12Chapter 20: Foreign Currency Futures and Options13Chapter 20:
Foreign Currency Futures and Options
Chapter
20Foreign Currency Futures and Options
questions1. How does a futures contract differ from a forward
contract?
Answer: Foreign currency futures contracts, or futures contracts
for short, allow individuals and firms to buy and sell specific
amounts of foreign currency at an agreed-upon price determined on a
given future day. Although this sounds very similar to forward
contracts, there are a number of important differences between
forward contracts and futures contracts.
The first major difference between foreign currency futures
contracts and forward contracts is that futures contracts are
traded on an exchange, whereas forward contracts are made by banks
and their clients. Orders for futures contracts must be placed
during the exchanges trading hours, and pricing occurs in the pit
by floor traders or on an electronic trading platform where demand
is matched to supply. In contrast to forward contracts, where
dealers quote bid and ask prices at which they are willing either
to buy or sell a foreign currency, for each party that buys a
futures contract, there is a party that sells the contract at the
same price. The price of a futures contract with specific terms
changes continuously, as orders are matched on the floor or by
computer.
A second major difference is that futures exchanges standardize
the amounts of currencies that one contract represents. Thus,
futures contracts cannot be tailored to a corporations specific
needs as can forward contracts. But the standardized amounts are
relatively small compared to a typical forward contract, and if
larger positions are desired, one merely purchases more contracts.
Standardization with small contract sizes makes the contracts easy
to trade, which contributes to market liquidity.
A third major difference involves maturity dates. In the forward
market, a client can request any future maturity date, and active
daily trading occurs in contracts with maturities of 30, 60, 90,
180, or 360 days. The standardization of contracts by the futures
exchanges means that only a few maturity dates are traded. For
example, IMM contracts mature on the third Wednesday of March,
June, September, and December. These dates are fixed, and hence the
time to maturity shrinks as trading moves from 1 day to the next,
until trading begins in a new maturity. Typically, only three or
four contracts are actively traded at any given time because
longer-term contracts lose liquidity.
The final major difference between forward contracts and futures
contracts concerns credit risk. This issue is perhaps the chief
reason for the existence of futures markets. In the forward market,
the two parties to a forward contract must directly assess the
credit risk of their counterparty. Banks are willing to trade with
large corporations, hedge funds, and institutional investors, but
they typically dont trade forward contracts with individual
investors or small firms with bad credit risk.
The futures market is very different. In the futures markets, a
retail client buys a futures contract from a futures brokerage
firm, which in the United States is typically registered with the
Commodity Futures Trading Commission (CFTC) as a futures commission
merchant (FCM). Legally, FCMs serve as the principals for the
trades of their retail customers. Consequently, FCMs must meet
minimum capital requirements set by the exchanges and fiduciary
requirements set by the CFTC. In addition, if an FCM wants to trade
on the IMM, it must become a clearing member of the CME. In years
past, clearing memberships used to be tradable, and the prices at
which they traded were indications of how profitable futures
trading on the exchange was expected to be. In 2000, the CME became
a for-profit stock corporation, and its shares now trade on the
NYSE. To obtain trading rights, an FCM must buy a certain amount of
B-shares of CME stock and meet all CME membership requirements.
When a trade takes place on the exchange, the clearinghouse of
the exchange, which is an agency or a separate corporation of a
futures exchange, acts as a buyer to every clearing member seller
and a seller to every clearing member buyer. The clearinghouse
imposes margin requirements and conducts the daily settlement
process known as marking to market that mitigates credit concerns.
These margin requirements are then passed on to the individual
customers by the futures brokers.
2. What effects does marking to market have on futures
contracts?
Answer: The process of marking to market implies that futures
contracts have daily cash flows associated with them. One can be
either long (having bought the contract) or short (having sold the
contract) in the futures market at a particular price. Since both
sides are treated symmetrically, lets assume you are long. You must
post funds in a margin account, and if on subsequent days, the
futures price moves in your favor, that is, the foreign currency
futures prices rises as the foreign currency strengthens; funds are
placed into your margin account and are taken out of the margin
accounts of those who sold the foreign currency futures contract.
