Lecture 07 student

International Finance
IBS 621

Lecture 6

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World Financial Markets and Institutions

• International Banking and Money Market
• International Bond Market
• International Equity Markets
• Futures and Options on Foreign Exchange
• Currency and Interest Rate Swaps
• International Portfolio Investment

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Futures Contracts
• A futures contract specifies that a certain currency will be exchanged for
another at a specified time in the future at prices specified today.
• A futures contract is different from a forward contract:
– Futures are standardized contracts trading on organized exchanges with
daily resettlement through a clearinghouse.
• Standardizing Features: easier to find a counterparty compared to forwards
– contract Size
– delivery Month: reduced counterparty (credit) risk compared to
forwards
– Daily resettlement: among other things, it allows you to close your
position and get out of the contract on any day. it is called “to offset the
position” if you are 1 contract long and want to get out, take 1 short
position in the same contract on the same exchange and your done.
• margin requirements (initial, maintenance margins)
– initial margin
– maintaince margin- in your account in order to be active
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Currency Futures Markets
• The Chicago Mercantile Exchange (CME) is by far the largest.
• Others include:
– The Philadelphia Board of Trade (PBOT)
– The MidAmerica Commodities Exchange
– The Tokyo Financial Exchange
– The London International Financial Futures Exchange (LIFFE)
– expiry cycle: march, june, september, december. deliver date 3rd
wednesday of delivery month. last trading day is the second
business day preceding the delivery day
– cme hours 7:20 am to 2:00 pm cst

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After Hours Trading
• extended -hours trading on CME GLOBEX runs from 2:30 p.m. to
4:00 p.m dinner break and then back at it from 6:00 p.m. to 6:00
a.m. CST.
• Singapore Exchange (SGX) offers contracts.
• There are other markets, but none are close to CME and SGX
trading volume.
•

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Daily Resettlement: An Example
• Suppose you want to speculate on a rise in the $/¥
exchange rate (specifically you think that the
dollar will appreciate).

Currently $1-Y140. The 3-month forward price is $1-Y150.
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Daily Resettlement
• Currently $1 = ¥140 and it appears that the dollar is strengthening.
• If you enter into a 3-month futures contract to sell ¥ at the rate of $1 =
¥150 you will make money if the yen depreciates. The contract size is
¥12,500,000
• You do not have to have ¥ now, either way you have committed yourself to
sell ¥12,500,000 and receive in exchange ¥12,500,000 * 1/150 [$/ ¥] = $
83,333.33
• Your initial margin is 4% of the contract value:
• initial margin- to initiate deal, maintenance is roughly 75% of the initial,
lets say 3% here. if your margin account is bellow maintenance, ass $ up
to the initial margin, otherwise your position will be liquidated.

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Daily Resettlement
• If tomorrow, the futures rate closes at $1 = ¥149, then your position’s value
drops. Here’s why.
• Your original agreement was to sell ¥12,500,000 and receive $83,333.33
• But now ¥12,500,000 is worth: ¥12,500,000 * 1/149 [$/ ¥] = $
$83,892.62,
• If you sell ¥ under the new terms, you receive $559.28 more compared your
current contract.
• That is, you have lost $ $559.28 overnight
• The $559.28 comes out of your $3,333.33 margin account, leaving $2,774.05
• maintainance margin is 0.03*¥12,500,00*1/149[$/¥]=$2516.78
• no need to add money now to your margin account. note that the initial margin
requirement is now 0.04*¥12,500,000*1/149[$/¥]=$3355.70

