A futures or forward contract locks in a rate, good and bad. An option is different: you pay for protection against the bad outcome and keep the good one. The price is the premium, paid whatever happens. The same idea works for currencies and interest rates.
A cap protects a borrower for several periods at once, a floor protects a depositor, and a collar cuts the cost by giving up some of the upside.
This topic covers the terms and features of options, calls and puts, American and European styles, buying and writing, premiums and the zero-sum nature of options, in-the-money and out-of-the-money, hedging with options, currency options, interest rate options (borrowers’ and lenders’ options), swaptions, caps, floors and collars. The previous topic covered currency futures and short-term interest rate futures. The next covers option pricing and the Black-Scholes model.
Neither the May 2014 nor the November 2014 Pathfinder sets a stand-alone question on hedging with options.
In 30 seconds
An option gives the holder the right but not the obligation to buy (call) or sell (put) at a fixed strike price. Buyers pay a premium; writers receive it and must perform if the option is exercised. An option is exercised only if it is in the money. To hedge a rise in the price of the underlying, buy calls; to hedge a fall, buy puts.
A hedge with options has a cost (the premium) but lets the holder keep favourable moves. For currency options on futures: contracts = exposure ÷ contract size; effective rate = (spot or strike cost + premium) ÷ amount. An interest rate option (borrower’s = call, lender’s = put) guarantees a maximum or minimum rate; the effective borrowing rate is at most strike + premium.
A cap is a series of borrowers’ options, a floor a series of lenders’ options, a collar buys a cap and sells a floor to cut the premium (a zero-cost collar if the premiums match). Cap and floor payments are at the end of the period, not discounted.
Key terms in plain English
| Term | What it means |
|---|---|
| Call / put option | The right to buy / sell the underlying at the strike price |
| Strike (exercise) price | The fixed price at which the holder can buy or sell |
| Premium | The price paid by the buyer to the writer when the option is agreed |
| Writer | The seller of an option, who must perform if it is exercised |
| In / at / out of the money | The strike is better than / equal to / worse than the market price |
| Cap / floor / collar | A series of borrowers’ options / lenders’ options / a cap bought and a floor sold |
Syllabus check
This topic is in syllabus area E (treasury and advanced risk management). It covers:
- defining and explaining option terminology;
- using options to hedge foreign exchange and interest rate risk;
- explaining caps, floors and collars.
CAMA 2020 and option contracts
The Companies and Allied Matters Act 2020 (CAMA 2020) is the company law of Nigeria.
| Section | What it says | Link to this topic |
|---|---|---|
| s. 305 | A director must act in good faith in the best interests of the company | Hedging should protect the company without exposing it to unplanned risk |
| s. 308 | A director must use the care, diligence and skill of a reasonably prudent director | Directors should approve limits for option positions and the premiums paid |
| s. 377(1) and s. 378 | Directors prepare statements that follow IFRS and give a true and fair view | Decisions later affect reported assets, profit and cash |
| s. 385 | The directors’ report covers performance and risk | Major plans and risks are reported to shareholders |
Features of options
A financial option is a contract giving its holder the right, but not the obligation, to buy or sell a quantity of a financial item on or before a date at a price fixed in the contract: on currencies, interest rates, share prices and indices. A commodity option relates to a commodity.
A real option (next topics) is a choice in a capital project, such as to expand, abandon or defer.
- Call: the right to buy; put: the right to sell.
- American options can be exercised on or before expiry; European only at expiry; Bermudan on a set of dates. The names do not refer to places.
- OTC options are negotiated directly (borrowers’ and lenders’ options, caps, floors, collars, many currency options); exchange-traded options have a limited range of strike prices and expiry dates.
Buying and writing
The holder may exercise; the writer must sell (call) or buy (put) if the holder exercises. The buyer pays the premium at the start, and the writer keeps it whatever happens. ICAN’s CME example: a September call at a strike of $1.22 per € priced at 0.34 US cents costs 125,000 × $0.0034 = $425 per contract; a December put at 1.25 priced at 4.90 cents costs 125,000 × $0.0490 = $6,125.
Options are a zero-sum game: the buyer’s gain is the writer’s loss. An option is exercised only if in the money: a call if the market price is above the strike; a put if it is below.
ICAN’s example. A company buys a European call on €1,000,000 with a strike of 1.2500; the premium is 2.4 cents per euro ($24,000).
- Spot 1.2350: not exercised; the buyer loses the premium, $24,000.
- Spot 1.2670: exercise, gain 0.0170 × 1,000,000 = $17,000; net −$7,000.
- Spot 1.2930: gain $43,000; net +$19,000. The writer’s result is the opposite.
