British pound futures, ¥/£ (CME) Contract = 125,000 pounds
Open
Maturity Open High Low Settle Change High Interest
c. If Mariko buys 3 December pound futures, and the spot rate at maturity is ¥138.90/£, what is the value of her position?
d. If Mariko sells 12 March pound futures, and the spot rate at maturity is ¥139.95/£, what is the value of her position?
a) b) c) d)
Assumptions Values Values Values Values
Pounds (₤) per futures contract
£125,000 £125,000 £125,000 £125,000
Maturity month
March December December March
Ending spot rate (¥/₤) ¥139.9500 ¥138.9000 ¥138.9000 ¥139.9500
Pound futures contract, settle price (¥/₤) ¥139.9000 ¥139.7500 ¥139.7500 ¥139.9000
Value of position at maturity (¥)¥31,250.00 ¥1,275,000.00 -¥318,750.00 -¥75,000.00
buys: Notional x (Spot – Futures) x contracts
sells: – Notional x (Spot – Futures) x contracts
Interpretation
Sells a future: Mariko buys at the ending spot price and sells at the futures price. She therefore profits when the futures price is greater than the
ending spot price.
Problem 7.1 Mariko Fujimoto at Sakura Bank
Mariko Fujimoto, a currency trader for Tokyo-based Sakura Bank, uses the following futures quotes on the British pound (£) to speculate on the value of the pound.
Buys a futures: Mariko buys at the futures price and sells at the ending spot price. She therefore profits when the futures price is less than the
ending spot price.
a. What is the value of her position at maturity if the ending spot rate is $0.12000/Ps?
b. What is the value of her position at maturity if the ending spot rate is $0.09800/Ps?
a. b. c.
Assumptions Values Values Values
Number of pesos per futures contract 500,000 500,000 500,000
Number of contracts 8.00 8.00 8.00
Buy or sell the peso futures? Sell Sell Sell
Interpretation
Problem 7.2 Laura Cervantes
Laura Cervantes, the currency speculator we met earlier in the chapter,sells eight June futures contracts for
500,000 pesos at the closing price quoted in Exhibit 7.1.
Laura buys at the spot price and sells at the futures price. If the futures price is greater than the ending spot
price, she makes a profit.
Option Strike Price Premium
Put on Sing $ $0.6500/S$ $0.00003/S$
Call on Sing $ $0.6500/S$ $0.00046/S$
a. Should Cece buy a put on Singapore dollars or a call on Singapore dollars?
b. What is Cece’s breakeven price on the option purchased in part (a)?
Option choices on the Singapore dollar: Call on S$ Put on S$
Strike price (US$/Singapore dollar)
$0.6500 $0.6500
Premium (US$/Singapore dollar)
$0.00046 $0.00003
Assumptions Values
Current spot rate (US$/Singapore dollar)
$0.6000
Days to maturity
90
Expected spot rate in 90 days (US$/Singapore dollar)
$0.7000
a. Should Cece buy a put on Singapore dollars or a call on Singapore dollars?
b. What is Cece’s breakeven price on the option purchased in part a)?
Per S$
Strike price $0.65000
Note this does not include any interest cost on the premium. Plus premium
$0.00046
Breakeven $0.65046
c. What is Cece’s gross profit and net profit (including premium) if the ending spot rate is $0.70/S$?
Gross profit Net profit
(US$/S$) (US$/S$)
$0.70000 $0.70000
d. What is Cece’s gross profit and net profit (including premium) if the ending spot rate is $0.80/S$?
Gross profit Net profit
(US$/S$) (US$/S$)
Spot rate
$0.80000 $0.80000
a. b.
Assumptions Values Values
Initial investment (funds available)
10,000,000.00 CHF 10,000,000.00 CHF
30-day forward rate (CHF/€)1.1027 CHF 1.1027 CHF
Expected spot rate in 30 days (CHF/€)1.1375 CHF 1.0927 CHF
Strategy for Part a):
30 day forward rate (CHF/€) 1.1027 CHF
Profit in CHF 315,589.01 CHF
therefore buy euros forward 30 days (requires no actual cash flow up-front), and at the end of 30 days take delivery of those
euros and sell in the spot market at the higher Swiss franc rate for profit.
