The document discusses various currency futures and options concepts: - Currency futures allow standardized hedging of currency exposure at fixed maturity dates and amounts. They require daily margin adjustments while forward contracts only require settlement at maturity. - Currency options provide the right but not obligation to buy (call) or sell (put) a currency at a fixed strike price by a future date. They allow setting price floors and ceilings on currency receivables and payables. - A company can hedge currency risk from foreign cash flows by writing covered calls on the currency. This provides premium income while capping upside, reducing downside exposure from currency depreciation. The tradeoff is lower premium but also lower risk of the

1. Futures and Options Market

2. Currency futures
• Currency futures are a standardized form of forward type of
financial instrument. Currency futures are very similar to
commodity futures.
• Currency futures are usually traded in a formal market place, like
the International Monetary Market (IMM) of the Chicago
Mercantile Exchange or the London International Financial Futures
Exchange (LIFFE).
• The contracts are only for a limited number of dates (four dates, the
3rd Wednesday of March, June, September and December) and for
fixed amounts. E.g.:
• Contract Face Amount
£ 62,500
DM 125,000
Can$ 100,000
• INR 50,00,000

3. • Futures Forward
• Daily cash flow Single CF at maturity
• Futures are traded only in standardized amts; Fwds any
• Futures have fixed maturity (only 4) dates; Fwds don't
• Futures are traded in central mkts; Fwds in OTC markets
• Futures have daily price limits; Fwds do not

4. • The major difference is that while a fwd
contract requires cash flows only on the
maturity date, future contracts (may) require
daily cash flows to maintain your margin at
the required level.

5. Margin and maintenance level
• When one opens a futures contract, one is
required pay a fee to the broker and to post a
margin. The margin is posted to ensure that
deals are honored.
• When the equity position falls, then this
margin must be supplemented by additional
cash to bring it up to the maintenance level.

6. • Suppose the margin on a futures contract on
the £ is $3000 and the maintenance level is
$2500.
• Then as long as the decline in the futures
position is less than $500 you need not take
any action, but once the futures position
declines by more than $500 you need to post
additional margin equal to the full decline in
value in the futures position.

7. Hedging with futures
• Suppose you have exported goods to the UK and
expect to receive £ in the future. Thus, you want
to sell the £ in future.
• You are expecting the future £ price to decline, so
you would like to hedge this position.
• To hedge this, you wish to take short position in
the futures that when your original position loses
money, the position in the futures should gain
money.

8. Example on hedging with futures and cost of borrowing
• On March 31, a Canadian firm borrows DM 2 m for 3 months
at 6% p.a. compounded annually in Germany. Since the firm
needs the money in Canada, it hedges against exchange risk.
• On March 31, the spot rate $ .50/DM, the 90-day forward rate
is $ .51/DM and the DM June futures is $ .51.
• At the end of June, the spot rate is $ .48. Assume the firm
hedges only the principal and not the interest payments.
• (a) What is the effective cost of borrowing (in percent p. a.) if
the firm hedges in the forward market?
(b) What is the effective cost of borrowing (in percent p. a.) if
the firm hedges in the futures market? Assume that the
margin is $3000 per contract (remember, each contract is for
DM 125,000), that the firm liquidates the futures contracts at
a price of $ .48 at the end of June, and that the firm borrows $
at 14% in order to pay for the margins.

9. • To calculate the effective rate of interest we
need to find out how much we are receiving
today, and how much we are paying at the
end of 3 months; and we need to look at
these amounts in Can$ terms.
• The amount that is received today is DM 2m
($0.50/DM) = $1m

11. Unhedged position
• First, let us calculate the interest on this loan:
• DM interest on the loan is DM 2m [(1.06)1/4 -
1] = DM 0.029348m
• Since we do not hedge this, the $ value of this
(at St+1) is
• = DM 0.029348 ($ 0.48/DM) = $0.014087m

12. 2 m DM loan taken
$0.50/DM
1 m $ loan taken
Interest @ 6% pa
=1.06^1/4 – 1 =
0.14674
Loan to be repaid
=2.029348 m
$0.48/DM
0.97408 m $