This process continues every day until the maturity date of the
contract.
3. What are the differences between foreign currency option
contracts and forward contracts for foreign currency?
Answer: The primary difference between a foreign currency option
contract and a forward contract is that the option contract gives
the purchaser of the option, the right, but not the obligation to
transact. If the state of the world in the future is favorable to
the purchasers of the option, they will transact. If the state of
the world is unfavorable, the option is worthless. Forward
contracts are completely uncontingent on the state of the world in
the future.
4. What are you buying if you purchase a U.S. dollar European
put option against the Mexican peso with a strike price of
MXN10.0/$ and a maturity of July? (Assume that it is May and the
spot rate is MXN10.5/$.)
Answer: A European put option gives you the right to sell the
underlying asset at the strike price on the maturity date of the
contract. Thus, you are buying the right to sell USD for MXN at the
price of MXN10.0/$ on the maturity date of the contract in July.
This option is currently said to be out of the money because the
strike price is lower than the current exchange rate.
5. What are you buying if you purchase a Swiss franc American
call option against the U.S. dollar with a strike price of
CHF1.30/$ and a maturity of January? (Assume that it is November
and the spot rate is CHF1.35/$.)
Answer: American options can be exercised anytime between the
purchase of the option and the maturity date. Thus, a Swiss franc
American call option against the U.S. dollar with a strike price of
CHF1.30/$ and a maturity of January gives the buyer the right, but
not the obligation, to purchase CHF with USD at a price of
CHF1.30/$ between November and the maturity date in January. The
option is currently said to be out of the money because the strike
price (expressed in dollars per Swiss franc) is higher than the
current exchange rate [(1/1.30) > (1/1.35)] and you are
purchasing CHF.
6. What is the intrinsic value of a foreign currency call
option? What is the intrinsic value of a foreign currency put
option?
Answer: The immediate revenue from exercising an option is
called the options intrinsic value. Let K be the strike price, and
let S be the current spot rate, both in domestic currency per unit
of foreign currency. Then, the intrinsic value per unit of foreign
currency can be represented as
Call option: max[S K, 0]
Put option: max[K S, 0]
where max denotes the operation that takes the maximum of the
two numbers between square brackets.
7. What does it mean for an American option to be in the
money?
Answer: If an American option is in the money, its intrinsic
value is positive. For a call option, this means that the strike
price is less than the current market price; while for a put
option, this means that the strike price is greater than the
current market price.
8. Why do American option values typically exceed their
intrinsic values?
Answer: The time value of an option is the current price or
value of the option minus its intrinsic value:
Time value of an option = Option price Intrinsic value
Options have time value because the stochastic evolution of the
underlying asset price provides possibilities of even better
payoffs in the future compared to the intrinsic value. If this were
not the case, the owner of the American option would exercise
it.
9. Suppose you go long in a foreign currency futures contract.
Under what circumstances is your cumulative payoff equal to that of
buying the currency forward?
Answer: The payoffs of futures contracts and forward contracts
are only essentially the same because a slight difference in
payoffs arises due to the fact that interest is earned on future
profits, or interest must be paid on future losses, in the marking
to market process. Technically, if the path of short-term interest
rates could be foreseenthat is, if there were no random changes in
future short-term interest ratesthere would be an arbitrage
possibility if the forward exchange rate were different from the
futures price because you would know how you could invest the
profits or borrow to finance your losses. However, future interest
rates are not known with certainty, so forward prices and futures
prices can be different, in theory. In practice, though, the price
differentials are minimal, and they appear to be within the
transaction costs of the forward market. Therefore, we argue that
futures prices are essentially the same as forward prices.