Strategy for Part b):
higher Swiss franc rate, wait 30 days and buy the euros needed on the open market at CHF1.0925, and immediately then use
those euros to fulfill his forward contract to sell euros for Swiss francs at CHF1.1027. For a profit.
Stefan had sold these euros forward at the start of the 30 day period.
30 day forward rate (CHF/€) 1.1027 CHF
CHF proceeds (euros sold forward into CHF) 10,091,516.43 CHF
Profit in CHF 91,516.43 CHF
Again, a profitable strategy can be executed without any actual cash flow changing hands at the beginning of the period. Since
b. If Stefan believes the euro will depreciate in value against the Swiss franc and expect the spot rate to be SF1.0925/€ at the
end of 30 days, what should he do?
Problem 7.4 Hoffman Bank, Basel (A)
Stefan Boerig trades currency for the Hoffman Bank in Basel, Switzerland. Stefan has 10 million Swiss francs (SF) to begin
with, and he must state all profits at the end of any speculation while the 30-day forward rate is SF1.1027/€.
a. If Stefan believes the euro will continue to rise in value against the Swiss franc and expects the spot rate to be SF1.1375/€ at
the end of 30 days, what should he do?
One of the more interesting dimensions of speculating in the forward market, is that if the speculator has access to the forward
market (bank lines or relationships when working on behalf of an established firm), many forward speculation strategies require
no actual cash flow position up-front. In this case, Stefan believes the Swiss franc will be trading at CHF1.1375/€ in the open
a. Calculate Stefan’s expected profit, assuming a pure spot market speculation strategy.
b. Calculate Stefan’s expected profit, assuming he buys and sells Swiss francs three months forward.
a. b.
Assumptions Values Values
Current spot rate (£/Swiss franc) £0.7829 £0.7829
Three-month forward rate (£/Swiss franc) £0.7640 £0.7640
Expected spot rate in three months (£/Swiss franc) £0.7995 £0.7995
Strategy for Part a:
1. Use the £250,000 today to buy SF at spot rate SFr. 319,325.58
2. Hold the SF indefinitely.
5. Realize profit (revenues less £250,000 initial invest) £5,300.80
Strategy for Part b:
1. Buy SF forward six months (no cash outlay required)
2. Fulfill the six months forward in six months SFr. 327,225.13
Problem 7.5 Hoffman Bank, Basel (B)
Stefan Boerig of Hoffman Bank now believes that the Swiss franc will appreciate against the British pound in the
coming 3-month period. He has £250,000 to invest. The current spot rate is £0.7829/SF, the 3-month forward rate
is £0.7640/SF, and he expects the spot rates to reach £0.7995/SF in three months.
a) b) c) d) e) f) g)
Assumptions Values Values Values Values Values Values Values
Notional principal (¥)12,500,000 12,500,000 12,500,000 12,500,000 12,500,000 12,500,000 12,500,000
Maturity (days)
180 180 180 180 180 180 180
Strike price (US$/¥)$0.008000 $0.008000 $0.008000 $0.008000 $0.008000 $0.008000 $0.008000
Premium (US$/¥)$0.000080 $0.000080 $0.000080 $0.000080 $0.000080 $0.000080 $0.000080
Ending spot rate (¥/US$) 110.00 115.00 120.00 125.00 130.00 135.00 140.00
Net profit (US$/¥)($0.000080) ($0.000080) ($0.000080) ($0.000080) $0.000228 $0.000513 $0.000777
Problem 7.6 Kiko Peleh’s Puts
Kiko Peleh writes a put option on Japanese yen with a strike price of $0.008000/¥ (¥125.00/$) at a premium of 0.0080¢ per yen and with an expiration date six month from
now. The option is for ¥12,500,000. What is Kiko’s profit or loss at maturity if the ending spot rates are ¥110/$, ¥115/$, ¥120/$, ¥125/$, ¥130/$, ¥135/$, and ¥140/$.