13. Forward hedge calculation
• (1) Buy DM 2m fwd, @ $0.51/DM to hedge
the principal payment = - $1.02m
• (2) Add the interest payment amount = -
$0.014087m
• (3) Total amount to be paid back is (1) +(2) = -
$1.034087m
• Thus, the effective rate of interest is =
1.0340874 - 1 = 0.14347 pa

14. 2 m DM loan taken
$0.50/DM
1 m $ loan taken
Interest @ 6% pa
=1.06^1/4 – 1 =
0.14674
Loan to be repaid
=2.029348 m
$0.48/DM
0.97408 m $
$0.51/DM
Sign a long forward to buy 2m DM You need $1.02 to buy 2m DM @ 0.51
You need $0.014087 to buy
0.029348 m DM @ 0.48
Total $1.034087 needed
Equivalent to 14.34% pa in $ terms
$0.48/DM

15. Hedging with futures
• (1) The interest payment amount = - $0.014087m
• (2) Add the interest payment on the margins = - $3000 (16)
(1.141/4 - 1) = - $0.001598m
• (3) Change in value of underlying position = - DM2m ($/DM
0.48 - 0.50) = + $0.04m
• (4) Change in value of futures position = + DM2m ($/DM
0.48 - 0.51) = - $0.06m
• (5) Total amount to be paid back is (1) +(2) + (3) +(4) - $1m
= - $1.035587
• Thus, the effective rate of interest is = 1.0355874 - 1 =
0.1505% pa
• Thus it was cheaper to hedge with forwards, ex post.
No. of contracts
=2 m/125000=16

16. $0.51/DM
Sign a long futures to buy 2m DM
You sell the futures contract @0.48
With a loss of $0.03/DM. Total loss
= $0.06 m
$0.48/DM
$0.50/DM
You want to buy 2DM in Spot market
$0.48/DM
Gain of $0.02/DM. Total gain = $0.04 m
Total position = 0.04-0.06 = loss of $0.02m
2 m DM loan taken
$0.50/DM
Interest @ 6% pa
=1.06^1/4 – 1 =
0.14674
Loan to be repaid
=2.029348 m
$0.48/DM
Margin amount borrowed
= 3000*16=$48,000
Interest on margin amount
to be paid = $48,000 [(1.14^1/4) -1]
=$0.001598 m
It is given in the problem that only principal $1 m will be hedged. i.e.
Interest of DM 0.029348 or equivalent of $ 0.014087 m will not be hedged.
Total amount to be paid =$1.035587 which is equivalent to 15.05%

17. CURRENCY OPTIONS

18. Call option
• A call option is a right to buy the underlying
security (in our case the fx) for a fixed price
(strike or exercise price) on or before a certain
date (maturity date).
• The normal logic will work if the price of the
option is quoted as HC/FC. Otherwise, either
convert the price, or think of the call on the HC as
put on the FC, and vice-versa.
• European option: can be exercised only at
maturity
American option: can be exercised at any time

19. Example
• Suppose that you went shopping during a X'mas sale for a Sony
camcorder, selling for $700 - a must have item in today’s yuppie
world and the store had run out of this item. Then the store might
issue you with a rain-check which would permit you to get back to
the store within a month and buy the camcorder for $700. Suppose
the day you went back to the store camcorders were selling for
$680 then would you use your rain-check? No the rain-check would
be worthless and you would just throw it away.
• Going back to call options, suppose you have an option on the £,
with a strike price of $1.75, and a life of 3 months. This means that
during the next 3 months you may buy a £ by paying $1.75, and if
the £ is selling for less than that then your option is worthless.
Thus,
• c = max {S - K, 0 }

20. Payoff diagram
X +
C0T
X
Long call
Expiration date price of the underlying security
Contract payoff
0
C0T
- C0T
Out the money
In the money

21. Put Option
• The story with put options is the similar. Put
options give you the right to sell the
underlying security for a fixed price (strike
price) on or before a certain date (the
expiration date).

22. Example
• Suppose you buy a new BMW for $30,000 and
you have it insured for $25,000.
• This means that in the event of an accident
you have the right to sell the car to the
insurance company for a price of $25,000.
However, if the damage done to the car is
slight and the car is worth $28,000 after the
accident then you would obviously not
exercise the option to sell your car.