10. What is basis risk?
Answer: The basis is the difference between the price of the
futures contract at time t, for a particular maturity in the
future, and the spot rate at time t. At the maturity date, the
basis is zero. If the maturity of your foreign currency asset or
liability does not match a settlement date in the futures market,
the relationship between the spot exchange rate at the time the
transaction takes place and the futures price of the foreign
exchange is somewhat uncertain (as the basis is not zero). To
provide a perfect hedge, the price of the futures contract should
move one-for-one with the spot exchange rate. Then, being long in
the foreign currency from an underlying transaction can be hedged
by going short in the corresponding futures contract. If this is
not the case, the hedge is said to suffer basis risk.
11. Your CEO routinely approves changes in the fire insurance
policies of your firm to protect the value of its buildings and
manufacturing equipment. Nevertheless, he argues that the firm
should not buy foreign currency options because, he says, We dont
speculate in FX markets! How could you convince him that his
positions are mutually inconsistent?
Answer: Options provide payoffs that are analogous to insurance
and can be used in hedging situations. With fire insurance, you pay
the insurance premium, and if there is a fire, the insurance
company compensates you. The realization of the fire is a bad state
of the world, but if the fire does not occur, you needlessly paid
for the insurance. If you are receiving foreign currency, the bad
state of the world is that the foreign currency weakens relative to
the domestic currency. To avoid this loss, you can buy a foreign
currency put option, which gives you the right but not the
obligation to sell foreign currency at the strike price. If the bad
state of the world occurs, you exercise your put, but if the good
state of the world occurs, you ignore you option and sell the
foreign currency which has appreciated in value relative to the
domestic currency. The put option places a floor on your domestic
currency revenue, which provides a hedge and is not speculation. Of
course, ex post you will regret having hedged, but this is exactly
like the insurance situation in which the fire did not occur.
12. Why do options provide insurance against foreign exchange
risks in bidding situations? Why cant you hedge with a forward
contract in a bidding situation?
Answer: Lets assume the bidding situation involves the company
determining a particular amount of foreign currency for providing a
service or selling some goods. By bidding a fixed amount of foreign
exchange, a company incurs a contingent transaction foreign
exchange risk. If the company wins the bid and the foreign currency
weakens relative to the domestic currency, the domestic currency
value of the contractual foreign currency revenue may already have
fallen such that the entire dollar profit could be eliminated
before the project begins. If the firms strategy is to get the
contract and then hedge, it could be too late.
Foreign exchange options provide a hedging solution. Because the
company ultimately wants to sell the foreign currency if it wins
the bid, the company should hedge by buying a foreign currency put
against the domestic currency. Then, if company wins the contract
and the foreign currency has weakened relative to the domestic
currency, the loss of value on the contract is offset by a gain in
the value of the foreign currency put. The company can sell the
foreign currency from the contract at the exercise price, which is
higher than the spot market.
If the company does not win the contract, the value of the
foreign currency put is the maximum that the firm can lose. This is
exactly like an insurance contract.
If the company sells foreign currency forward, it acquires an
uncontingent foreign currency liability. No matter what happens at
maturity, the company will have to sell a specific amount of
foreign currency to the bank. Everything will be fine if the
company gets the contract, but if the company does not get the
contract, it will have to buy foreign currency to fulfill the
uncontingent commitment of the forward contract. If the foreign
currency has strengthened, the company will lose money, and the
potential loss is essentially unbounded.
13. Suppose that you have a foreign currency receivable
(payable). What option strategy places a floor (ceiling) on your
domestic currency revenue (cost)?
Answer: If you have a foreign currency receivable, you
eventually want to sell foreign currency. Purchasing the option
that gives you the right to sell (a put option) provides a hedge
that places a floor on your domestic currency revenue. If you have
a foreign currency payable, you eventually want to buy foreign
currency. Purchasing the option that gives you the right to buy (a
call option) provides a hedge that places a ceiling on your
domestic currency cost.
14. Describe qualitatively how changing the strike price of the
option provides either more or less expensive insurance.