New York interest rate practices
Interest calculation uses:
Exact number of days in period 56
Number of days in financial year 360
So the interest charge on this principal is 77,777.78$
Great Britain interest rate practices
Interest calculation uses:
Swiss interest rate practices
Interest calculation uses:
Assumed 30 days per month for two months 60
Number of days in financial year 360
So the interest charge on this principal is 83,333.33$
Problem 7.7 Chavez S.A.
Chavez S.A., a Venezuelan company, wishes to borrow $8,000,000 for eight weeks. A rate
of 6.250% per annum is quoted by potential lenders in New York, Great Britain, and
Switzerland using, respectively, international, British, and the Swiss-Eurobond definitions
Option Strike Price Premium
Put on Malaysian ringgit MYR0.1600/THB THB0.005
Call on Malaysian ringgit MYR0.1600/THB THB0.0025
a. Should Baradan buy a put on Malaysian Ringgit or a call on Malaysian Ringgit?
Assumptions Values
Current spot rate (MYR/THB) 0.1382
Call on ringgit Put on ringgit
Strike price (MYR/THB) MYR 0.1600 MYR 0.1600
in THB/MYR THB 6.25000 THB 6.25000
Premium (US$/yen) THB 0.00500 THB 0.00250
a. Should Baradan buy a put on Malaysian Ringgit or a call on Malaysian Ringgit?
Baradan should buy a put on Malaysian ringgit to profit from the rise of the Thai bhat (the fall of the ringgit).
b. What is Baradan’s break-even price on the option purchase in part (a)?
Cachita buys a put on Malaysian ringgit. Pays premium today.
c. What are Baradan’s gross and net profit (including premium) if the spot rate
at the end of 90 days is MYR0.2000/THB? Gross profit Net profit
(THB/MYR) (THB/MYR)
Strike price THB 6.25000 THB 6.25000
spot rate at the end of 90 days is RM0.2000/THB?
Problem 7.8 Valdor Capital
Baradan Kuppusamy works as a currency speculator for Valdor Capital headquartered in Kuala Lumpur. His
most recent speculative position is to profit from his expectation that the Thai baht will rise significantly
against the Malaysian ringgit. The current spot rate is RM0.1382/THB. He must choose between the
following 90-day options on the Malaysian ringgit.
a. b. c. d. e. f. g.
Assumptions Values Values Values Values Values Values Values
Ending spot rate (US$/euro)
$1.1000 $1.1500 $1.2000 $1.2500 $1.3000 $1.3500 $1.4000
Gross profit on option
$0.0000 $0.0000 $0.0000 $0.0000 $0.0500 $0.1000 $0.1500
Problem 7.9 Henrik’s Options
Assume Henrik writes a call option on euros with a strike price of $1.2500/€ at a premium of 3.80 cents per euro ($0.0380/€) and with an expiration date three months from
now. The option is for €100,000. Calculate Henrik’s profit or loss should he exercise before maturity at a time when the euro is traded spot at strike prices beginning at
$1.10/€, rising to $1.40/€ in increments of $0.05.
Strike Price Maturity Premium
$1.36/£ 30 days $0.00081/£
$1.34/£ 30 days $0.00021/£
$1.32/£ 30 days $0.00004/£
Assumptions Values
Current spot rate (US$/£)$1.4260
Expected endings spot rate in 30 to 60 days (US$/£)$1.3200
Potential investment principal per person (£)£250,000.00
Put options on pounds Put #1 Put #2 Put #3
Strike price (US$/£)$1.36 $1.34 $1.32
Maturity (days)
30 30 30
Premium (US$/£)$0.0008 $0.0002 $0.0000
Put options on pounds Put #4 Put #5 Put #6
Strike price (US$/£)$1.36 $1.34 $1.32
60 60 60
Premium (US$/£)$0.0033 $0.0015 $0.0006
Issues for Sydney to consider:
1. Because his expectation is for “30 to 60 days” he should confine his choices to the 60 day options to be sure and capture
the timing of the exchange rate change. (We have no explicit idea of why he believes this specific timing.)
2. The choice of which strike price is an interesting debate.
* The lower the strike price (1.34 or 1.32), the cheaper the option price.
