ACCA P4 Advanced Financial Management - 2010 - Study text - Emile Woolf Publishing
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Chapter 15: Options and hedging with options
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Hedging with options
Main features of hedging with options
Creating a hedge
4 Hedging with options
4.1 Main features of hedging with options
Financial options can be used to hedge exposures to the risk of adverse movements
in exchange rates, interest rates, bond prices and share prices. Hedging with options
differs from hedging with forward contracts, money market hedges, FRAs and
futures, in several important ways.
The hedge has a cost. A hedge should normally be created by buying options
rather than selling/writing options, and the option buyer must pay the premium
to obtain the options to create the hedge.
An option does not have to be exercised. It will only be exercised if it is in-the-
money. If it is out-of-the-money, the option holder will let the option lapse and
buy or sell the underlying item in the cash market, at the more favourable
market price. This means that an option holder can use the options as a
protection against adverse movements in the market rate, but can take
advantage of any favourable movement in the market rate.
Example
An investor holds 5,000 shares in another company, XYZ, which have a current
market price of $6.00. The investor will want to sell the shares in a few months’
time, in April, but not before then. He is concerned that the share price might fall
between now and April, but is also aware of the possibility that it could rise.
The investor can hedge the exposure to market risk (share price risk) by purchasing
a put option on 5,000 shares in XYZ, for expiry in April. Suppose the strike price of
the option is $6.00, so that the option is at-the-money when written.
If the share price falls below $6.00 before April, say to $5.50, the investor can
exercise the option and sell at the strike price of $6.00.
On the other hand, if the share price rises above $6.00, say to $7.00, he can let the
option lapse and sell the shares at the market price of $7.00.
4.2 Creating a hedge
The rule for creating a hedge with options is as follows:
To hedge against the risk of a rise in the price of the underlying item, buy call
options
To hedge against the risk of a fall in the price of the underlying item, buy put
options
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Currency options
Features of currency options
Hedging with currency options
Gains or losses on options and the effective exchange rate
Imperfect hedges
5 Currency options
5.1 Features of currency options
The main features of currency options have already been described.
A currency option gives its holder the right to buy (call option) or sell (put
option) a quantity of one currency in exchange for another, on or before a
specified date, at a fixed rate of exchange (the strike rate for the option).
Currency options can be purchased over-the-counter or on an exchange.
Examination questions are more likely to feature exchange-traded options than
OTC options. Currency options are traded on some exchanges, notably the
Philadelphia Stock Exchange, and options on currency futures are traded on the
CME exchange in Chicago.
Traded currency options are for a standard quantity of one currency in exchange
for another currency, and strike prices are quoted as exchange rates. The
premiums are normally quoted as an amount in one currency per unit of the
other currency. For example, traded options on currency futures for US$ - £ are
for £62,500 and are priced in US cents per £1.
5.2 Hedging with currency options
The rules for using exchange-traded currency options to hedge an exposure to
currency risk are as follows:
Establish what the exposure is. The company will have a future intention or
obligation to buy or sell a quantity of currency in exchange for another. Establish
whether the currency will be bought or sold, how much will be bought or sold,
and when.
Decide whether a call option or a put option is required to hedge the exposure.
Decide on the strike price for the option. For exchange-traded options, there will
normally be a small range of strike prices to choose from.
Calculate how many option contracts must be purchased to create the hedge.
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Example
A US company expects to pay 1 million euros to a supplier in Belgium. It is now
November and the payment is due in March. The company wants to use currency
options to hedge the exposure. Each currency option is for 125,000 euros.
The company will need to buy euros to make the payment to the supplier; therefore
it wants to hedge against the risk of a rise in the value of the euro (= a fall in the
value of the dollar). The company should therefore buy call options.
We shall suppose that the company chooses a strike price of 1.2400 (US$/€1) for the
options, and that the premium for a March call option at this strike price is 3.43 US
cents per euro.
The company should buy 8 call option contracts (€1,000,000/€125,000 per contract).
The cost of the premium will be $34,300 (1,000,000 × $0.0343).
5.3 Gains or losses on options and the effective exchange rate
The effective exchange rate that is obtained from a hedge with options on currency
futures depends on what happens when the settlement date arrives, and whether
the option is exercised or not.