Hedging with options
Differences from forwards, FRAs and futures: the hedge has a cost (the premium, so you normally buy, not write); and the holder need not exercise, so the option protects against adverse moves yet lets the holder gain from favourable ones. Rule: to hedge against a rise in the price of the underlying, buy calls; against a fall, buy puts.
An investor with 5,000 shares at $6.00 who plans to sell in April can buy a put at $6.00: if the price falls to $5.50 he exercises at $6.00; if it rises to $7.00 the option lapses and he sells at $7.00.
Currency options
A currency option gives the right to buy (call) or sell (put) a quantity of one currency for another at a fixed strike rate. Traded options are for standard amounts (€125,000; £62,500 for dollar–pound futures) and are priced in cents per unit. Steps: establish the exposure; choose call or put; choose a strike; calculate contracts.
ICAN’s example (perfect). A US company must pay €1m in March. Strike 1.2400; premium 3.43 cents. It fears a rise in the euro, so it buys 8 call contracts (1,000,000 ÷ 125,000); premium = $34,300.
| Spot in March | 1.2000 | 1.2200 | 1.2500 | 1.2800 | 1.3000 |
|---|---|---|---|---|---|
| Exercise? | No | No | Yes | Yes | Yes |
| Cost of €1m | $1,200,000 | $1,220,000 | $1,240,000 | $1,240,000 | $1,240,000 |
| Total with premium | $1,234,300 | $1,254,300 | $1,274,300 | $1,274,300 | $1,274,300 |
| Effective rate | 1.2343 | 1.2543 | 1.2743 | 1.2743 | 1.2743 |
The maximum effective rate is $1.2743, and the company gains if the spot rate is below the strike.
ICAN’s example (imperfect). A Belgian company pays US$2m in March; spot is 1.2100; strike 1.2200; contracts are €125,000, tick $12.50; premium 2.75 cents. The dollar is bought with euros, so it buys put options on euros.
- € equivalent at the strike = 2,000,000 ÷ 1.2200 = €1,639,344
contracts = 13.1, so 13.
Premium = 13 × 125,000 × $0.0275 = $44,687.50, or €36,931.82 at 1.2100. - Spot 1.2500: the options lapse.
Cost = 2,000,000 ÷ 1.25 = €1,600,000 + 36,931.82 = €1,636,931.82
effective rate = 2,000,000 ÷ 1,636,931.82 = 1.2218. - Spot 1.1800:
exercise (sell futures at 1.2200 and buy at 1.1800): gain 13 × 400 × $12.50 = $65,000.
Dollars to buy = 1,935,000, costing €1,639,830.51 at 1.1800
plus premium €36,931.82 = €1,676,762.33
effective rate = 1.1928.
Interest rate options
An interest rate option is on a notional loan or deposit (or a future); it guarantees a maximum or minimum rate (an interest rate guarantee, IRG) against a benchmark such as LIBOR or Euribor. A call guarantees a maximum rate, a put a minimum rate. It is cash-settled by a payment from the writer. The premium may be a percentage of the notional or an annual rate.
A borrower’s option guarantees a maximum borrowing rate: if the reference rate is above the strike at expiry the writer pays the difference (settled at the start of the notional period, so discounted); otherwise the option lapses. A lender’s option guarantees a minimum deposit rate and works in reverse.
ICAN’s example. A company borrows $10m for three months in four months. LIBOR is 3.75%. It buys a borrower’s option with a strike of 4% and a premium of 0.5% a year, and can borrow at LIBOR.
- LIBOR 6%: exercise.
Cost 6.00% − 2.00% received + 0.50% premium = 4.50%. - LIBOR 3%: lapse.
Cost 3.00% + 0.50% = 3.50%. - The maximum cost is the strike plus the premium, 4.50%.
A swaption is an option on a swap: the right to enter a swap on terms fixed now. It is uncommon because of the premium cost.
Caps, floors and collars
These are OTC options over a series of consecutive interest periods, instead of many single-period options. A cap is a series of borrowers’ options. ICAN’s example: £8m borrowed for five years at six-month LIBOR + 0.50%; LIBOR is 5% for the first six months. The company buys a cap at a 5% strike for the next nine periods.
- The maximum effective LIBOR is 5%, so the maximum loan rate is 5.5% (strike + margin).
- If the cap premium is 1% a year, the maximum rate becomes 6.50%.
- With LIBOR at 4.0, 4.5, 5.25, 5.75 and 6.0%, the cap pays nothing at the first two dates; at 5.25% it pays 0.25% (net 5.50%), at 5.75% 0.75% (net 5.50%) and at 6.0% 1.00% (net 5.50%), before premium.
- The payment for the fifth date is (6.00 − 5.00)% × £8m × 6÷12 = £40,000, paid at the end of the period, so not discounted.