* The reason they are cheaper is that, statistically speaking, they are increasingly less likely to end up in the money.
* The choice, given that all the options are relatively “cheap,” is to pick the strike price which will yield the required return.
* The $1.32 strike price is too far ‘down,’ given that Sydney only expects the pound to fall to about $1.32.
Put #4 Put #5 Put #6
Net profit Net profit Net profit
Strike price
$1.36000 $1.34000 $1.32000
Less expected spot rate
(1.32000) (1.32000) (1.32000)
Less premium
(0.00333) (0.00150) (0.00060)
Profit
$0.03667 $0.01850 ($0.00060)
Problem 7.10 Baker Street
Arthur Doyle is a currency trader for Baker Street, a private investment house in London. Baker Street’s clients are a collection of
wealthy private investors who, with a minimum stake of £250,000 each, wish to speculate on the movement of currencies. The investors
expect annual returns in excess of 25%. Although officed in London, all accounts and expectations are based in U.S. dollars.
Arthur is convinced that the British pound will slide significantly — possibly to $1.3200/£ — in the coming 30 to 60 days. The current
following put options would you recommend he purchase. Prove your choice is the preferable combination of strike price, maturity, and
up-front premium expense.
Option Strike Price Premium
Put on C$ £0.6500
£0.0035
Call on C$ £0.6500 £0.0055
a. Should Bambang buy a put on Canadian dollars or a call on Canadian dollars?
b. What is Bambang’s break-even price on the option purchased in part (a)?
Assumptions Values
Current spot rate (£/Canadian dollar) £0.5931
Days to maturity
90
Strike price (£/Canadian dollar) £0.6500 £0.6500
Premium (£/Canadian dollar) £0.0055 £0.0035
a) Which option should Bambang buy?
Since Bambang expects the Canadian dollar to appreciate versus the pound, he should buy a call on Canadian dollars.
b) What is Bambang’s breakeven price on the option purchased in part a)?
c) What is Bambang’s gross profit and net profit (including premium) if he ending spot rate is £0.730/C$?
Gross profit Net profit
(£/C$) (£/C$)
Spot rate
£0.7300 £0.7300
d) What is Bambang’s gross profit and net profit (including premium) if the ending spot rate is £0.7850/C$?
Gross profit Net profit
(£/C$) (£/C$)
£0.7850 £0.7850
Problem 7.11 Bambang Pamungkas at CCB Bank
Bambang Pamungkas works for CCB Bank Currency Trading Desk in Montreal, Canada. Bambang is something of a
contrarian – as opposed to most of the forecasts, he believes the Canadian dollar (C$) will appreciate versus the British
pound over the coming 90 days. The current spot rate is £0.5931/C$. Bambang may choose between the following
options on the Canadian dollar.
Pricing Currency Options on the Euro
Variable Value Variable Value
Spot rate (domestic/foreign)
S0$1.2480 S0€ 0.8013
Strike rate (domestic/foreign) X $1.2500 X€ 0.8000
Domestic interest rate (% p.a.)
rd1.453% rd2.187%
Time (years, 365 days) T 1.000 T1.000
Days equivalent 365.00 365.00
Volatility (% p.a.) s 12.000% s 12.000%
Call option premium (per unit fc) c $0.0534 c € 0.0412
Put option premium (per unit fc) p $0.0643 p € 0.0342
(European pricing)
Call option premium (%) c 4.28% c 5.15%
Put option premium (%) p 5.15% p 4.27%
Problem 7.12 U.S. dollar/Euro
A U.S.-based firm wishing to buy
A European firm wishing to buy
or sell euros (the foreign currency)
or sell dollars (the foreign currency)
Pricing Currency Options on the Japanese yen
Variable Value Variable Value
Spot rate (domestic/foreign)
S0JPY 105.64 S0$0.0095
Strike rate (domestic/foreign) X JPY 100.00 X$0.0100
Time (years, 365 days) T 1.000 T1.000
Days equivalent 365.00 365.00
Volatility (% p.a.) s 12.000% s12.000%
Call option premium (per unit fc) c JPY 7.27 c $0.0003
Put option premium (per unit fc) p JPY 3.06 p $0.0007
(European pricing)
Call option premium (%) c 6.88% c 3.06%
Put option premium (%) p 2.90% p 7.27%
Put option premium (JPY/US$) JPY 3.06
Notional principal (US$) $750,000
Total cost (JPY) JPY 2,297,243
or sell dollars (the foreign currency)
or sell yen (the foreign currency)
Problem 7.13 U.S. Dollar/Japanese Yen
A Japanese firm wishing to buy
A U.S.-based firm wishing to buy
Pricing Currency Options on the Euro/Yen Crossrate
Variable Value Variable Value
Spot rate (domestic/foreign)
S0JPY 133.89 S0€ 0.0072
Strike rate (domestic/foreign) X JPY 136.00 X€ 0.0074
Domestic interest rate (% p.a.)