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Reading a Futures Quote

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Reading a Futures Quote

Daily Change Highest and lowest
prices over the
Closing price lifetime of the
Lowest price that day contract.
Highest price that day
Opening price
Expiry month Number of open contracts
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Currency Futures Trading: Example
• $CAN futures contract expiring on June 14 trades on CME at US
$0.7761 on January 9. On the last trading day of the contract in June
the spot rate is US$0.7570. The contract size is CAN$100,000.
1. What is the profit/loss for a trader who took a long position in the
contract on January 9?
2. What is the profit/loss for a trader who took a short position in the
contract on January 9?
3. 1. long position. the futures contract locked at US$0.7761 while in
June it is possible to buy $CAN at US$0.07570. the trade overpaid for
$CAN-
4. -> loss. how much? US$ (0.07570-0.7761)*100=-1,910
5. as F-> S with T->0 the $1,910 would be the total $ subtracted from
the traders margin account during the daily resettlements.
6. effective cost of the CAN$100,00 is $75,700+$1910=$77,610

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Currency Futures Trading: Example
short position. the trader can sell at US$.07761 while in june it is only possible
to sell $CAN at US $0.7570. the trader gets more $CN at US$0.7570. the
trader gets more $CAN -> profit. how much?
->US$ (0.7761-0.7570)*100,000= 1,910
as F-> S with T->0 the $1910 would be the total $ added to the traders margin
account during the daily resettlement.
effective revenue from the short position is CAN$100,000 is $75,700+1,910=
$77,610
**it is possible to buy at $0.7570 and immediately deliver at $0.7761
**point #1. futures is a zero sum game, your gain is your counterpaty’s loss,
and vice cersa. however, if you want to hedgeFX risk, you can lock in a fixed
rate

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Eurodollar Interest Rate Futures
• Widely used futures contract for hedging short-term U.S. dollar interest
rate risk.
• The underlying asset is a $1,000,000 90-day Eurodollar deposit—the
contract is cash settled.
• Traded on the CME and the Singapore International Monetary Exchange.
• Eurodollar futures prices are stated as an index number of three-month
LIBOR calculated as F = 100 – LIBOR.
– For example, if the closing price for is 98.23, the implied yield is 5.77
percent = 100-98.23
• Hedging/speculation just like with forwards, except standardized amounts
and daily resettlement
• ***no physical delivery. in the case of a forward/future. this is notional amount multiplied by the difference
between the market price of the underlying asset at maturity and the forward’s delivery price.
in the case of an option, it is the intrinsic value of the option.

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Example
• The size of a yen futures contract at CME is 12.5 million yen. The initial margin
is $2,025 per contract and the maintenance margin is $1,500. You decide to
buy ten contracts with maturity on June 17, at the current futures price of
$0.01056. Today is April 1 and the spot rate is $0.01041. Indicate cash flows
on your position if the following prices are subsequently observed.
April 1 April 2 April 3 April 4 June 16 June 17
Spot, $/Y 0.01041 0.01039 0.01000 0.01150 0.01150 0.01100
Futures, $/Y 0.01056 0.01054 0.01013 0.01160 0.01151 0.01100

•

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Example solved
April 1 April 2 April 3 April 4 June 16 June 17
Spot, $/Y 0.01041 0.01039 0.01000 0.01150 0.01150 0.01100
Futures, $/Y 0.01056 0.01054 0.01013 0.01160 0.01151 0.01100
Gain/Loss -2500 -51250 -184750 -11250 -63750
Margin before CF 17750 -33500 2040000 9000 -43500

CF from investor 20250 0 0.010395 -184750 11250 43500
Margin after CF 20250 17750 20250 20250 20250 0

Text

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Example
• It is 1 April now and current 3-month LIBOR is 6.25%. Eurodollar futures contracts
are traded on CME with size of $1 million at 93.280 with June delivery. The initial
margin is $540 and the maintenance margin is $400. You are a corporate
treasurer and you know your company will have to pay $10 million in cash for
goods that will be delivered on June 17. You will sell the goods for profit, but you
will not receive payment until September 17. Thus, you know you will have to
borrow $10 million for 3 months in June.
1. What is the forward rate implicit in the Eurodollar futures price?
2. How to lock in 3-month borrowing rate for June 17 using Eurodollar futures?
3. On June 17, the Eurodollar futures is quoted at 91%, and the current Eurodollar
rate is 9%. You close your position at that time. What are your cash flows?

