OPTIONS
- What is the difference between an American and a European option? Which
one should trade at a higher price?
An American option can be exercised at any time until it expires at maturity. A
European option can be exercised only on the expiration date. An American option
should trade at a higher price. - If the exchange rate is $0.66/EUR, the strike price of a call option expiring in 3
months is $0.70/EUR and the option premium is $0.06/EUR, what is the
intrinsic value of the option? Does it have time value?
The intrinsic value of the option is zero, which is the maximum [0, ‐0.04]. Time value
is the difference between the option premium and the intrinsic value. Hence, the
time value is $0.06. - What is the difference between options on spot currency and options on
currency futures?
The underlying asset in the first case is the spot currency. Examples include the
DEM and Yen options that trade on the PHLX.
The underlying asset in the 2nd case is a currency futures contract such as those
traded on the CME.
International Financial Management
2 - Suppose you can buy on the PHLX a call option [contract size is Yen 6,250,000]
to buy yen at $0.01/Yen for maturity in two months. The premium is 1.26 cents
per 100 yen. What would be the total cost of purchasing this call option?
The PHLX ¥ option is for 6,250,000 Yen. If the premium is $0.0126 per 100 Yen, the
total cost of the call option is $787.50 plus transactions costs. - Citicorp sells a call option on Deutsche marks [contract size is EUR 500,000
(EUR 62,500 * 8)] at a premium of $0.04 per EUR. If the exercise price is $0.71
and the spot price of the EUR at expiration date is $0.73, what is Citicorp’s
profit (loss) on the call option?
Since the spot price exceeds the exercise price, the option will be exercised. Since,
Citicorp sells a call option its profit is capped at the premium of $20,000 ($0.04/EUR *
EUR 500,000) it receives from the buyer of the call option (between $0.71/EUR and
0.75/EUR the profit is diminishing). Its loss is potentially unlimited.
At $0.71/EUR, cash flows for Citicorp are as follows
Inflows: $20,000 + $355,000 (EUR500000 * $0.71) = $375,000
Outflows: $365,000 (EUR500000 * $0.73)
Profit = $10,000
The buyer of the call will exercise and the profit made is $ 10,000 (EUR 500,000 *
0.02). However, the profit is not large enough to cover the premium paid. The total
loss for the buyer is $10,000, which is less than the loss the buyer would have
otherwise incurred.
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Payoff diagram for the Option Seller (Citicorp) - Suppose that Bechtel Group wants to hedge a bid on a Japanese construction
project. But because the yen exposure is contingent on acceptance of its bid,
Bechtel decides to buy a put option for the ¥15 billion bid amount rather than
sell it forward. In order to reduce its hedging cost, however, Bechtel
simultaneously sells a call option for ¥15 billion with the same strike price.
Bechtel reasons that it wants to protect its downside risk on the contract and is
willing to sacrifice the upside potential in order to collect the call premium.
Comment on Bechtelʹs hedging strategy.
The combination of buying a put option and selling a call option at the same strike
price is equivalent to selling ¥15 billion forward at a forward rate equal to the strike
price on the put and call options. That is, Bechtel is no longer holding an option; it is
now holding a forward contract. If the yen appreciates and Bechtel loses its bid, it
will face an exchange loss equal to 15 billion x (actual spot rate ‐ exercise price). - A trader executes a “bear spread” on the Japanese yen consisting of a long
PHLX 103 March put and a short PHLX 101 March put.
$20,000
Call Premium
X = $0.71 $0.75
PROFIT (LOSS)
Potentially Unlimited
Loss
Profit limited to Call
Premium
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4
a. If the price of the 103 put is 2.81 (100ths of ¢/¥), while the price of the 101 put
is 1.6 (100ths of ¢/¥), what is the net cost of the bear spread?
Going long on the 103 March put costs 0.0281¢/¥ G while going short on the 101
March put yields 0.016¢/¥.
The net cost is therefore 0.0121¢/¥ (0.0281 ‐ 0.016).
On a contract of ¥6,250,000, this is equivalent to $756.25.
b. What is the maximum amount the trader can make on the bear spread in the
event the yen depreciates against the dollar?
To begin, the 103 March put gives the trader the right but not the obligation to sell
yen at a price of 1.03¢/¥. Similarly, the 101 March put gives the buyer the right but
not the obligation to sell yen at a price of 1.01¢/¥.
If the yen falls to 1.01¢/¥ or below, the trader will earn the maximum spread of
0.02¢/¥.
