Chapter 07 Foreign Currency Derivatives 1. Foreign currency futures quotation, valuation, and speculation Foreign currency futures and forward contracts

1

Chapter 07

Foreign Currency Derivatives

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• Foreign currency futures quotation, valuation, and speculation

• Foreign currency futures and forward contracts

• Foreign currency option quotation and use• Tracking option profits from Buying (long

position) and writing (selling or short position)• Option valuation

3


• Derivatives drive their values from the underlying asset• They might be used for two distinct management objectives:

– Speculation – the financial manager takes a position in the expectation of profit

– Hedging – the financial manager uses the instruments to reduce the risks of the corporation’s cash flow

• In the wrong hands, derivatives can cause a corporation to collapse, but used wisely they allow a financial manager the ability to plan cash flows

• The derivatives we will consider are:– Foreign Currency Futures– Foreign Currency Options

4

Foreign Currency Futures

• A foreign currency futures contract is an alternative to a forward contract– It calls for future delivery of a standard amount of currency at a

fixed time, place, and price– These contracts are traded on exchanges with the largest being

the Chicago Mercantile Exchange (CME)• Contract Specifications:

– Size of contract – called the notional principal, trading in each currency must be done in an even multiple

– Method of stating exchange rates – “American terms” are used; quotes are in US dollar cost per unit of foreign currency, also known as direct quotes

5


• Contract Specifications – continued – Maturity date – contracts mature on the 3rd Wednesday of

January, March, April, June, July, September, October or December

– Last trading day – contracts may be traded through the second business day prior to maturity date

– Collateral & maintenance margins – the purchaser or trader must deposit an initial margin or collateral• At the end of each trading day, the account is marked to market

and the balance in the account is either credited if value of contracts is greater or debited if value of contracts is less than account balance

6


• Contract Specifications– Settlement – only 5% of futures contracts are settled by

physical delivery, most often buyers and sellers offset their position prior to delivery date by taking offsetting positions• The complete buy/sell or sell/buy is termed a round turn

– Commissions – customers pay a single commission to their broker to execute a round turn

– Use of a clearing house as a counterparty – All contracts are agreements between the client and the exchange clearing house. Therefore, there is no counter-party risk

7

Using Foreign Currency Futures

• If an investor wishes to speculate on the movement of a currency can pursue one of the following strategies– Short position – selling a futures contract based on

view that currency will fall in value– Long position – purchase a futures contract based

on view that currency will rise in value– Example: Amber believes that Mexican peso will fall

in value against the US dollar, she looks at quotes in the WSJ for Mexican peso futures

8


• All contracts are for 500,000 new Mexican pesos. “Open,” “High” and “Low” all refer to the price on the day. “Settle” is the closing price on the day and “Change” indicates the change in the settle price from the previous day. “High” and “Low” to the right of Change indicates the highest and lowest prices for this specific contact during its trading history. “Open Interest” indicates the number of contracts outstanding

Maturity Open High Low Settle Change High LowOpen

InterestMar .10953 .10988 .10930 .10958 --- .11000 .09770 34,481June .10790 .10795 .10778 .10773 --- .10800 .09730 3,405Sept .10615 .10615 .10610 .10573 --- .10615 .09930 1,4181

9


• Example (cont.): Amber believes that the value of the peso will fall, so she sells a March futures contract

• By taking a short position on the Mexican peso, Amber locks-in the right to sell 500,000 Mexican pesos at maturity at a set price above their current spot price

• Using the quotes from the table, Amber sells one March contract for 500,000 pesos at the settle price: $0.10958/Ps

• Value at maturity (Short position) = – Notional principal × (Spot – Futures)

10

Using Foreign Currency Futures• To calculate the value of Amber’s position we use the following

formula• Value at maturity (Short position) = – Notional principal × (Spot –

Futures)• Using the settle price from the table and assuming a spot rate of

$0.09450/Ps at maturity, Amber’s profit is• Value = – Ps500,000 × ($0.09450/Ps – $0.10958/Ps) = $7,540• If Amber believed that the Mexican peso would rise in value, she

would take a long position on the peso• Value at maturity (Long position) = Notional principal × (Spot –

Futures)• Using the settle price from the table and assuming a spot rate of

$0.11500/Ps at maturity, Amber’s profit is • Value = Ps500,000 × ($0.11500/Ps – $0.10958/Ps) = $2,710

11

Daily Marking-to-Market

• Value at maturity (Long position) = Notional principal × (Spot – Futures)• Value at maturity (Long position) = €125,000 × ($1.2645/€ - $1.2724/€) = -$987.50

Initial Margin $2,835.00 Quotes = $ per € Contracts = 1

Maintenance Margin

$2,100.00Contract Size

in €125,000

Minimum Price Change (Tick)

$0.00010

Date TradeSettlement

PriceSettlement Price ($)

Mark-to-Market

Other EntriesAccount Balance

Margin Call by

3/7/2005 O/L 1.2724 $159,050.00 $2,835.00 $2,835.00 $0.003/7/2005 1.2728 $159,100.00 $50.00 $0.00 $2,885.00 $0.003/8/2005 1.2765 $159,562.50 $462.50 $0.00 $3,347.50 $0.003/9/2005 1.2665 $158,312.50 -$1,250.00 $0.00 $2,097.50 $737.50

3/10/2005 1.2715 $158,937.50 $625.00 $737.50 $3,460.00 $0.003/11/2005 1.2612 $157,650.00 -$1,287.50 $0.00 $2,172.50 $0.003/14/2005 C/S 1.2645 $158,062.50 $412.50 $0.00 $2,585.00 $0.00

Totals $3,572.50 $2,585.00Profit -$987.50Profit -$987.50

Dollar value of each tick $12.50Amount that could be lost without a margin call $735.00Number of tick moves wiping out the amount 58.80Adjusted tick move 59.00 =ROUNDUP(NUMBER,NUM_DIGITS)Note that contract prices are reported in $ per € Round up to next integer.Total dollar amount of tick moves for a margin call $0.0059Price as quoted that cause a margin call 1.2665

Buy (Long) One € Futures Contract (Earliest Expiration Available)

12

Foreign Currency Futures Versus Forward Contracts

Forward Markets Futures Markets Contract size Customized. Standardized. Delivery date Customized. Standardized. Participants Banks, brokers, MNCs. Public

speculation not encouraged Banks, brokers, MNC. Qualified public speculators.

Security deposit Compensating bank balances or credit lines needed

Small security deposit required

Clearing operation

Handled by individual banks and brokers

Handled by exchange clearinghouse. Daily settlements.

Marketplace Worldwide Central exchange Regulation Self-regulating. Commodity Futures Trading

Commission (CFTC) and National Futures Association

Liquidation Mostly settled by actual delivery Mostly settled by offsetting transactions

Transaction Costs

Bank’s bid/ask spread Negotiated brokerage fees

13

Foreign Currency Options

• A foreign currency option is a contract giving the purchaser of the option the right to buy or sell a given amount of currency at a fixed price per unit for a specified time period– The most important part of clause is the “right, but not

the obligation” to take an action– Two basic types of options, calls and puts

• Call – buyer has right to purchase currency• Put – buyer has right to sell currency

– The buyer of the option is the holder and the seller of the option is termed the writer

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• Every option has three different price elements– The strike or exercise price is the exchange rate at which the

foreign currency can be purchased or sold– The premium, the cost, price or value of the option itself

paid at time option is purchased– Spot exchange rate in the market

• There are two types of option maturities– American options may be exercised at any time during the

life of the option– European options may not be exercised until the specified

maturity date

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• Options may also be classified as per their payouts– At-the-money (ATM) options have an exercise

price equal to the spot rate of the underlying currency

– In-the-money (ITM) options may be profitable, excluding premium costs, if exercised immediately

– Out-of-the-money (OTM) options would not be profitable, excluding the premium costs, if exercised

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Foreign Currency Options Markets• Over-the-Counter (OTC) Market – OTC options are most

frequently written by banks for US dollars against British pounds, Swiss francs, Japanese yen, Canadian dollars and the Euro– Main advantage is that they are tailored to purchaser– Counterparty risk exists– Mostly used by individuals and banks

• Organized Exchanges – similar to the futures market, currency options are traded on an organized exchange floor– The Chicago Mercantile and the Philadelphia Stock Exchange serve

options markets– Clearinghouse services are provided by the Options Clearinghouse

Corporation (OCC)

17

Foreign Currency Options Markets

• Table shows option prices on British pound taken from the online edition of Wall Street Journal

Feb Mar Apr Feb Mar Apr1620 2.36 2.94 - 0.16 0.74 -1630 1.5 2.32 2.14 0.3 1.12 2.021640 0.86 1.7 - 0.66 1.5 -1650 0.5 1.36 1.34 - 2.16 -1660 0.26 1.02 1 - - -1670 0.12 0.76 0.92 - - -

BRITISH POUND (CME)62,500 pounds; cents per pound

Strike Price

Calls Puts

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Foreign Currency Options Markets

• The spot rate on the same day was $1.6440/£• The strike price means the price per pound

that must be paid if the option is exercised. The February call option of 1620 suggests a strike price of $1.6200/£

• The premium, or cost, of the March 1620 option was 2.94 cents per pound or $0.0294– For a call option on £62,500, the total cost would

be £62,500 x $0.0294/£ = $1,837.50

19

Foreign Currency Speculation

• Hans Schmidt is a currency speculator. He is willing to risk his money based on his view of currencies and he may do so in the spot, forward or options market

• Assume Hans has $100,000 and he believes that the six month spot rate for Swiss francs will be $0.6000/Sfr. Hans thinks that Swiss franc will appreciate or dollar will depreciate.

• The current spot rate and six-month forward rates are $0.5851/Sfr and $0.5760/Sfr, respectively

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• Speculating in the spot market– Hans should take the following steps– Use the $100,000 to purchase Sfr170,910.96 today at a

spot rate of $0.5851/Sfr– Hold the francs indefinitely, because Hans is in the spot

market he is not committed to the six month target– When target exchange rate is reached, sell the

Sfr170,910.96 at new spot rate of $0.6000/Sfr, receiving Sfr170,910.96 x $0.6000/Sfr = $102,546.57

– This results in a profit of $2,546.57 or 2.5% ignoring cost of interest income and opportunity costs

21


• Speculating in the forward market– If Hans were to speculate in the forward market, his viewpoint would

be that the future spot rate will differ from the forward rate– Today, Hans should purchase Sfr173,611.11 forward six months at

the forward quote of $0.5760/Sfr. This step requires no cash outlay– In six months, fulfill the contract receiving Sfr173,611.11 at

$0.5760/Sfr at a cost of $100,000– Simultaneously sell the Sfr173,611.11 in the spot market at Hans’

expected spot rate of $0.6000/Sfr, receiving Sfr173,611.11 x $0.6000/Sfr = $104,166.67

– This results in a profit of $4,166.67 with no investment required and assumes Hans is right

22


• Speculating in the options market– If Hans were to speculate in the options market, his

viewpoint would determine what type of option to buy or sell

– As a buyer of a call option, Hans purchases the August call on francs at a strike price of $0.5850/Sfr and a premium of $0.0050/Sfr

– At spot rates below the strike price, Hans would not exercise his option because he could purchase francs cheaper on the spot market than via his call option

23

Long Call Option

• Speculating in the options market– Hans’ only loss would be limited to the cost of the

option, or the premium ($0.0050/Sfr)– At all spot rates above the strike of $0.5850/Sfr

Hans would exercise the option, paying only the strike price for each Swiss franc• If the franc were at $0.5950/Sfr, Hans would exercise

his options buying Swiss francs at $0.5850/Sfr instead of $0.5950/Sfr

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Long Call Option

• Speculating in the options market– Hans could then sell his Swiss francs on the spot

market at $0.5950/Sfr for a profit– At any spot rate, profit from a long call option can

be determined by:– Net Profit = Maximum [ (Spot Rate – Strike Price),

0 ] – Premium– Net Profit = Maximum [ ($0.595/Sfr – $0.585/Sfr),

0 ] – $0.005/Sfr– Net Profit = $0.005/Sfr

25

Long Call Option

• Speculating in the options market– Hans could also wait to see if the Swiss franc

appreciates more, this is the value to the holder of a call option – limited loss, unlimited upside

– Hans’ break-even price can also be calculated by combining the premium cost of $0.005/Sfr with the cost of exercising the option, $0.5850/Sfr• This matched the proceeds from exercising the option

at a price of $0.5900/Sfr

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Profit & Loss for the Buyer of a Call Option

Loss

Profit (US cents/SF)

+ 1.00

+ 0.50

0

- 0.50

- 1.00

57.5 58.0 59.0 59.558.5Limited loss

Unlimited profit

Break-even price

Strike price

“Out of the money” “In the money”

“At the money”

Spot price(US cents/SF)

The buyer of a call option on SF, with a strike price of 58.5 cents/SF, has a limited loss of 0.50 cents/SF at spot rates less than 58.5 (“out of the money”), and an unlimited profit potential at spot rates above 58.5 cents/SF (“in the money”).

27

Short Call Option

• Speculating in the options market– Hans could also write a call, if the future spot rate is

below $0.5850/Sfr, then the holder of the option would not exercise it and Hans would keep the premium

– If Hans went uncovered and the option was exercised against him, he would have to purchase Swiss francs on the spot market at a higher rate than he is obligated to sell them at

– Here the writer of a call option has limited profit and unlimited losses if uncovered

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Profit & Loss for the Writer of a Call Option

• Speculating in the options market• Hans’ payout on writing a call option would be• At any spot rate, profit from a short call option

can be determined by:– Net Profit = – Maximum [ (Spot Rate – Strike

Price), 0 ] + Premium – Net Profit = – Maximum [ ($0.595/Sfr –

$0.585/Sfr), 0 ] + $0.005/Sfr– Net Profit = – $0.005/Sfr

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Profit & Loss for the Writer of a Call Option

Loss


+ 1.00

+ 0.50

0

- 0.50

- 1.00

57.5 58.0 59.0 59.558.5

Limited profit

Unlimited loss

Break-even price


The writer of a call option on SF, with a strike price of 58.5 cents/SF, has a limited profit of 0.50 cents/SF at spot rates less than 58.5, and an unlimited loss potential at spot rates above (to the right of) 59.0 cents/SF.

Strike price

30

Long Put Option

• Speculating in the options market– Hans could also buy a put, the only difference

from buying a call is that Hans now has the right to sell currency at the strike price

– If the franc drops to $0.575/Sfr Hans will deliver to the writer of the put and receive $0.585/Sfr

– The francs can be purchased on the spot market at $0.575/Sfr

– With the cost of the option being $0.005/Sfr, Hans realizes a net gain of $0.005/Sfr

31

Long Put Option

• Speculating in the options market• Hans’ payout on buying a put option would be• At any spot rate, profit from a long put option

can be determined by:– Net Profit = Maximum [ (Strike Price – Spot Rate),

0 ] – Premium– Net Profit = Maximum [ ($0.585/Sfr – $0.575/Sfr),

0 ] – $0.005/Sfr– Net Profit = $0.005/Sfr

32

Profit & Loss for the Buyer of a Put Option

Loss


+ 1.00

+ 0.50

0

- 0.50

- 1.00

57.5 58.0 59.0 59.558.5Limited loss

Profit upto 58.0

Strike price

“In the money” “Out of the money”

“At the money”


The buyer of a put option on SF, with a strike price of 58.5 cents/SF, has a limited loss of0.50 cents/SF at spot rates greater than 58.5 (“out of the money”), and a profit potential at spot rates less than 58.5 cents/SF (“in the money”) up to 58.0 cents.

Break-evenprice

33

Short Put Option

• Speculating in the options market– And of course, Hans could write a put, thereby

obliging him to purchase francs at the strike price– If the franc drops below $0.5800/Sfr Hans will lose

more than the premium received– If the spot rate does not fall below $0.5850/Sfr

then the option will not be exercised and Hans will keep all the premium from the option

34

Short Put Option

• Speculating in the options market• Hans’ payout on writing a put option would be• At any spot rate, profit from a short put option

can be determined by:– Net Profit = – Maximum [ (Strike Price – Spot

Rate), 0 ] + Premium– Net Profit = – Maximum [ ($0.585/Sfr –

$0.575/Sfr), 0 ] + $0.005/Sfr– Net Profit = – $0.005/Sfr

35

Profit & Loss for the Writer of a Put Option

Loss


+ 1.00

+ 0.50

0

- 0.50

- 1.00

57.5 58.0 59.0 59.558.5

Loss upto 58.0

Limited profit

Strike price


The writer of a put option on SF, with a strike price of 58.5 cents/SF, has a limited profit of0.50 cents/SF at spot rates greater than 58.5, and a loss potential at spot rates less than 58.5 cents/SF up to 58.0 cents.

Break-evenprice

36

Option Pricing and Valuation

• The pricing of any foreign currency option combines the following:– Domestic risk-free interest rate– Foreign risk-free interest rate– Strike price– Time-to-maturity– Volatility

37


• The intrinsic value is the financial gain if an option is exercised immediately (at-the-money)– This value will reach zero when the option is out-of-

the-money– When the spot rate rises above the strike price, the

call option will be in-the-money– When the spot rate falls below the strike price, the

put option will be in-the-money– At maturity date, the call and put options will have

values equal to their intrinsic values

38

Valuing a Call Option

• Assume you have the following information

US Interest Rate 1.09% (WSJ)UK Interest Rate 4.00% (WSJ)Strike Price $1.6300 (WSJ)Time to Maturity 0.25 (WSJ)(in years)Volatility 8.20% (NY FED)April 1630 Price $0.0214 (WSJ)Spot Rate $1.6440 (WSJ)

39

Option Pricing and Call Valuation• The formula value column (shown on the next slide) is based on the following:

Tσ dd

Trr

dNEedNS=eC

fd

FCTr

FCtTr

tdf

12

2t

1

d

f

$/FC

t,$/FC

t

2/$1/,$

y volatilitrate exchangeT

2ES

ln

=d

rateinterest domesticr

rateinterest foreign r

yearsin expiration toTimeT

FC)per ($ rate exchange strikeor exerciseE

(d) of valuezgiven afor on distributi normal cumulativeN(d)

gdiscountin timecontinuouse

FC)per ($ t at time rate exchangespot S

tat timeoption call theof value=C

subscript period time=t

40

Option Pricing and Call ValuationSpot Rate Intrinsic Value Formula Value Time Value$1.5500 $0.0000 $0.0021 $0.0021$1.5600 $0.0000 $0.0030 $0.0030$1.5700 $0.0000 $0.0042 $0.0042$1.5800 $0.0000 $0.0057 $0.0057$1.5900 $0.0000 $0.0076 $0.0076$1.6000 $0.0000 $0.0099 $0.0099$1.6100 $0.0000 $0.0128 $0.0128$1.6200 $0.0000 $0.0162 $0.0162$1.6300 $0.0000 $0.0202 $0.0202$1.6400 $0.0100 $0.0248 $0.0148$1.6500 $0.0200 $0.0300 $0.0100$1.6600 $0.0300 $0.0358 $0.0058$1.6700 $0.0400 $0.0421 $0.0021$1.6800 $0.0500 $0.0490 -$0.0010$1.6440 $0.0140 $0.0268 $0.0128

41

Option Pricing and Call Valuation

Valuing a Call Option

$0.00

$0.01

$0.02

$0.03

$0.04

$0.05

$0.06

$1.55 $1.56 $1.57 $1.58 $1.59 $1.60 $1.61 $1.62 $1.63 $1.64 $1.65 $1.66 $1.67 $1.68

Spot Exchange Rate

Val

ue

Intrinsic Value Formula Value

42

Valuing a Put Option

• Assume you have the following information

US Interest Rate 1.09% (WSJ)UK Interest Rate 4.00% (WSJ)Strike Price $1.6300 (WSJ)Time to Maturity 0.25 (WSJ)(in years)Volatility of FX 8.20% (NY FED)April 1630 Price $0.0202 (WSJ)Spot Rate $1.6440 (WSJ)

43

Option Pricing and Put Valuation• The formula value column (shown on the next slide) is based on the following:

Tσ dd

Trr

dNSedNE=eP

fd

FCtTr

FCTr

tfd

12

2t

1

d

f

$/FC

t,$/FC

t

1/,$2/$

y volatilitrate exchangeT

2ES

ln

=d

rateinterest domesticr

rateinterest foreign r

yearsin expiration toTimeT

FC)per ($ rate exchange strikeor exerciseE

(d) of valuezgiven afor on distributi normal cumulativeN(d)

gdiscountin timecontinuouse

FC)per ($ t at time rate exchangespot S

tat timeoption call theof value=P

subscript period time=t

44

Option Pricing and Put ValuationSpot Rate Intrinsic Value Formula Value Time Value$1.5500 $0.0800 $0.0934 $0.0134$1.5600 $0.0700 $0.0844 $0.0144$1.5700 $0.0600 $0.0757 $0.0157$1.5800 $0.0500 $0.0673 $0.0173$1.5900 $0.0400 $0.0593 $0.0193$1.6000 $0.0300 $0.0518 $0.0218$1.6100 $0.0200 $0.0448 $0.0248$1.6200 $0.0100 $0.0383 $0.0283$1.6300 $0.0000 $0.0324 $0.0324$1.6400 $0.0000 $0.0271 $0.0271$1.6500 $0.0000 $0.0224 $0.0224$1.6600 $0.0000 $0.0182 $0.0182$1.6700 $0.0000 $0.0147 $0.0147$1.6800 $0.0000 $0.0117 $0.0117$1.6440 $0.0000 $0.0251 $0.0251

45

Option Pricing and Put ValuationValuing a Put Option

$0.00

$0.01

$0.02

$0.03

$0.04

$0.05

$0.06

$0.07

$0.08

$0.09

$0.10

$1.55 $1.56 $1.57 $1.58 $1.59 $1.60 $1.61 $1.62 $1.63 $1.64 $1.65 $1.66 $1.67 $1.68

Spot Exchange Rate

Val

ue

Intrinsic Value Formula Value

46


• The time value of the option exists because the price of the underlying currency can potentially move further into the money between today and maturity– In the exhibits, time value is shown as the area

between formula value and intrinsic value

47

Currency Option Pricing Sensitivity

• Forward rate sensitivity:– Standard foreign currency options are priced around the

forward rate because the current spot rate and both the domestic and foreign interest rates are included in the option premium calculation

– The option-pricing formula calculates a subjective probability distribution centered on the forward rate

– This approach does not mean that the market expects the forward rate to be equal to the future spot rate, it is simply a result of the arbitrage-pricing structure of options

48


• Spot rate sensitivity (delta or Δ):– The sensitivity of the option premium to a small change in the spot

exchange rate is called the delta

– The higher the delta, the greater the probability of the option expiring in-the-money

– What is the delta of a deep-in the-money call option?– What is the delta of a deep-in the-money put option?– What is the delta of a deep out-of-the money call option?– What is the delta of a deep out-of-the money put option?

Spot

emium

Pr

49


• Time to maturity – value and deterioration (theta or θ):– Option values increase with the length of time to maturity– Time value of an option deteriorates as we approach to

maturity– This deteriorates is measured by theta– The deteriorates is non-linear, increases at a faster rate as

expiration nears

– A trader will normally find longer-maturity option better values, giving the trader the ability to alter an option position without suffering significant time value deterioration

Time

emium

Pr

50

Theta: Option Premium Time Value Deterioration

• Days remaining to maturity

• Option Premium• (US cents/£) • A Call Option on British Pounds: Spot Rate = $1.70/£

• 0.0

• 1.0

• 2.0

• 3.0

• 4.0

• 5.0

• 6.0

• 7.0

• 90 • 80 • 70 • 60 • 50 • 40 • 30 • 20 • 10 • 0

• In-the-money (ITM) • call ($1.65 strike price)

• At-the-money (ATM) • call ($1.70 strike price)

• Out-of-the-money (OTM) • call ($1.75 strike price)

51


• Sensitivity to volatility (lambda or λ):– Option volatility is defined as the standard deviation

of daily percentage changes in the underlying exchange rate

– An option on a volatile underlying asset is more valuable than a similar option on a less volatile underlying asset

– The denominator uses change in the annual volatility

Volatility

emium

Pr

52


• The primary problem with volatility is that it is unobservable, there is no single correct method for its calculation

• Thus, volatility is viewed in three ways– Historic – normally measured as the percentage movement in the

spot rate on a daily basis, or other time period– Forward-looking – a trader may adjust recent historic volatilities for

expected market swings– Implied – calculated by backing out of the market option premium

• Traders who believe that volatilities will fall significantly in the near-term will sell (write) options now, hoping to buy them back for a profit immediately volatilities fall, causing option premiums to fall.

53


• Sensitivity to changing interest rate differentials (rho or ρ and phi or φ):– Currency option prices and values are linked to the forward rate

• Option valuation formula contains spot rate and currency interest rates

– The forward rate is in turn based on the theory of Interest Rate Parity

– Interest rate changes in either currency will alter the option’s premium or value

• A trader who is purchasing a call option on foreign currency should do so before the domestic interest rate rises. This timing will allow the trader to purchase the option before its price increases.

54


• The expected change in the option premium from a small change in the domestic interest rate (home currency) is the term rho.

• The expected change in the option premium from a small change in the foreign interest rate (foreign currency) is termed phi.

RateInterest $

Pr

US

emium

RateInterest

Pr

Foreign

emium

55

Interest Differentials and Call Option Premiums

• Interest differential: iUS$ - i £ (percentage)

• Option Premium (US cents/£)

• A Call Option on British Pounds: Spot Rate = $1.70/£

• 0.0

• 1.0

• 2.0

• 3.0

• 4.0

• 5.0

• 6.0

• 7.0

• -4.0 • -3.0 • -2.0 • -1.0 • 0 • 1.0 • 2.0 • 3.0 • 4.0 • 5.0

• ITM call ($1.65 strike price)

• ATM call ($1.70 strike price)

• OTM call ($1.75 strike price)

• 8.0

56


• The sixth and final element that is important to option valuation is the selection of the actual strike price.

• A firm must make a choice as per the strike price it wishes to use in constructing an option (OTC market).

• Consideration must be given to the tradeoff between strike prices and premiums.

57

Option Premiums for Alternative Strike Rates

• Call strike price (U.S. dollars/£)

• Option Premium• (US cents/£)

• 0.0

• 1.0

• 2.0

• 3.0

• 4.0

• 5.0

• 6.0

• 7.0

• 1.66• 1.67• 1.68• 1.69• 1.70 • 1.71• 1.72• 1.73• 1.74• 1.75

• Current spot rate = $1.70/£

• OTM Strike rates

• ITM Strike rates

58

Summary of Option Premium Components

Documents

Chapter 07 Foreign Currency Derivatives 1. Foreign currency futures quotation, valuation, and speculation Foreign currency futures and forward contracts