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Example solved
you
inte
wh
bor
exp

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Example solved
1. Implicit rate = 100-93.280 = 6.72% Note that forward rate 6.72% > spot
6.25%, term structure upward sloping
you
inte
wh
bor
exp

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Example solved
you
2. You will have to borrow $10 million for 3 months as you know. Borrow = inte
sell deposite instruments. Borrow in the future and lock in the % rate = wh
sell forward. You sell 10 Eurodollar contracts. bor
exp

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Example solved
you
exp
3. Interest rates 6.25% to 9%

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Example solved
you
exp
But your profit from the short position in the futures contracts is
10*1,000,000*(0.9328-0.9100)/4-$57,000.

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Example solved
you
exp
10*1,000,000*(0.9328-0.9100)/4-$57,000.
Your borrowing cost is 10,000,000*0.9/4=$225,000

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Example solved
you
exp
10*1,000,000*(0.9328-0.9100)/4-$57,000.
Your borrowing cost is 10,000,000*0.9/4=$225,000
Your total borrowing CF = $225,000-$57,000 = $168,000. For 3
months borrowing you pay $168,000/ 10,000,000 = 1.68% Convert this
into per annum: 1.68% *4= 6.72%

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Options Contracts
• An option gives the holder right, but not the obligation, to buy or sell a given
quantity of an asset in the future, at prices agreed upon today.
• Call vs. Put options. Call/Put options gives the holder the right, to buy/sell a given
quantity of some asset at some time in the future, at prices agreed upon today.
• European vs. American options.
– European options can only be exercised on the expiration date. American
options can be exercised at any time up to and including the expiration date.
– Since this option to exercise early generally has value, American options are
usually worth more than European options, other things equal.
–

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Options Contracts
• In-the-money options
– Profitable to exercise today
• At the money options
– Profit = 0 if exercise today
• Out of the money options
– loss if exercise under the option’s terms
• Intrinsic Value
– In the money: The difference between the exercise price of the option
and the spot price of the underlying asset.
– Out of the money: zero

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Currency Options Markets
• Currency
– 20-hour trading day.
– OTC is much bigger than exchange volume.
– Trading is in six major currencies against the U.S. dollar.
– View standard specifications from PHLX
• Options on currency futures
– Options on a currency futures contract. Exercise of a currency
futures option results in a long futures position for the ________
of a call or the __________of a put.
– Exercise of a currency futures option results in a short futures
position for the __________ of a call or the __________ of a put.

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Basic Relationships at Expiry
• At expiry, an American call option is worth the same as a European option
with the same characteristics.
• If the call is in-the-money, it is worth Sr-E
• If the call is out-of-the-money, it is worthless.
• CaT = CeT = Max[ST - E, 0]

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Basic Relationships at Expiry
• At expiry, an American call option is worth the same as a European option
with the same characteristics.
• If the call is in-the-money, it is worth Sr-E
• If the call is out-of-the-money, it is worthless.
• CaT = CeT = Max[ST - E, 0]

• At expiry, an American put option is worth the same as a European
option with the same characteristics.
• If the put is in-the-money, it is worth E-Sr
• If the put is out-of-the-money, it is worthless.
• PaT = PeT = Max[E - ST, 0]

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Basic Option Profit Profiles
Call. Long position (buy). If the call is in-the-money, it is worth ST – E. If the
call is out-of-the-money, it is worthless and the buyer of the call loses his
entire investment of c0.

Call. Short position (sell). If the call is in-the-money, the writer loses ST – E. If
the call is out-of-the-money, the writer keeps the option premium.

Put. Long position (buy). If the put is in-the-money, it is worth E –ST. If the put is
out-of-the-money, it is worthless and the buyer of the put loses his entire
investment of p0.

Put. Short position (sell). If the put is in-the-money, it is worth E –ST. If the put is
out-of-the-money, it is worthless and the seller of the put keeps the option
premium of p0.