The following example illustrates this point:
Example
Continuing the previous example, a US company expects to pay €1 million at the
end of March and buys 8 call options on March euro currency futures at a strike
price of 1.2400.
We can look at the position of the US company if the spot exchange rate (US$/€1) in
March is:
(a) $1.2000
(b) $1.2200
(c) $1.2500
(d) $1.2800
(e) $1.3000
Answer
The call option will be exercised if the futures price at the end of March is over
1.2400. At the end of March when the futures contract reaches settlement, the futures
settlement price should be the current spot exchange rate.
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Spot rate at expiry
1.2000
1.2200
1.2500
1.2800
1.3000
Do not
exercise
Do not
exercise
Exercise
Exercise
Exercise
$
$
$
$
$
Cost of buying
€1 million
1,200,000
1,220,000
1,240,000
1,240,000
1,240,000
Cost of
premium
34,300
34,300
34,300
34,300
34,300
Total cost 1,234,300
1,254,300
1,274,300
1,274,300
1,274,300
Effective
exchange rate
$1.2343
$1.2543
$1.2743
$1.2743
$1.2743
The hedge has enabled the company to fix a maximum effective exchange rate of
$1.2743 for buying the euros, but at the same time allowing the company to obtain a
lower effective exchange rate if the spot price is below the strike price, and the
option is not exercised.
5.4 Imperfect hedges
When a hedge is created with exchange-traded currency options, the hedge is often
imperfect, for reasons similar to those already explained for hedging with futures.
When a hedge with exchange-traded currency options is imperfect, and the options
are exercised, the un-hedged or over-hedged amount of currency should be bought
for sold in the spot currency market, at the spot rate, at the same time that the
options are exercised.
Example: imperfect hedge
A company in Belgium expects to pay US$2 million to a supplier in Arabia. It is now
November and the payment is due in March. The current spot rate is 1.2100. The
company wants to use currency options to hedge the exposure. Each currency
option is for 125,000 euros and the value of 1 tick (0.0001) is $12.50.
The company will need to buy US dollars and sell euros to make the payment to the
supplier; therefore it wants to hedge against the risk of a rise in the value of the
dollar and a fall in the value of the euro. Since the contracts are for euros, the
company should therefore buy put options.
We shall suppose that the company chooses a strike price of $1.2200 = €1 for the
options, and that the premium for a March put option at this strike price is 2.75 US
cents per euro.
At a strike price of $1.2200, $2,000,000 is the equivalent of 1,639,344 euros.
To hedge 1,639,344 euros, the company needs to buy 13.1 put options (1,639,344
euros/125,000 euros per contract).
The company will probably buy 13 put options. The cost of the premium will be 13
contracts × 125,000 × $0.0275 = $44,687.50. The company will buy these dollars spot
at $1.2100, and so the cost of buying the options (in euros) will be €36,931.82.
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(a) The spot exchange rate moves in the option holder’s favour
Suppose that the exchange rate moves in the time to expiry such that the company
does not want to exercise the options to sell futures at 1.2200 because the euro is
worth more than 1.2200. In this example, suppose that the spot rate in March when
the dollars must be paid is $1.2500 = €1. The company will let the option lapse and
purchase the dollars spot at $1.2500. The effective exchange rate is as follows:
€
Purchase $2,000,000 at $1.2500
1,600,000.00
Cost of option premium 36,931.82
Total cost 1,636,931.82
Effective exchange rate for $2 million
$1.2218 =
€
1
($2 million/€1,636,931.82)
(b) The spot exchange rate moves adversely
Suppose that the exchange rate moves in the time to expiry such that the company
wants to exercise the options. In this example, suppose that the spot rate in March
when the dollars must be paid is $1.1800 = €1. The company will exercise the option
to sell the 13 futures contracts at $1.2200.
$
November: sell options at 1.2200
March: close by buying at 1.1800
Profit per contract 0.0400
Profit on futures position = 13 contracts × 400 ticks × $12.50 per tick = $65,000
$
Payment to be made in $ 2,000,000
Gain on futures
(65,000)
Dollars to be purchased at the spot rate
1,935,000
€
Cost of buying $1,935,000 spot at 1.1800
1,639,830.51
Original cost of option premium 36,931.82
Total cost 1,676,762.33
Effective exchange rate for $2 million
$1.1928 =
€
1
($2 million/€1,676,762.33)
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Interest rate options
Features of interest rate options
Types of interest rate option
Borrowers’ options
Lenders’ options
Swaptions
6 Interest rate options
6.1 Features of interest rate options
An interest rate option is an option on a notional loan or deposit (or an option on an
interest rate future), where the loan or deposit period begins:
on the expiry date for the option for a European-style option, or
on or before the expiry date for the option, for an American-style option.