23. Fx example
• Going back to options on fx, suppose you have a
put option on the DM with a strike price of $2.00,
and a life of 3 months.
• This means that during the next 3 months you
have the right to sell your DM for $2. You will
obviously do this only if the DM price in the
market is less than $2. Otherwise, it would be to
your advantage to throw away the put option and
sell the £ in the open market. Thus,
• p = max { K - S, 0 )

24. Payoff diagram
X +
C0T
X Expiration date price of the underlying security
Long put
Contract payoff
0
C0T
- C0T
in the money
out the money

25. Using options to set a ceiling on a fx
payment
• Suppose a Canadian firm has to pay £5 m
sometime during the next 3 months. On
the £, the call option premium is
$0.0220/£, for options with K = $1.50/£
• Q1. What option should the importer
buy?
Q2. What is the cost incurred today?

26. Solution
• 1. Since the importer is has to make a £
payment, that is £ will be bought in future. To
hedge this, the importer buys a call options
• 2. £ 5 m * 0.0220 = $0.11 m

27. • Q3. What is the ceiling that the importer has
set on the price of the £?
Q4. What is the actual amount that the
importer will pay if the spot rate at the end of
3 months is $1.46/£?
Q5. What is the actual amount that the
importer will pay if the spot rate at the end of
3 months is $1.55/£?

28. Solution
• 3. The max that he will have to pay for each £ is
$.022/£ + $1.50/£ = $1.552/£
• 4. Since ST < K, the options are worthless and the
importer can do better by buying at the market
rate of $1.46/£. Thus, his total cost, ignoring time
value of the payments, is $1.46 +$.022 =
$1..482/£
• 5. Now, ST > K and therefore it is worth exercising
the options. The importer will pay his ceiling
price, $1.522/£.

29. Using put options to set a floor on a
fx receivable
• Suppose a Japanese company, Matsushita, has
to sell Can$ 50 m sometime during the next 6
months, and would like to lock in a minimum
¥ value for this. The price of a put option with
a strike price of K = ¥ 230/$ is ¥ 4/$
• Q1. What option should the importer buy?
Q2. What is the cost incurred today?

30. • 1. Since Matsushita wishes to sell $, it should
buy a put option on the $. This is, of course,
the same as wanting to buy ¥, and therefore,
an call option on the ¥.
• 2. $ 50 m . ¥ 4 /$= ¥ 200

31. • Q3. What is the floor that the Matsushita has
set on the price of the £?
Q4. What is the actual amount that they
receive if the spot rate at the end of 3 months
is ¥ 245/$?
Q5. What is the actual amount that they
receive if the spot rate at the end of 3 months
is ¥ 215/$?

32. • 3. The min that they will have to receive for each $ is
= K - premium
= ¥ 230 - ¥4 = ¥ 226/$
• 4. Since ST >K, the options are worthless and
Matsushita can do better by selling at the market rate
of ¥ 245/$, rather than the exercise price of ¥ 230/$.
Thus, their total receipts will be
= ¥ 245/$ - ¥ 4/$
= ¥ 241/$
• 5. Now, ST < K and therefore it is worth exercising the
options. Matsushita will receive their floor price, ¥ 230
- ¥4 = ¥ 226/$

33. Writing options to hedge against fx
risk.
• Texaco, USA has a large fx exposure in the form of a Can$ cash inflow from
its Canadian operations. The risk to Texaco is that the Can$ may
depreciate, thereby decreasing the US$ value of Texaco's Can$.
• Texaco can reduce its long position in the Can$ by writing options on the
Can$. This strategy is called "fully covered call writing.“
• The advantage of this strategy is that when Texaco writes options it
receives a positive cash flow today (from the premium on the options). If
the value of the Can$ falls (S($/c$) decreases) then this positive cash flow
helps offset the loss from depreciation. The price of this strategy is that if
the Can$ appreciates, then the option buyer reaps the gains from this -
rather than Texaco.
• As a financial officer, your job would be to pick the best strike price. There
is the following trade-off between the risk and return:
As you increase K, the premium decreases, so your revenue falls, but the
chance of the options being exercised against you decreases.
As you decrease K, ...