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American Option Pricing
• With an American option, you can do everything that you can do with a
European option—this option to exercise early has value.
• CaT > CeT = Max[ST - E, 0]

• PaT > PeT = Max[E - ST, 0]
•

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Market Value, Time Value and
Intrinsic Value for an American Call

The black line shows
the payoff at maturity
(not profit) of a call
option.
Note that even an out-
of-the-money option
has value—time value.

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Example
• Calculate the payoff at expiration for a call option on the euro in which
the underlying is $0.90 at expiration, the option is on EUR 62,500, and
the exercise price is
1. $0.75
2. $0.95
3. E=$0.75. C=max(.90-.75,0)*62500=$9,375
4. E=$.95. C=max (0.90-.95,0)*62500=0

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Example
• Calculate the payoff at expiration for a put option on the euro in which
the underlying is $0.90 at expiration, the option is on EUR 62,500, and
the exercise price is
1. $0.75
2. $0.95
3. E=$0.75. P=max(.75-.90,0)*62,500=$ 0
4. E=$0.95. P=max(.95-.90,0)*62,500= $3,125

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Example this is futures rate no spot rate

• Calculate the payoff at expiration for a call option on a currency futures
contract in which the underlying is at $1.13676 at expiration, the futures
contract is for CAN$1,000,000 and the exercise price is:
1. $1.13000
2. $1.14000
3. E=1.130
4. C=max(1.13676-1.30,0)*1,000,000=6,760
5. E= $1.14000
6. C= max(1.13676-1.40,0)*1,000,000=0

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Example
• Calculate the payoff at expiration for a put option on a currency futures
contract in which the underlying is at $1.13676 at expiration, the futures
contract is for CAN$1,000,000 and the exercise price is:
1. $1.13000
2. $1.14000
3. E= $1.13000
4. P=max(1.130-1.13676 ,0)*1,000,000= $0
5. E=$1.140
6. P=max(1.140-1.13676 ,0)*1,000,000=$3,240

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Pricing currency options
• Bounds on option prices are imposed by arbitrage conditions (ignore in this
course)
• Exact pricing formulas (theoretical)
– Lattice models, for example binomial model (ignore for now)
– Pricing based on continuous time modeling and stochastic calculus
(mathematics used in modeling heat transfers, flight dynamics, and
semiconductors). No derivations here. More precise than binomial.
• Idea: model evolution of the underlying asset’s price in continuous
time (i.e. not week-by-week) and calculate expected value of the
option payoff.

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Currency Option Pricing

r = the interest rate (foreign or
domestic), T – time to expiration,
years
S – current exchange rate, E –
exercise exchange rate, DC/FC

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Example
• Consider a 4-month European call option on GBP in the US. The
current exchange rate is $1.6000, the exercise price is $1.6000,
the riskless rate in the US is 8% and in the UK is 11%. The
volatility is 20%. What is the call price?

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Example
• Consider a 2-month European put option on GBP in the US. The
current exchange rate is $1.5800, the exercise price is $1.6000,
the riskless rate in the US is 8% and in the UK is 11%. The
volatility is 15%. What is the put price?

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Put-call parity for currency options

put +underlying asset= call +pv of exercise
price
-put and call have the same strike price
and maturity

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Option Value Determinants
Call Put
1. Exchange rate + -
2. Exercise price - +
3. Interest rate at home + -
4. Interest rate in other country - +
5. Variability in exchange rate + +
6. Expiration date + +

The value of a call option C0 must fall within
max (S0 – E, 0) < C0 < S0.
The precise position will depend on the above
factors.
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Empirical Tests
• The European option pricing model works fairly well in
pricing American currency options.
• It works best for out-of the money and at the money
options.
• When options are in-the-money, the European option
pricing model tends to underprice American options.