Answer: Lets consider hedging a foreign currency receivable with
a put option. High-quality insurance in this context means that the
floor we create on our domestic currency revenue is high. The floor
is directly related to the strike price of the put option. The
higher the strike price of the option, the less the foreign
currency must depreciate before we can exercise the option and cut
our losses. But, just as insurance that covers more losses is more
expensive, put options with higher strike prices are more
expensive. Thus, if the foreign currency strengthens and you do not
need the insurance of the put option, you will have spent more
money on the insurance and will need more appreciation of the
foreign currency before you do better than you could have by
locking in a forward contract.
15. Why does an increase in the strike price of an option
decrease the value of a call option and increase the value of a put
option?
Answer: We know that holding constant the maturity date of two
options implies that the distribution of possible future exchange
rates is the same for the two options. Hence, it should be apparent
that increasing the exercise price of a call option must decrease
its value because doing so removes possible states of the world
over which the contract provides revenue when the strike price is
lower. Conversely, increasing the exercise price of a put option
must increase its value because doing so adds possible states of
the world over which the contract provides revenue compared to when
the strike price is lower.
16. Why does an increase in the volatility of foreign exchange
rates increase the value of foreign currency options?
Answer: The easiest way to understand how an increase in
variance affects option prices is to place the strike price of a
call option at the conditional mean of two probability
distributions, one with a low variance and the other with a high
variance. The increase in the variance of the possible future
exchange rate clearly increases the possible range of future
exchange rates. But, because the conditional mean is the same, the
probability that the option will finish in the money is still
one-half because one-half of the probability distribution remains
above the strike price. However, if the option does finish in the
money, the distribution with the larger variance yields possibly
larger payoffs, and the option will cost more. A symmetrical
argument can be applied to a put option.
17. How does increasing time to maturity affect foreign currency
option value?
Answer: Here, it is important to distinguish clearly between
American-style and European-style options. For American options,
the effect is unambiguous: Increasing the time to maturity always
increases an options value because it increases the uncertainty of
the spot exchange rate at maturity. When this effect is combined
with the fact that the holder of a 6-month option can always treat
the option as a 3-month option, we clearly see that the additional
3 months of maturity cannot hurt the payoff to the holder of the
option as long as the holder of the option can exercise it
early.
For European options, the situation is not so simple. Although
the effect of an increase in time to maturity is technically
ambiguous, in most situations, the effect of the increased
uncertainty of the spot exchange rate at maturity dominates, and
option prices increase. Nevertheless, this is not always true
because it is possible for a European option that is currently in
the money to lose value as time evolves. You would like to be able
to exercise the option to lock in the revenue now, but you cannot
do so prior to maturity.
18. What is the payoff on an average-rate pound call option
against the dollar?
Answer: The payoff per pound on an average-rate pound call
option against the dollar with a strike price of K($/) is max[0,
($/) K($/)], where ($/) defines the average dollar-pound exchange
rate between the initiation of the contract and the expiration
date. To calculate the average exchange rate, the counterparties to
the option contract must agree on a source for the data and a way
of computing the average. They must decide on a time interval for
the observations entering the average, which could be daily,
weekly, or monthly, and they must decide whether the average is an
arithmetic or geometric average. At the maturity of an average-rate
option, the seller of the option settles the contract by delivering
the dollar value of the option payoff to the buyer. Because an
average of future exchange rates is less volatile than the future
spot rate at maturity, average-rate options are less expensive than
standard European options.
19. Suppose the current spot rate is $1.29/. What is your payoff
if you purchase a down-and-in put option on the euro with a strike
price of $1.31/, a barrier of $1.25/, and a maturity of 2 months?
When would someone want to do this?