After paying the cost of the bear spread, the trader will net 0.0079¢/¥ (0.02¢ ‐
0.0121¢), or $493.75 on a ¥6,250,000 contract.
c. Redo your answers to parts a and b assuming the trader executes a “bull
spread” consisting of a long PHLX 97 March call priced at 0.0321¢/¥ and a
short PHLX 103 March call priced at 0.0196¢/¥. What is the traderʹs maximum
profit? Maximum loss? [Contract size is Yen 6,250,000]
In this case, the trader will pay 0.0321¢/¥ for the long 97 March call and receive
0.0196¢/¥ for the short 103 March call. The net cost to the trader, therefore, is
0.0125¢/¥, which is also the trader’s maximum potential loss. At any price of 1.03¢/¥
or greater, the trader will earn the maximum possible spread of 0.06¢/¥. After
subtracting off the cost of the bull spread, the trader will net 0.0475¢/¥, or $2,968.75
per ¥6,250,000 contract.
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FUTURES - Explain the basic differences between the operation of the currency forward
market and the futures market.
The forward market is an OTC market where the forward contract for the
purchase/sale of foreign currency is tailor‐made between the client and its bank.
There is no intermediate cash flows and delivery & receipt takes place on the
maturity date.
A futures contract is an exchange‐traded instrument with standardized features with
the contract size and delivery date being specified. It is marked‐to‐market on a daily
basis and this reflects changes in settlement price. - Why are most future positions closed out through a reversing trade rather than
held to delivery?
While, futures contracts are useful for speculation and hedging, their standardized
delivery dates make them unlikely to correspond to the actual future dates when
foreign exchange transactions will occur. Thus, they are generally closed out in a
reversing trade. - What is the major difference in the obligation of one with a long position in a
futures (or forward) contract in comparison to an options contract?
A futures (or forward) contract is a vehicle for buying or selling a stated amount of
foreign exchange at a stated price per unit at a specified time in the future. If the
contract is held long till the delivery date, the holder pays the effective contractual
futures (or forward) price, regardless of whether it is an advantageous price in
comparison to the underlying spot price.
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The options contract provides the holder with the right and not the obligation to
buy/sell the underlying asset at a specified price. This allows the holder to exercise
the option if the spot price is more favorable than the exercise price. Therefore,
doesn’t have to exercise the option if it is to his disadvantage and the only loss
incurred is the premium. - Assume today’s settlement price on a CME EUR futures contract is
$0.9716/EUR. You have a short position in one contract. Your margin account
currently has a balance of $1,700. The next three days’ settlement prices are
$0.9702, $0.9709 and $0.9625. Calculate the changes in the margin account from
daily marking‐to‐market and the balance of the margin account after the third
day. [Contract size is EUR125,000]
Note: At the end of each day, profit/loss is tallied up. So, in this case, your profit/loss
is determined in the following manner. You have initially sold a contract.
Balance in margin account = $1,700 + [($0.9716 ‐ $0.9702) + ($0.9702 ‐ $0.9709) +
($0.9709 ‐ $0.9625)] * EUR 125,000 = $2,837.50 - Do question 4 again assuming you have a long futures position in the futures
contract.
Balance in margin account = $1,700 + [($0.9702 ‐ $0.9716) + ($0.9709 ‐ $0.9702) +
($0.9625 ‐ $0.9709)] * EUR 125,000 = $562.50
Likely to receive a margin call requesting additional cash be added to the margin
account to bring it back to the initial level. - The price of the March 2002 Mexican Peso (MXP) futures contract is $ 0.10068.
You believe the spot price in December will be $ 0.11000. What speculative
position would you enter into to attempt to profit from your beliefs? Calculate
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your anticipated profit assuming you take a position in three contracts. What is
the size of your profit (loss) if the futures price is indeed an unbiased predictor
of the future spot price and this price materializes? [Contract size is MXP
500,000]
If the expectation is that the MXP is likely to rise in the future, the speculator will
take a long position as the futures position is lower than the expected spot price.
Anticipated profit = 3 * ($0.11000 – $0.10068)* MXP 500,000 = $13,980 (MXP 500,000 is
the contract size.
If the futures price is an unbiased predictor of the expected spot price, the expected
spot price is the futures price of $0.10068/MXP. If this materializes, then profit (loss)
would equal zero [3 x ($0.10068 – $0.10068) * MXP 500,000]. - What is the difference between maintenance and variation margin?