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Types of Swaps
• In a swap, two counterparties agree to a contractual
arrangement wherein they agree to exchange cash flows at periodic
intervals.
• There are two types of interest rate swaps:
– Single currency interest rate swap
• “Plain vanilla” fixed-for-floating swaps are often just called
intrest rate swaps
– Cross-Currency interest rate swap
• This is often called a currency swap; fixed for fixed rate
debt service in two (or more) currencies.

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Swap Market
• In 2001 the notional principal of:
Interest rate swaps was $58,897,000,000.
Currency swaps was $3,942,000,000
• The most popular currencies are:
– US$, JPY, Euro, SFr, GBP

• A swap bank is a generic term to describe a financial institution that
facilitates swaps between counterparties. It can serve as either a broker or
a dealer.
– A broker matches counterparties but does not assume any of the risks
of the swap.
– A dealer stands ready to accept either side of a currency swap, and
then later lay off their risk, or match it with a counterparty.

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Size of the Swap Market

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Example of an Interest Rate Swap

• Consider this example of a “plain vanilla” interest rate swap.
• Bank A is a AAA-rated international bank located in the u.k. and
wishes to raise $10,000,000 to finance floating-rate Eurodollar
loans.
– Bank A is considering issuing 5-year fixed-rate Eurodollar bonds
at 10 percent.
– It would make more sense to for the bank to issue floating-rate
notes at LIBOR to finance floating-rate Eurodollar loans.

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• Firm B is a BBB-rated u.s company. It needs $10,000,000 to finance an
investment with a five-year economic life.
– Firm B is considering issuing 5-year fixed-rate Eurodollar bonds at
11.75 percent.
– Alternatively, firm B can raise the money by issuing 5-year floating-
rate notes at LIBOR + ½ percent.
– Firm B would prefer to borrow at a fixed rate.

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• The borrowing opportunities of the two firms area:

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1/2% of
$10,000,000=50,0
00. thats quite a
cost saving per
Swap
year for 5 yrs
Bank
10 3/8%

libor -1/8%
Bank 10 3/8-10-(libor- 1/8)
A Libor- 1.2% which is 1/2% better than they can borrow
10% floating without a swap

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1/2% of
$10,000,000=50,0
The swap bank makes
00. thats quite a
cost saving per
Swap this offer to Bank A: You
year for 5 yrs
pay libor -1/8% per year
Bank on $10 million for 5 years
10 3/8%
and we will pay you 10
3.8% on $10 million for 5
libor -1/8% years
Bank 10 3/8-10-(libor- 1/8)
10% floating without a swap

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1/2% of
$10,000,000=50,0
00. thats quite a
cost saving per
Swap
year for 5 yrs
Bank
10 3/8%

LIBOR – 1/8%
Bank 10 3/8-10-(libor- 1/8)
floating without a swap

10%

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Swap
Bank
10 ½%
LIBOR – ¼%

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The swap bank makes
this offer to company B: Swap
You pay us 10 1/2% per
year on $10 million for 5 Bank
years and we will pay you
10 ½%
libor 1/4% per year on
$10 million for 5 years. LIBOR – ¼%
Company
B

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Swap
1/2% of 10,000,000=
Bank 50,000 thats quite a
10 ½% cost saving per year
LIBOR – ¼% for 5 years
they can borrow externally at
Libor +1/2% and have a net borrowing
position of Company
10 1/2 +(libor+1/2)=(libor-1/2)=11.25%
which is 1/2% better then they can borrow floatinf=g B

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Here’s what’s in it for B:
Swap
1/2% of 10,000,000=
position of Company
10 1/2 +(libor+1/2)=(libor-1/2)=11.25%

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Here’s what’s in it for B:
Swap
1/2% of 10,000,000=
position of Company LIBOR+ ½%
10 1/2 +(libor+1/2)=(libor-1/2)=11.25%

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1/4% of 10M
Swap
Bank
10 3/8% 10 ½%

LIBOR – 1/8% LIBOR – ¼%
Bank Company
A B

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1/4% of 10M
Swap
Bank
10 3/8% 10 ½%