A floor is a series of lenders’ options and fixes a minimum rate. A collar reduces cost: a borrower buys a cap and sells a floor at a lower strike, so rates are fixed between the two (collar premium = cap premium paid − floor premium received).
An investor can buy a floor and sell a cap. A zero-cost collar has equal premiums, which usually means the two strikes are very close, or a narrow band.
The rules in more depth
Why you buy, not write, to hedge
Writing leaves you exposed; buying gives protection at a known cost.
Why a hedge with options costs more than a forward
You pay for the right to benefit from favourable moves.
Why interest rate option payments are discounted but cap payments are not
A borrower’s option is settled at the start of the period; cap and floor payments are made at the end.
Why collars cut the cost
The premium received for the sold option offsets the premium paid, at the price of giving up part of the favourable range.
Effect on analysis
State the exposure, choose the option type, find the exercise decision at each outcome and give the effective rate including the premium.
Worked examples
Example 1: choose the option. A US importer must pay euros in six months and fears a rise in the euro.
- A rise in the euro costs more.
- It needs protection against a rise.
- Buy call options on euros.
Example 2: premium. A €125,000 call is priced at 0.34 cents per euro.
- Premium = 125,000 × $0.0034.
- = $425.
- This is paid at the start, win or lose.
Example 3: a borrower’s option. Strike 4%, premium 0.5%, LIBOR at expiry 5%.
- Exercise: receive 1.00%.
- Cost = 5.00% − 1.00% + 0.50%.
- Effective rate = 4.50%.
Example 4: a collar. A borrower buys a 6% cap (premium 0.9%) and sells a 4% floor (premium 0.6%).
- Net premium = 0.9% − 0.6%.
- = 0.3%.
- LIBOR is effectively held between 4% and 6%.
How to score full marks
- Identify the exposure and pick a call or a put.
- Decide at each outcome whether the option is exercised.
- Include the premium in the effective rate.
- State the maximum or minimum rate secured.
- For caps, do not discount the payment.
- Comment on the cost against forwards, futures and swaps.
Common mistakes in the exam
- Buying a put when the exposure needs a call.
- Forgetting the premium.
- Exercising an out-of-the-money option.
- Not rounding contracts sensibly.
- Discounting cap payments.
- Calling the premium refundable.
Quick revision
- Call = right to buy; put = right to sell; buyer pays premium.
- Hedge a rise: buy calls. Hedge a fall: buy puts.
- Exercise only if in the money.
- Maximum effective rate = strike + premium (+ margin).
- Cap = borrowers’ options; floor = lenders’ options; collar = cap bought and floor sold.
- CAMA 2020: ss. 305, 308, 377(1), 378, 385.
Practice questions
These are original questions written in the style of the Institute of Chartered Accountants of Nigeria (ICAN) exam. Try each one before you open the answer. Full model answers follow the written questions.
Recall check: multiple choice
Recent ICAN papers are written, although older papers such as May 2014 included multiple-choice questions. These questions are for quick recall. The written questions that follow are closer to the exam.
Question 1. A call option gives the holder the right to:
- Buy at the strike price
- Sell at the strike price
- Receive a premium
- Cancel the premium
Show the answer
A. Without any obligation.
Question 2. The writer of an option receives:
- The premium
- Nothing
- The strike price only
- A refund
Show the answer
A. Whether or not it is exercised.
Question 3. To hedge a rise in the price of the underlying, buy:
- Calls
- Puts
- Futures sold
- Nothing
Show the answer
A. They gain when the price rises.
Question 4. An option is exercised only if it is:
- In the money
- Out of the money
- At a loss
- Expired
Show the answer
A. Otherwise it lapses.
Question 5. A European option can be exercised:
- Only at expiry
- Any time
- Never
- On several dates
Show the answer
A. American is any time.
Question 6. A borrower’s option with strike 4% and premium 0.5% gives a maximum cost of:
- 4.5%
- 4.0%
- 0.5%
- 5.5%
Show the answer
A. Strike plus premium.
Question 7. A cap is a series of:
- Borrowers’ options
- Lenders’ options
- Swaps
- Futures
Show the answer
A. A floor is lenders’ options.
Question 8. A collar for a borrower is:
- Buy a cap and sell a floor
- Sell a cap and buy a floor
- Buy a floor only
- Sell both
Show the answer
A. The floor premium offsets the cap premium.
Question 9. A cap payment is made:
- At the end of the interest period, undiscounted
- At the start, discounted
- Never
- At maturity of the loan
Show the answer
A. Unlike a borrower’s option.
Question 10. Which section of CAMA 2020 sets the director’s duty of care and skill?