Answer: For a down-and-in option, the exchange rate must first
cross the barrier to activate the contract. Then, the buyer of the
option has the right to exercise at maturity. So, the payoff on the
option described above is max[0, $1.31/ - S(T,$/)], where S(T,$/)
is the exchange rate at maturity, but only if the exchange rate
falls from its current value of $1.29/ to $1.25/ sometime during
the 2 months between the initiation of the contract and the
maturity date. Such an option is less expensive than a standard put
option. It might therefore be purchased by someone who is bearish
on the euro, believes initial volatility in the market will
activate the option with reasonably high probability, and wants to
cut the cost of obtaining a relatively high payoff, even in the
currency strengthens somewhat towards the end of the contract.
problems
1. If you sold a Swiss franc futures contract at time t and the
exchange rate has evolved as shown here, what would your cash flows
have been?
DayFutures Price
$/CHFChange in Futures PriceGain or LossCumulative Gain or
LossMargin Account
t0.7335$2,000.00
t + 10.7391 0.0056-$700.00-$700.00$2,000.00
t + 20.7388-0.0003 $37.50-$662.50$2,037.50
t + 30.7352-0.0036 $450.00-$212.50$2,487.50
t + 40.7297-0.0055$687.50 $475.00$3,175.00
Answer: Because you sold the Swiss franc futures contract, you
will gain when the Swiss franc depreciates versus the dollar and
you will lose when the Swiss franc strengthens. On the first day,
we assume you established your account with an initial margin of
$2,000, and that you sold your contract at the closing price of
$0.7335/CHF. The contract size is CHF125,000. On the second day,
the futures price increases from $0.7335/CHF to $0.7391/CHF. You
consequently lose $0.0056/CHF CHF125,000 = $700, which would take
your margin account to $1,300. Because this is less than the
maintenance margin of $1,400, you would receive a margin call that
would require you to bring you margin account back to $2,000. On
the third day, the futures price moves in your favor, and you gain
$0.0003/CHF CHF125,000 = $37.50. You have the option of leaving
this extra money in your margin account or taking it out. We assume
that you leave it in. On the fourth day, the futures price again
moves in your favor, and you gain $0.0036/CHF CHF125,000 = $450.
Finally, on the fifth day, the futures price again moves in your
favor, and you gain $0.0055/CHF CHF125,000 = $687.50. The
cumulative gain is $475.00.
2. Given the following information, how much would you have paid
on September 16 to purchase a British pound call option contract
with a strike price of 155 and a maturity of October?
Data for September 16
CallsPuts
50,000 Australian Dollar Options (cents per unit)
64 Oct0.48
65 Oct0.90
67 Oct0.22
31,250 British Pounds (cents per unit)
152 Dec4.10
155 Oct1.503.62
155 Nov2.35
Answer: The correct price on September 16 for a British pound
call option with a strike price of 155 and a maturity of October is
1.50. The units are cents per pound or $0.0150/. The contract size
is 31,250. Therefore, you would have paid
3. Using the data in problem 2, how much would you have paid to
purchase a Australian dollar put option contract with a strike
price of 65 and an October maturity?
Answer: The correct price on September 16 for an Australian
dollar put option with a strike price of 65 and a maturity of
October is 0.90. The units are cents per Australian dollar or
$0.0090/AUD. The contract size is AUD50,000. Therefore, you would
have paid
4. Suppose that you buy a 1,000,000 call option against dollars
with a strike price of $1.2750/. Describe this option as the right
to sell a specific amount of dollars for euros at a particular
exchange rate of euros per dollar. Explain why this latter option
is a dollar put option against the euro.
Answer: The 1,000,000 call option against dollars with a strike
price of $1.2750/ gives the buyer the right, but not the
obligation, to buy 1,000,000 at the strike price of $1.2750/ in
which case the person would pay $1,275,000 for the euros. Clearly,
this is the same as an option to sell $1,275,000 at a strike price
of [1 / ($1.2750/)] = 0.784314/$. This latter option is a
$1,275,000 dollar put option against euros with a strike price of
0.784314/$.
5. Assume that today is March 7, and, as the newest hire for
Goldman Sachs, you must advise a client on the costs and benefits
of hedging a transaction with options. Your client (a small U.S.
exporting firm) is scheduled to receive a payment of 6,250,000 on
April 20, 44 days in the future. Assume that your client can borrow
and lend at a 6% p.a. U.S. interest rate.
a. Describe the nature of your clients transaction exchange
risk.