LIBOR – 1/8% LIBOR – ¼%
Bank Company
LIBOR – 1/8 – [LIBOR – ¼ ]= 1/8
A 10 ½ - 10 3/8 = 1/8 B
¼

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The Quality Spread Differential
• The Quality Spread Differential represents the potential
gains from the swap that can be shared between the
counterparties and the swap bank.
– QSD = Fixed Differential – Floating Differential =
– answer in notebook

• There is no reason to presume that the gains will be
shared equally.
• In the above example, company B is less credit-worthy
than bank A, so they probably would have gotten less
of the QSD, in order to compensate the swap bank for
the default risk.
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Example
• Determine the upcoming payment in a plain vanilla interest rate swap in which the notional principal is 70 million
Euro. The end user makes semi-annual fixed 7% payments, and the dealer makes semi-annual floating payments
at Euribor, which was 6.25% on the last settlement period. The floating payments are made on the basis of 180
days in the settlement period and 360 days in a year. The fixed payments are made on the basis 180 days in the
settlement period and 365 days in a year. Payments are netted, determine which party pays and what amount.
• fx payment= 70,000,000*0.07*(180/365)=2,416,483 Euro
• floating payment= 70,000,000*0.0625*(180/360)= 2,187,500 Euro
• fixed payment is greather, the swap end user will pay the dealer 2,416, 438-2,187,500= 228,928 Euro

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Example
• A US company enters into an interest rate swap with a dealer. In this swap, the notional principal is $50 million
and the company will pay a floating rate of LIBOR and receive a fixed rate of 5.75%. Interest is paid
semiannually and the current LIBOR is 5.15%. The floating rate are made on the basis of 180/360 and the fixed
rate payments are made on the basis of 180/365. Calculate the first payment and indicate which party pays.
• fx payments= 50,000,000*0.0575*(180/365)= 1,417,808
• floating payment= 50,000,000*0.0515*(180/360)= 1,287,500
• fx payment s greater the dealer will pay to the us company $1,417,808-1,287500=$130,308

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Interest rate swap valuation
• You can represent a swap as a bond portfolio or a series of FRAs. We use bond portfolio representation.
• From the point of view of floating-rate payer, this is a long position in the fixed rate bond and short position
in the floating rate bond.

– Vswap=Bffixed-Bfloating

• From the point of view of fixed-rate payer, this is a long position in the floating rate bond and short position
in the fixed rate bond.

– Vswap=Bflaoting-Bfixed

• Immediately after the interest payment, the floating rate bond is worth exactly the notional amount

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Example
• Consider a financial institution that pays LIBOR – 0.25% and receives 10.50% p.a. (annual compounding) from a
swap end user on a notional principal of $10 million. The swap has remaining life of 4 years. The fixed rates have
fallen from 10.5% to 9% and the swap end user wants to get out of the deal. How much should the financial
institution charge for the right to cancel the agreement?
• the swap bank pays floating and receives fixed rate, therfore the value of the wao for the institution
Vswap=Bffixed-Bfloating

• Bfloating= 10,000,000 right after the coupon payment

• Bfixed= [N=4 omt=1,050,000; i/y=0; fv=10000000= 10, 485, 957.98

– Vswap=Bffixed-Bfloating= 10485,957.98-10000000=485957.98

– the bank will be willing to cancel the deal for a fee of 485957.98

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Currency Swaps
• Currency swaps evolved from parallel and back-to-back loans – a way to hedge
long-term exchange exposure
• The two counterpart firms lend directly to each other

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An Example of a Currency Swap
• Suppose a Us wants to finance a £10,000,000 expansion of a British plant.
• They could borrow dollars in the US where they are well known and exchange for
dollars for pounds.
– This will give them exchange rate risk: financing a sterling project with dollars.
• They could borrow pounds in the international bond market, but pay a premium
since they are not as well known abroad.