- Section 308
- Section 400
- Section 405
- Section 409
Show the answer
A. Directors should test the assumptions behind a decision.
Written questions
Question 11 (10 marks). (a) Distinguish call and put options and American and European options. (4 marks) (b) Explain why hedging with options differs from hedging with futures. (3 marks) (c) Explain a zero-cost collar. (3 marks)
Question 12 (20 marks). A US company must pay €1m in March. It buys March euro call options at a strike of 1.2400 (€125,000 per contract) for a premium of 3.43 US cents per euro. (a) State the number of contracts and the premium. (3 marks) (b) Calculate the effective rate if spot is 1.2200 and if it is 1.2800. (6 marks) (c) A company borrows £8m at LIBOR + 0.50% and buys a cap at 5% with an annual premium of 1%.
State the maximum effective rate and the payment when LIBOR is 6.0% for six months. (5 marks) (d) Explain how a collar would reduce the cost. (3 marks) (e) Explain why options protect against adverse but not favourable moves. (3 marks)
Question 13 (10 marks). (a) A company borrows $10m for three months and buys a borrower’s option with a strike of 4% and a premium of 0.5%. Calculate the effective rate if LIBOR is 6% and if 3%. (4 marks) (b) A Belgian company pays $2m and buys 13 euro put contracts at a strike of 1.2200. Spot is 1.2500. Explain what happens and calculate the euro cost excluding the premium. (4 marks) (c) State one disadvantage of options. (2 marks)
Model answers
Show the model answer to Question 11
(a) Terms (4 marks). A call gives the right to buy and a put the right to sell at the strike price. (2) An American option can be exercised on or before expiry, a European option only at expiry. (2)
(b) Differences (3 marks). An options hedge costs a premium. (1.5) The holder need not exercise, so favourable moves can be enjoyed. (1.5)
(c) Zero-cost collar (3 marks). A collar buys a cap and sells a floor. (1) If the cap premium equals the floor premium, the net premium is nil. (1) The strikes are then close together, so the range is narrow. (1)
Show the model answer to Question 12
(a) Contracts (3 marks).
- The company fears a rise in the euro, so buys calls: 1,000,000 ÷ 125,000 = 8 contracts. (2)
- Premium = 1,000,000 × $0.0343 = $34,300. (1)
(b) Effective rates (6 marks).
- Spot 1.2200: not exercised; cost = $1,220,000 + $34,300 = $1,254,300; rate = 1.2543. (3)
- Spot 1.2800: exercise at 1.2400; cost = $1,240,000 + $34,300 = $1,274,300; rate = 1.2743. (3)
(c) Cap (5 marks).
- The maximum LIBOR is 5%, so the loan costs 5.5%; with the premium of 1% the maximum rate is 6.50%. (3)
- Payment = (6.0 − 5.0)% × £8m × 6÷12 = £40,000, at the end of the period, undiscounted. (2)
(d) Collar (3 marks). The company buys the cap and sells a floor at a lower strike. (1) The floor premium received offsets the cap premium paid. (1) The cost is lower, but the company gives up the benefit of rates below the floor strike. (1)
(e) Protection (3 marks). If the market moves against the company, the option is in the money and is exercised at the strike. (1.5) If it moves in its favour, the option lapses and the company uses the market rate, losing only the premium. (1.5)
Show the model answer to Question 13
(a) Borrower’s option (4 marks).
- LIBOR 6%: 6.00 − 2.00 + 0.50 = 4.50%. (2)
- LIBOR 3%: lapse; 3.00 + 0.50 = 3.50%. (2)
(b) Put options (4 marks).
- The euro is worth 1.2500, above the 1.2200 strike, so the put is out of the money and lapses. (2)
- The company buys the dollars spot.
2,000,000 ÷ 1.2500 = €1,600,000. (2)
(c) Disadvantage (2 marks). The premium is paid whether or not the option is exercised, so the hedge is more costly than a forward or future. (2)
Pathfinder on Option terms, currency options, interest rate options, caps, floors and collars
These are the ICAN Pathfinder questions that test this topic. ICAN owns the questions and the suggested solutions, so we point you to them and do not copy them. Open your Pathfinder, attempt each question under exam conditions, then check your answer against the notes above.
Neither the May 2014 nor the November 2014 Pathfinder sets a stand-alone question on hedging with options. Practise the effective rate tables in the currency options section and the cap example.
Revise first: Currency options
Questions ask for the maximum rate secured by a cap or collar. See the section on caps, floors and collars.
Revise first: Caps, floors and collars
Source: ICAN Pathfinder, Strategic Financial Management. Diets covered: No stand-alone question in the May 2014 or November 2014 Pathfinder.
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