Answer: Your client is scheduled to receive 6,250,000 in 44
days. If no hedging is done, and the euro weakens in value relative
to the dollar, the client will lose money. The amount of the loss
could be substantial if a major weakening occurs.
b. Use the appropriate American option with an April maturity
and a strike price of 129/ to determine the dollar cost today of
hedging the transaction with an option strategy. The cost of the
call option is 3.93/, and the cost of the put option is 1.58/.
Answer: To hedge foreign currency revenue with an option, you
must purchase a put option that gives you the right to sell euros.
This puts a floor on your revenue. The cost of the option would be
1.58/, or
c. What is the minimum dollar revenue your client will receive
in April? Remember to take account of the opportunity cost of doing
the option hedge.
Answer: If the exchange rate is less than $1.29/ in April, your
client will be able to sell euros at that value. If the future spot
exchange rate is higher, the client will sell euros at the future
spot exchange rate. In either case, if they hedge with the option
contract, they will have less revenue. The future value of $98,750
at 6% for 44 days is
Thus, the minimum net revenue that the client will have is
d. Determine the value of the spot rate ($/) in April that would
make your client indifferent ex post to having done the option
transaction or a forward hedge. The forward rate for delivery on
April 20 is $1.30/.
Answer: If the client does the forward hedge, their revenue will
be
If the client does the option hedge and does not have to
exercise the option, they will sell the euros in 42 days, and their
revenue will
If this option revenue is to equal the forward revenue, we
know
Solving this equation gives .
6. Assume that today is September 12. You have been asked to
help a British client who is scheduled to pay 1,500,000 on December
12, 91 days in the future. Assume that your client can borrow and
lend pounds at 5% p.a.
a. Describe the nature of your clients transaction exchange
risk.
Answer: Your client is scheduled to pay 1,500,000 in 91 days. If
no hedging is done, and the euro strengthens in value relative to
the pound, the client will lose money. The amount of the loss could
be substantial if a major strengthening occurs.
b. What is the option cost for a December maturity and a strike
price of 0.72/ to hedge the transaction? The option premiums per
100 euros are 1.70 for calls and 2.40 for puts.
Answer: To hedge foreign currency costs with an option, you must
purchase a call option that gives you the right to buy euros. This
puts a ceiling on your costs. The cost of the option would be 1.70
per 100 euro, or
c. What is the maximum pound cost your client will experience in
December?
Answer: If the exchange rate is greater than 0.72/ in December,
your client will be able to buy euros at that value. If the future
spot exchange rate is lower than 0.72/, the client will buy euros
at the future spot exchange rate. In either case, if they hedge
with the option contract, they will have higher costs. The future
value of 25,500 at 5% for 91 days is
Thus, the minimum net cost that the client will face is
d. Determine the value of the spot rate (/) in December that
makes your client indifferent ex post to having done the option
transaction or a forward hedge if the forward rate for delivery on
December 11 is 0.70/.
Answer: If the client does the forward hedge, their cost will
be
If the client does the option hedge and does not have to
exercise the option, they will buy the euros in 91 days, and their
cost will be
If this option cost is to equal the forward cost, we know
Solving this equation gives .
7. Assume that today is June 11. Your firm is scheduled to pay
500,000 on August 15, 65 days in the future. The current spot is
$1.75/, and the 65-day forward rate is $1.73/. You can borrow and
lend dollars at 7% p.a. Suppose you think options are overpriced
because you think the dollar will be in a tight trading range in
the near future. You have been thinking about selling an option as
a way to reduce the dollar cost of your pound payable.
a. If an August pound option with a strike price of 175/ costs
4.5/ per pound for the call and 4/ for the put, what is the minimum
that you will have to pay in August to eliminate your pound
payable? Over what range of future exchange rates will this price
be achieved?