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An Example of a Currency Swap
• If they can find a britsh MNC with a mirror-image financing need they may both
benefit from a swap.
• If the spot exchange rate is S0($/£) = $1.60/£, the U.S. firm needs to find a British
firm wanting to finance dollar borrowing in the amount of $16,000,000

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Comparative Advantage as the
Basis for Swaps
• Firm A has a comparitive advantage in borrowing in dollars.
• Firm B has a comparative advantage in borrowing in pounds.
• If they borrow according to their comparative advantage and then swap, there will be gains for both parties.
– Caution: credit risk

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Swap Market Quotations
• Swap banks will tailor the terms of interest
rate and currency swaps to customers’
needs
• They also make a market in “plain vanilla”
swaps and provide quotes for these. Since
the swap banks are dealers for these
swaps, there is a bid-ask spread.

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Variations of Basic Currency and
Interest Rate Swaps

• Currency Swaps
– fixed for fixed
– fixed for floating
– floating for floating
• Interest Rate Swaps
– zero for floating
– floating for floating

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Risks of Interest Rate and
Currency Swaps
• Interest Rate Risk
– Interest rates might move against the swap
bank after it has only gotten half of a swap
on the books, or if it has an unhedged
position.
• Basis Risk
– If the floating rates of the two
counterparties are not pegged to the same
index (i.e. LIBOR)
• Exchange rate Risk

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Risks of Interest Rate and
Currency Swaps
• Credit Risk
– This is the major risk faced by a swap dealer—the
risk that a counter party will defult on its end of the
swap.
• Mismatch Risk
– It’s hard to find a counterparty that wants to borrow
the right amount of money for the right amount of
time.
• Sovereign Risk
– The risk that a country will impose exchange rate
restrictions that will interfere with performance on
the swap.
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Swap Market Efficiency
• Swaps offer market completeness and that has
accounted for their existence and growth.
• Swaps assist in tailoring financing to the type desired
by a particular borrower.
– Since not all types of debt instruments are available
to all types of borrowers, both counterparties can
benefit (as well as the swap dealer) through
financing that is more suitable for their asset
maturity structures.

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Example
• A US company can issue a US$-denominated bond but needs to borrow in GBP. Consider a currency swap in
which the US company pays a fixed rate in the foreign currency, GBP, and the counterparty pays a fixed rate in US
$. The notional principals are $50 million and GBP 30 million, and the fixed rates are 5.6% in US$ and 6.25% in
GBP. Both sets of payments are made on the basis of 30 days per month, 365 days per year, and the payments
are made semi-annually.
• What are the following cash flows: (i) initial, (ii) semi-annual, (iii) final
• (i)US company pays 50M, uk company pays GBP 30M
• (ii) us company pays GBP 30m*0.0625*(180/365)= gbp 924,658
• uk company pays 50m*o.056*(180/360)=1,380,822
• us company pays GBP 30 m, uk company pays 50 m

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Valuation of currency swaps
• Currency swaps can be represented as bond portfolios
or a series of forwards. We use bond representation.
• From the point of view of foreign currency payer
(domestic currency receiver), this is a long position in
the domestic bond and short position in the foreign
bond.
– ________________________________________________
• From the point of view of domestic currency payer
(foreign currency receiver), this is a long position in
the foreign bond and short position in the domestic
bond.
– ________________________________________________
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Example
• In Japan term structure of interest rates is flat at 4% and in the US
it is 9%. A financial institution has entered into a currency swap in
which it receives 5% p.a. in JPY and pays 8% p.a. in USD once a
year. The principals are $10 million and JPY 1,200 million. The swap
will last for another 3 years, and the current JPY/USD exchange rate
is JPY 110. What is the value of this swap for the financial
institution?

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Swaptions
• An option to enter into swap
• Types:
– Payer swaption
• Gives the right to enter into a swap as a _________ rate
payer and __________ rate receiver
• Equivalent to ___________ option
– Receiver swaption
• Gives the right to enter into a swap as a __________
rate payer and ___________ rate receiver
• Equivalent to ___________ option

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