PCP2-Step TreeBSM IntroBond PriceBasis Risk

In learning paths

Exam Revision Path

Sources

  1. Hull (2022), Chs. 2, 3, 11-15
    Hull, John C. Options, Futures, and Other Derivatives. 11th ed. Pearson, 2022. ISBN 978-0-13-693997-9.
    Covers margin (Ch. 2), basis risk (Ch. 3), put-call parity and binomial trees (Chs. 11, 13), BSM (Ch. 15), and swaps (Ch. 7).
  2. Hull (2022), §11.5 American calls
    Hull, John C. Options, Futures, and Other Derivatives. 11th ed. Pearson, 2022.
    Proves that early exercise of an American call on a non-dividend stock is never optimal.
  3. ASX, Futures margins and clearing
    Australian Securities Exchange. ASX 24 margining and clearing guidelines. ASX, accessed 2026.
    Local reference for initial and maintenance margin requirements on ASX 24 contracts.
  4. Black & Scholes (1973)
    Black, F. and Scholes, M. The Pricing of Options and Corporate Liabilities. Journal of Political Economy, Vol. 81, No. 3, 1973, pp. 637-654.
    Original derivation of the BSM formula tested in nearly every introductory derivatives exam.
How to cite this page
Dr. Phil's Quant Lab. (2026). Exam Hotspots. Derivatives Atlas. https://phucnguyenvan.com/concept/revision-hotspots
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