Maintenance margin is the lower bound for the acceptable level of margin. Touching
the maintenance margin level triggers a margin call. Variation margin is the amount
needed to restore the initial margin once a margin call has been issued. The variation
margin may change depending on how far the margin account has fallen below the
maintenance margin level. - On Monday morning, an investor takes a long position in a Pound futures
contract that matures on Wednesday afternoon. The agreed‐upon price is $1.78
for £62,500. At the close of trading on Monday, the futures price has risen to
$1.79. At Tuesday close, the price rises further to $1.80. At Wednesday close, the
price falls to $1.785, and the contract matures. The investor takes delivery of the
Pounds at the prevailing price of $1.785. Detail the daily settlement process.
What will be the investor’s profit (loss)?
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8
Time Action Cash Flow
Monday
Morning
Buy £ futures contract that matures in 2 days.
Price = $1.78
None
Monday Close Futures price s to $1.79. Contract is markedto‐
market
Receives 62,500 * (1.79 – 1.78)
= $625
Tuesday
Close
Futures price s to $1.80. Contract is markedto‐
market
Receives 62,500 * (1.80 – 1.79)
= $625
Wed. Close Futures price s to $1.785. Contract is
marked‐to‐market &
Investor takes delivery of £62,500
Pays 62,500 * (1.80 – 1.785) =
$937.50
Investor pays £62,500 * 1.785 =
$111,562.50 - Suppose that DEC buys a Swiss Franc futures contract (size is SFr $125,000) at a
price of $0.83. If the spot rate for the Swiss Franc at the date of settlement is SFr
1 = $0.8250, what is DEC’s gain or loss on this contract?
DEC has bought Swiss Francs worth $0.8250 at a price of $0.83. Thus it has lost
$0.005 per franc for a total loss of $125,000 * 0.005 = $625 - Suppose that Texas Instruments (TI) must pay a French supplier €10 million
in 90 days.
a. Explain how TI can use currency futures to hedge its exchange risk. How
many futures contracts will TI need to fully protect itself? [Contract size is
€125,000]
TI can hedge its exchange risk by buying euro futures contracts whose expiration
date is the closest to the date on which it must pay its French supplier. Given a
contract size of €125,000, TI must buy 10,000,000/125,000 = 80 futures contracts to
hedge its euro payable.
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9
b. Explain how TI can use currency options to hedge its exchange risk. How
many options contracts will TI need to fully protect itself?
TI can hedge its exchange risk by buying euro call options contracts whose
expiration date is the closest to the date on which it must pay its French supplier.
Given a contract size of €62,500, TI must buy 10,000,000/62,500 = 160 options
contracts to hedge its payable.
c. Discuss the advantages and disadvantages of using currency futures versus
currency options to hedge TIʹs exchange risk.
A futures contract is most valuable when the quantity of foreign currency being
hedged is known, as in the case here. An option contract is most valuable when the
quantity of foreign currency is unknown. Other things being equal, therefore, TI
should use futures contracts to hedge its currency risk. However, TI must honor its
futures contracts even if the spot rate at settlement is less than the futures price. In
contrast, TI can choose not to exercise currency call options if the call price exceeds
the spot price. Although this feature is an advantage of currency options, it is fully
priced out in the market via the call premium. Hence, options are not
unambiguously better than futures. In this case, since the quantity of the future
French franc outflow is known, TI should use currency futures to hedge its risk. - Suppose the interbank forward bid for December on AUD is $0.7515 and at the
same time the price of a futures contract for delivery in December is $0.7511. How
can the dealer use arbitrage to profit from this situation? [Contract size is
AUD100,000]
The dealer would buy the December Futures contract for $ 75,110 (100,000 x 0.7511)
and simultaneously sell an equal amount of AUD forward, worth $75,150 (100,000 x
0.7515), for delivery in December. At settlement the dealer earns a profit of $ 40.
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If the markets come back together before December, the dealer can still make the
same profit of $ 40 by unwinding his position i.e. simultaneously buy AUD 100,000
forward and sell a futures contract, both for delivery in December.
FAQs:
When should we be finding the Future value or Present value of the option
premium?
In some textbooks, they don’t distinguish the time value of money for option
premium since the difference is normally quite small when the time period is short.
Since option premium are paid upfront, technically, we should convert the premium
into present value if we are trying to work out the total cost today. Conversely, we
need to convert the premium into future value if we are trying to work out the total
cost on the expiry date.
In the exam, I will be very clear on how to treat the premium.
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SWAPS - Discuss the basic motivation for companies to enter into currency swaps.
Name recognition is extremely important in the international bond market. Without
it, even a creditworthy corporation will find itself paying a higher interest rate for
foreign denominated funds than a local borrower of equivalent creditworthiness.
Consequently, two firms of equivalent creditworthiness can each exploit their,
respective, name recognition by borrowing in their local capital market at a
favourable rate and then re‐lending at the same rate to the other. - Explain how Cisco Systems can use arbitrage to create a forward forward to fix
the interest rate on a three‐month $10 million loan to be taken out in nine
months. The loan will be priced off LIBOR.
Cisco can lock in a three‐month rate on a $10 million loan to be taken out in nine
months by buying a forward forward or by creating its own through arbitrage.
Specifically, Cisco can derive a nine‐month forward rate on LIBOR3 by
simultaneously lending the present value of $10 million for nine months and
borrowing that same amount of money for 12 months. - Deleted
- Suppose that IBM would like to borrow fixed-rate yen, whereas Korea
Development Bank (KDB) would like to borrow floating-rate dollars. IBM
can borrow fixed-rate yen at 4.5 percent or floating-rate dollars at LIBOR +
0.25 percent. KDB can borrow fixed-rate yen at 4.9 percent or floating-rate
dollars at LIBOR + 0.8 percent.
a. What is the range of possible cost savings that IBM can realize through an
interest rate/currency swap with KDB?
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The cost to each party of accessing either the fixed-rate yen or the floating-rate
dollar market for a new debt issue is as follows:
Borrower Fixed-Rate Yen Available Floating-Rate Dollars
Available
Korea Development Bank 4.9% LIBOR + 0.80%
IBM 4.5% LIBOR + 0.25%
Difference 0.4% 0.55%
Given the differences in rates between the two markets, the two parties can achieve
a combined 15 basis point savings through IBM borrowing floating-rate dollars at
LIBOR + 0.25% and KDB borrowing fixed-rate yen at 4.9% and then swapping the
proceeds. IBM would be able to borrow fixed-rate yen at 4.35% if all these savings
were passed along to it in the swap. This could be accomplished by KDB providing
IBM with floating-rate dollars at LIBOR + 0.25%, saving KDB 0.55%, which then
passed these savings along to IBM by swapping the fixed-rate yen at 4.9% – 0.55% =
4.35%. Thus, the potential savings to IBM range from 0 to 0.15%.
b. Assuming a notional principal equivalent to $125 million, and a current
exchange rate of ¥105/$, what do these possible cost savings translate into in
yen terms?
At a current exchange rate of ¥105/$, IBM’s borrowing would equal ¥13,125,000,000
(125,000,000105). A 0.15% savings on that amount would translate into ¥19,687,500 per annum (¥13,125,000,0000.0015).
c. Redo Parts a and b assuming that the parties use Bank of America, which
charges a fee of 8 basis points to arrange the swap.
In this case, the potential savings from a swap net out to 7 basis points. If IBM
realizes all these savings, its borrowing cost would be lowered to 4.43% (4.5% –
0.07%). The 7 basis point saving would translate into an annual saving of ¥9,187,500
(¥13,125,000,000*0.0007).
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13 - Company A, a low-rated firm, desires a fixed-rate, long-term loan. A currently
has access to floating interest rate funds at a margin of 1.5% over LIBOR. Its
direct borrowing cost is 13% in the fixed-rate bond market. In contrast,
company B, which prefers a floating-rate loan, has access to fixed-rate funds
in the Eurodollar bond market at 11% and floating-rate funds at LIBOR + ½%.
a. How can A and B use a swap to advantage?
Based on the numbers presented, there is an anomaly between the two markets:
One judges that the difference in credit quality between the two firms is worth 200
basis points, whereas the other determines that this difference is worth only 100
basis points. The parties can share among themselves the difference of 100 basis
points by engaging in a currency swap. This transaction would involve A
borrowing floating-rate funds and B borrowing fixed-rate funds and then swapping
the proceeds.
b. Suppose they equally split the cost savings. How much would A pay for its
fixed-rate funds? How much would B pay for its floating-rate funds?
If they split the cost savings, the resulting costs to the two parties would be 12.5%
for A and LIBOR for B, calculated as follows:
Party Normal Funding
Cost
Cost After Swap Difference
Counterparty A
Counterparty B
13.00%
LIBOR + 1/2%
12.50
LIBOR
Total
0.50%
0.50%
1.00% - What factors underlie the economic benefits of swaps?
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For swaps to provide economic benefits, they must allow the transacting parties to
engage in some form of tax, regulatory system, or financial market arbitrage. Thus,
underlying the economic benefits of swaps are barriers that prevent other forms of
arbitrage from functioning fully. This impediment must take the form of legal
restrictions on spot and forward foreign exchange transactions, different
perceptions by investors of risk and creditworthiness of the two parties, appeal or
acceptability of one borrower to a certain class of investor, tax differentials, and so
forth. If the world capital market were fully integrated, the incentive to swap would
be reduced because fewer arbitrage opportunities would exist. - In May 1988, Walt Disney Productions sold to Japanese investors a 20‐year
stream of projected yen royalties from Tokyo Disneyland. The present value of
that stream of royalties, discounted at 6 percent (the return required by the
Japanese investors), was ¥93 billion. Disney took the yen proceeds from the
sale, converted them to dollars, and invested the dollars in bonds yielding 10
percent. According to Disneyʹs chief financial officer, Gary Wilson, ʺIn effect,
we got money at a 6 percent discount rate, reinvested it at 10 percent, and
hedged our royalty stream against yen fluctuations‐‐all in one transaction.ʺ
a. At the time of the sale, the exchange rate was ¥124 = $1. What dollar amount
did Disney realize from the sale of its yen proceeds?
Disney realized 93,000,000,000/124 = $750,000,000 from the sale of its future yen
proceeds.
b. Demonstrate the equivalence between Walt Disneyʹs transaction and a
currency swap.
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15
In a currency/interest rate swap, one party trades a stream of payments in one
currency, at one interest rate, for a stream of payments in a second currency, at a
second interest rate. Disneyʹs stream of yen royalties can be treated as a yen bond,
which it traded for a dollar bond, with dollar payments. The only difference
between the Disney swap and a traditional swap is that the latter usually involve
cash outflows whereas the Disney swap involves cash inflows.
c. Comment on Gary Wilsonʹs statement. Did Disney achieve the equivalent of a
free lunch through its transaction?
Gary Wilson is committing the economistʹs unpardonable sin: He is comparing
apples with oranges, in this case, a 6% yen interest rate with a 10% dollar interest
rate. The international Fisher effect tells us that the most likely reason that the yen
interest rate is 4 percentage points less than the equivalent dollar interest rate is
because the market expects the dollar to depreciate by about 4% annually against
the yen.
International Financial Management
16 - A medium‐sized Australian Company (A) needs to borrow £6.7 million ($10
million at the current exchange rate of £/$ = 0.67) for five years to establish a
division in the U.K. A British firm (B) needs to borrow $10 million for five
years to set up an Australian division. The two face the following
borrowing costs (annual coupon payments):
r($) r(£)
A 5.50% 8.5%
B 5.25% 8.0%
Consider the following arrangement. A borrows $10 million, B borrows £6.7
million. Each agrees to pay the principal repayment obligation of the other,
and in addition A will pay B £562,800 at the end of each year, and B will pay
A $550,000 at the end of each year.
a. What are the effective yearly payments for each party? What are the interest
rates (no compounding)?
A’s cash flows:
$0.55 million (interest on loan) ‐ $0.55 million (received from B) + £0.5628 million
(payment to B) = £0.5628 million, or an interest rate of £0.5628/£6.7, i.e., 8.40% <
8.50%.
B’s cash flows:
£0.5360 million (interest on loan) – £0.5628 million (received from A) + $0.55
million (paid to A) = $0.55 million – £0.0268 million, so the cash flows depend on
the future spot exchange rate!
At an exchange rate of £0.67/$, the cash flows are:
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$0.55 million – (£0.0268/(£0.67/$))=$0.51, or an interest rate of 0.51/10=0.051, i.e.,
5.10% < 5.25%.
b. Who gains more from the swap, A or B? Why?
A gains 10 basis points in pound borrowing costs compared to its own borrowing
rate of 8.50%. B gains 15 basis points in dollar borrowing costs compared to its
own borrowing rate of 5.25% provided that the future spot exchange rate remains
at £0.67/$. However, the seemingly larger gains for B can quickly be diminished
since they depend on the future spot exchange rate. That is, B is still exposed to
exchange rate risk after the swap. If the Pound depreciates, the effective dollar
payments will go up. For example, if the exchange rate moves to £0.75/$, the
effective interest rate would be: $0.55 million – (£0.0268/(£0.75/$)) million =
$0.5143, or an interest rate of 0.5143/10 = 0.05143, i.e., 5.14%. The fact that B
obtains a larger benefit from the swap can be interpreted as compensation for the
exchange rate risk which remains in B’s cash flows after the swap. Another
reason for the larger share of the cake captured by B might be that it has an
absolute borrowing advantage in both markets, i.e., lower borrowing costs both
in dollars and in Pounds, than A. Hence, it probably has lower credit risk than A.
Note that this particular swap does not involve an intermediary, which means
that the parties themselves bear the risk of the counterpart defaulting on its
obligation.
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