The option guarantees a maximum or a minimum rate of interest for the option
holder, and interest rate options are therefore sometimes called interest rate
guarantees or IRGs.
A call option guarantees a maximum rate of interest.
A put option guarantees a minimum rate of interest.
The maximum or minimum rate of interest guaranteed by the option is the strike
rate for the option, in comparison with an agreed benchmark rate of interest, such as
LIBOR or euribor.
An interest rate option is for a notional loan or deposit. If it is exercised, an actual
loan or deposit is not created. Instead, the option is ‘cash-settled’ by a payment from
the writer of the option to the option holder.
6.2 Types of interest rate option
Many interest rate options are arranged over-the-counter (OTC). These include:
borrowers’ options and lenders’ options
caps, floors and collars.
Options on interest rate futures are traded on the futures exchanges where the
interest rate futures are also traded.
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6.3 Borrowers’ options
A borrower’s option guarantees a maximum borrowing rate for the option holder.
The strike rate for the option is compared with an agreed reference rate or
benchmark interest rate, such as LIBOR.
It the reference rate of interest is higher than the strike rate when the option
reaches expiry, the option will be exercised. The option writer must make a
payment to the option holder for the difference between the actual interest rate
(reference rate) and the strike rate for the option.
It the reference rate of interest is lower than the strike rate when the option
reaches expiry, the option holder will let the option lapse.
The premium for the option might be expressed either:
as an actual percentage of the notional principal amount, or
as an annual rate of interest on the notional principal amount.
A borrower’s option can be used to fix a maximum effective borrowing rate for a
future short-term loan, but allow the option holder to benefit from any fall in the
interest rate up to the expiry date for the option.
Example
A company intends to borrow US$10 million in four months’ time for a period of
three months, but is concerned about the volatility of the US dollar LIBOR rate. The
three-month US$ LIBOR rate is currently 3.75%, but might go up or down in the
next four months. The company therefore takes out a borrower’s option with a
strike rate of 4% for a notional three-month loan of US$10 million. The expiry date is
in four months’ time. The option premium is the equivalent of 0.5% per annum of
the notional principal. For simplicity, we shall suppose that the company is able to
borrow at the US dollar LIBOR rate.
(a) If the three-month US dollar LIBOR rate is higher than the option strike rate at
expiry, the option will be exercised. If the three-month LIBOR rate is 6%, the
company will exercise the option, and the option writer will pay the option
holder an amount equal to the difference between the strike rate for the option
(4%) and the reference rate (6%). The payment will be based on 2% of $10
million for three months. (This payment is discounted because a borrower’s
option is settled at the beginning of the notional interest period, and not at the
end of the interest period).
(b) If the three-month US dollar LIBOR rate is lower than the option strike rate at
expiry, the option will not be exercised. For example, if the LIBOR rate after
four months is 3%, the option will not be exercised and will lapse.
These possible outcomes are summarised in the table below, assuming (for the
purpose of illustration) a spot LIBOR rate at the option expiry date of (a) 6% and (b)
3%.
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LIBOR rate at expiry
6%
3%
Exercise the option
Do not exercise
%
%
Borrow for three months at 6.00
3.00
Receive from option writer (2.00)
-
Cost of option premium 0.50
0.50
Effective interest cost (% annual rate) 4.50
3.50
If the borrower can borrow at the reference rate of interest, a borrower’s option sets
the maximum borrowing cost at the strike rate plus the option premium cost.
6.4 Lenders’ options
A lender’s option guarantees a minimum deposit rate (savings rate) for the option
holder. In all other respects, it is similar to a borrower’s option. The strike rate for
the option is compared with an agreed reference rate or benchmark interest rate,
such as LIBOR.
It the reference rate of interest is lower than the strike rate when the option
reaches expiry, the option will be exercised. The option writer must make a
payment to the option holder for the difference between the actual interest rate
(reference rate) and the strike rate for the option.
It the reference rate of interest is higher than the strike rate when the option
reaches expiry, the option holder will let the option lapse.