rd0.088% rd2.187%
Foreign interest rate (% p.a.)
rf2.187% rf0.088%
Time (years, 365 days) T 0.247 T0.247
Days equivalent 90.00 90.00
Volatility (% p.a.) s 10.000% s10.000%
Call option premium (per unit fc) c JPY 1.50 c € 0.0001
Put option premium (per unit fc) p JPY 4.30 p € 0.0002
(European pricing)
Call option premium (%) c 1.12% c 1.30%
Put option premium (%) p 3.21% p 2.90%
Put option premium (euro/JPY) € 0.0002
Notional principal (JPY) JPY 10,400,000
Total cost (euro) € 2,167.90
Problem 7.14 Euro/Japanese Yen
A European-based firm like Legrand (France) would need to purchase a put option on the Japanese yen. The company wishes a strike rate of 0.0072 euro
for each yen sold (the strike rate) and a 90-day maturity. Note that the “Time” must be entered as the fraction of a 365 day year, in this case, 90/365 =
0.247.
A Japanese firm wishing to buy
A European firm wishing to buy
or sell euros (the foreign currency)
or sell yen (the foreign currency)
Pricing Currency Options on the British pound
Variable Value Variable Value
Spot rate (domestic/foreign)
S0$1.8674 S0£0.5355
Strike rate (domestic/foreign) X $1.8000 X£0.5556
Time (years, 365 days) T 0.493 T0.493
Days equivalent 180.00 180.00
Volatility (% p.a.) s 9.400% s9.400%
Call option premium (per unit fc) c $0.0696 c £0.0091
Put option premium (per unit fc) p $0.0306 p £0.0207
(European pricing)
Call option premium (%) c 3.73% c 1.70%
Put option premium (%) p 1.64% p 3.87%
Call option premiums for a U.S.-based firm buying call options on the British pound:
180-day maturity ($/pound) $0.0696
90-day maturity ($/pound) $0.0669
Difference ($/pound) $0.0027
Problem 7.15 U.S. Dollar/British Pound
A U.S.-based firm wishing to buy
A British firm wishing to buy
or sell pounds (the foreign currency)
or sell dollars (the foreign currency)
Pricing Currency Options on the British pound/Euro Crossrate
Variable Value Variable Value
Spot rate (domestic/foreign)
S0€ 1.4730 S0£0.6789
Strike rate (domestic/foreign) X € 1.5000 X£0.6667
Time (years, 365 days) T 0.247 T0.247
Days equivalent 90.00 90.00
Volatility (% p.a.) s 11.400% s11.400%
Call option premium (per unit fc) c € 0.0213 c £0.0220
Put option premium (per unit fc) p € 0.0487 p £0.0097
(European pricing)
Call option premium (%) c 1.45% c 3.24%
Put option premium (%) p 3.30% p 1.42%
When the euro’s interest rate rises from 2.072% to 4.000%, the call option premium on British pounds rises:
Call option on pounds when euro interest is 4.000% € 0.0213
Call option on pounds when euro interest is 2.072% € 0.0189
Change, an increase in the premium € 0.0213
Problem 7.16 Euro/British Pound
A European firm wishing to buy
A British firm wishing to buy
or sell pounds (the foreign currency)
or sell euros (the foreign currency)