Answer: You need to eventually buy pounds to eliminate your
liability of 500,000 due in 65 days. If you think options are too
expensive to buy, you can consider the speculative strategy of
selling someone an option that allows them to sell pounds to you.
This is a pound put option. You would take in 4/ for the put,
or
The future value of this amount would be available to offset
your costs in 65 days. This future value is
As long as the exchange rate is less than or equal to the strike
price of $1.75/, your costs will be
This is , much less than the forward rate.
b. How much must the pound appreciate before your speculative
option strategy ends up costing you more than the forward rate?
Answer: At the forward rate of $1.73/, you can lock in a dollar
cost of
The future spot rate that sets the speculative cost to the
forward cost is found by equating the two costs
Solving this equation for the spot rate gives
8. Upon arriving for work Monday, you observe a violation of
putcall parity. In particular, the synthetic forward price of
dollars per yen is above the current forward rate. How would you
capitalize on this information?
Answer: Because the actual forward rate is below the synthetic
forward rate, you would want to contract to buy yen forward and
then sell yen at the synthetic forward rate. Such an arbitrage
transaction is called a conversion. You synthetically sell yen
forward by buying a put and selling a call with the same strike
price. If the exchange rate in the future is less than the strike
price, the call is worthless and you exercise your put and sell yen
at the strike price. If the exchange rate in the future is greater
than the strike price, the put is worthless and the person to whom
you sold the call option exercises the option to buy yen from you
at the strike price. Therefore, you sell yen to them. By doing the
two option contracts you have sold yen forward at the strike price
minus the future value of the put you purchased plus the future
value of the call you sold. This synthetic forward price is greater
than the actual forward price, so you make money.9. Use interest
rate parity to demonstrate that you can represent put-call parity
as
The derivation of put-call parity used the no-arbitrage idea
that the forward rate should be equal to the strike price of the
options plus the future value of the cost of a call option minus
the future value of the cost of a put option because each of these
sides is a way to purchase foreign currency, in this case the euro,
without any contingencies. Thus,
We first divide by to get
From interest rate parity we know that
Substituting for F, cancelling , and multiplying by -1 gives the
desired result.10. On April 28, 1995, the Paine Webber Group
introduced a new type of security on the NYSE: U.S. dollar increase
warrants on the yen. At exercise, each warrant entitled the holder
to an amount of U.S. dollars calculated as
Greater of (i) 0 and (ii) $100 [$100 83.65/$ / Spot rate)]
The spot rate in the formula refers to the yen/dollar rate on
any day during the exercise period, which extended until April 28,
1996. The 1-year forward rate on April 28 was 79.72/$, and the spot
rate was 83.65/$.
a. What view on the future yen/dollar rate do investors in this
security hold?
Answer: The investor gets the greater of (i) 0 and (ii) $100
[$100 83.65/$ / S(/$)]. If the yen remains unchanged at 83.65/$,
the payoff is zero. If the yen strengthens, the ratio of 83.65/$ /
S(/$) > 1, and you would be subtracting an amount greater than
$100, so the payoff would be zero. As the yen weakens, the payoff
increases to a maximum of $100. Thus, the investor must think that
the yen is going to weaken.
b. This security was issued at a price of $5.50. To see whether
the security is fairly priced, which option prices would you want
to examine?
Answer: While the payoff on the security is non-linear in the
yen-dollar exchange rate, it is linear in the dollar-yen exchange
rate. The payoff is zero at exchange rates above 1 / (83.65/$) =
$0.0119546/ and it increases linearly along a forty-five degree
angle at exchange rates below $0.0119546/ until the payoff is $100
at an exchange rate of zero. This payoff is identical to the payoff
on a yen put with a strike price of $0.0119546/ for an amount of
yen equal to $100 83.65/$ = 8,365. Thus, you should examine the
price of a yen put for this amount against dollars to determine if
$5.50 is the correct price for the security.
2012 Pearson Education, Inc.
2012 Pearson Education, Inc.
2012 Pearson Education, Inc.
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