6.5 Swaptions
A swaption is an option on a swap. It gives its holder the right, but not the
obligation, to enter into a swap agreement at a future date, on terms that are fixed
now.
Swaptions are not commonly used, particularly by companies, because of the cost of
the option premium.
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Caps, floors and collars
Caps
Floors
Collars
Zero cost collars
Creating a short-term collar with options on interest rate futures
7 Caps, floors and collars
Borrowers’ and lenders’ options are options for one interest period only. Companies
that borrow might seek to hedge their interest rate risk for a number of consecutive
interest periods. For example, a company borrowing from a bank might have a five-
year loan with interest payable every six months, at a variable rate of interest. The
loan would therefore have ten consecutive interest periods, with the interest rate fixed
for just the first six-month period. The company might want to hedge its exposure to
the risk of a high interest rate in the next nine interest periods.
Caps, floors and collars are OTC interest rate options that allow a company to hold
interest rate options for a series of consecutive interest periods, instead of having to
arrange a number of separate single-period borrowers’ or lenders’ options.
7.1 Caps
An interest rate cap is a borrower’s option on a series of consecutive interest
periods. For example, a company might buy a cap fixing the maximum six-month
LIBOR rate at the strike rate for the option, for nine consecutive interest periods,
each expiring at six-monthly intervals.
Example
A company borrows £8 million for five years from a bank at a variable rate of
interest, with interest payable every six months at six-month LIBOR plus 0.50%. The
LIBOR rate for the first six months of the loan is 5%, therefore the company pays
interest for this first six months at 5.5%.
If the company wants to hedge the risk of a rise in the LIBOR rate for the next nine
interest periods, it can arrange a cap for a notional principal amount of £8 million. It
might select a strike rate of 5%. Alternatively, it might select a strike rate of 6%,
because the premium would be cheaper.
Suppose the strike rate for the cap is 5%, for the next nine interest periods. The
exercise dates for the cap can be arranged to coincide with the start of each six-
month interest period for the loan. The cap will fix the maximum effective rate of
interest on the loan for the next none periods.
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The cap fixes the maximum effective LIBOR rate at 5%.
The company will borrow at an effective maximum rate of 5.5% (strike rate +
0.50%).
However, the company has to pay the premium for the cap. This might be 1%
per year of the notional principal amount. The cost of the premium would make
the total maximum effective rate 6.50% per year.
For each notional interest period of the cap, the cap operates in a very similar way to
a borrower’s option.
If the reference rate of interest for the interest period (LIBOR or euribor) is
higher than the strike rate for the cap, the writer of the option must make a
payment to the option holder for the difference.
If the reference rate of interest for the interest period is lower than the strike rate
for the cap, the option in the cap will not be exercised.
Example
Returning to the previous example, suppose that the six-month LIBOR rates at the
first five exercise dates in the cap are as follows:
2nd interest period, Year 1 (1) LIBOR = 4.0%
1st interest period, Year 2 (2) LIBOR = 4.5%
2nd interest period, Year 2 (3) LIBOR = 5.25%
1st interest period, Year 3 (4) LIBOR = 5.75%
2nd interest period, Year 3 (5) LIBOR = 6.0%
The strike rate for the cap is 5%. The outcome for each interest period will be as
follows:
Interest period/
expiry date
LIBOR
Borrow at LIBOR
+ 0.50%
Receipt
from cap
Net interest
rate
(1) 4.0% Do not exercise
4.50%
- 4.50%
(2) 4.5% Do not exercise
5.00%
- 5.00%
(3) 5.25% Exercise
5.75%
(0.25)% 5.50%
(4) 5.75% Exercise
6.25%
(0.75)% 5.50%
(5) 6.0% Exercise
6.50%
(1.00)% 5.50%
The cap therefore sets an effective interest rate of 5.50% (the strike rate + 0.50%) and
also allows the option holder to benefit from a lower LIBOR rate, by choosing not to
exercise the option when this rate is more favourable than the strike rate for the
option. However, the effective interest rates are actually higher than in the table
above, because the cost of the option premium needs to be added.
With interest rate caps (and also with floors and collars), the payment by the option
writer when a cap is exercised is at the end of the notional interest period, not
when the option is exercised. The payment is therefore not discounted. In the
example above, the payment by the option writer for the fifth expiry date would be: