currency futures and options. spot exchange rates spot transactions are done immediately. a spot...

Currency Futures and OptionsCurrency Futures and Options

Spot Exchange RatesSpot Exchange Rates

Spot transactions are done Spot transactions are done immediately. A spot rate is the immediately. A spot rate is the current domestic currency price of current domestic currency price of a foreign currencya foreign currency

Transaction VolumeTransaction Volume

Spot33%

Forward11%

Swaps56%

Spot market volume is small relative to total currency volume

Forward ContractsForward Contracts

Forward contracts are purchases/sales of Forward contracts are purchases/sales of currencies to be delivered at a specific currencies to be delivered at a specific forward date (30,90,180, or 360 days)forward date (30,90,180, or 360 days)

ExampleExampleCAD/USDCAD/USD .7641.7641

1 month 1 month .7583.7583

3 months 3 months .7563.7563



Forward ContractsForward Contracts

Microsoft anticipates Microsoft anticipates labor expenses from labor expenses from Canadian operations Canadian operations (payable in Canadian (payable in Canadian Dollars) in 30 Days.Dollars) in 30 Days.

A Canadian A Canadian Prescription Drug Prescription Drug Importer is expecting Importer is expecting a shipment of Viagra a shipment of Viagra from Pfizer in 30 days from Pfizer in 30 days (payment due in (payment due in dollars)dollars)

Suppose that the current CAD/USD exchange rate is .7641.Suppose that the current CAD/USD exchange rate is .7641.

Microsoft would be worried about the dollar depreciating Microsoft would be worried about the dollar depreciating while the Canadian importer worries about the dollar while the Canadian importer worries about the dollar appreciating.appreciating.

Forward ContractsForward ContractsCommercial Bank

Microsoft Microsoft approaches a approaches a commercial commercial bank with an bank with an offer to offer to buy buy Canadian Canadian dollars dollars forward 30 forward 30 daysdays

The Canadian The Canadian drug importer drug importer approaches a approaches a commercial commercial bank with an bank with an offer to sell offer to sell Canadian Canadian dollars forward dollars forward 30 days30 days

The bank The bank negotiates a negotiates a price of .7583 price of .7583 per CAD for per CAD for 1M CAD1M CAD

0.735

0.74

0.745

0.75

0.755

0.76

0.765

0.77

0.7750 6 8

12

14

16

20

22

26

28

30

34

36

40

42

CAD

/U

SD

Spot30 Day

On Settlement day, Microsoft buys 1M On Settlement day, Microsoft buys 1M CAD for .7583 apiece and saves CAD for .7583 apiece and saves (.7668 - .7583)*1M = $8,500(.7668 - .7583)*1M = $8,500

On Settlement day, the drug importer sells 1M CAD On Settlement day, the drug importer sells 1M CAD for .7583 apiece and loses (.7583 - .7668)*1M = $8,500for .7583 apiece and loses (.7583 - .7668)*1M = $8,500

Non-Deliverable ForwardsNon-Deliverable Forwards

Note that the currencies need not Note that the currencies need not actually be delivered. A actually be delivered. A non-non-deliverable forwarddeliverable forward specifies that specifies that only the profits/losses will be only the profits/losses will be exchanged on settlement day. exchanged on settlement day.

Forward Forward Premiums/DiscountsPremiums/Discounts

In the previous example: In the previous example:

CAD = .7641CAD = .7641

30 Day = .758330 Day = .7583

Forward Premium =

.7583 - .7641

.7641100 360

30

Annualized

= -9.1%

The 30 Day CAD is selling at a discount of 9.1%

Futures ContractsFutures Contracts

Forward contracts are written on an individual Forward contracts are written on an individual basis. Futures are standardized, traded basis. Futures are standardized, traded commodities (Chicago Mercantile Exchange)commodities (Chicago Mercantile Exchange) JPY: 12,500,000 YenJPY: 12,500,000 Yen GBP: 62,500 PoundsGBP: 62,500 Pounds Euro: 125,000 EuroEuro: 125,000 Euro CAD: 100,000 Canadian DollarsCAD: 100,000 Canadian Dollars

Therefore, to make the previous trade (buy 1M Therefore, to make the previous trade (buy 1M CAD, you would purchase 10 futures contracts)CAD, you would purchase 10 futures contracts)

Futures ContractsFutures ContractsChicago

Mercantile Exchange

Microsoft makes an offer to buy 10, 30 Day Futures Contracts

The Canadian drug importer makes an offer to sell 10, 30 day Futures contracts

The CME simultaneously buys 10 contracts from Microsoft and sells 10 contracts from the drug importer

Futures Futures QuotesQuotes

StrikeStrike OpenOpen HighHigh LowLow SettlSettlee

Pt Pt ChgeChge

VolumVolumee

InteresInterestt

Feb05Feb05 .7600.7600 .7615.7615 .7559.7559 .7570.7570 +170+170 35003500 89938993

Mar05Mar05 .7850.7850 .7900.7900 .7800.7800 .7825.7825 -150-150 33 3434

Apr05Apr05 ------------ ------------ ------------ ---------- UNCUNCHH

---------- ----------

CAD 100,000

Settlement Date Change From Prior Day (in Pips)

Opening, High, Low, and Closing Price

Contracts Outstanding (000s)

Total Contracts bought/sold that day

Pricing Currency Pricing Currency Forwards/FuturesForwards/Futures

Consider the following investment strategy:

Borrow $1,000 in the US

Convert the $s to Euros

Invest the Euros in European Bonds

Convert the proceeds from the Euro bonds back to dollars

Profit = Proceeds from Euro Bonds less Repayment of initial loan plus interest

i = 6% e = $1.35/E

i* = 4% e’ = $1.40/E

Pricing Currency Pricing Currency Forwards/FuturesForwards/Futures

Consider the following investment strategy:

Borrow $1,000 in the US

E741 (1.04) = E770i = 6% e = $1.35/E

i* = 4% e’ = $1.40/E

$10001.35 =

(E770.31)(1.40) = $1,078

E741

Profit = $1,078 - $1,000(1.06) = $18

Uncovered Interest ParityUncovered Interest Parity

$1

1e

(1+i*)e

(1+i*)e’

e

(1+i*)e’(1+i*)e’eeProfit =Profit = - (1+i) = 0- (1+i) = 0

UncoveredUncovered Interest Parity Interest Parity

(1+i*)e’(1+i*)e’

eeProfit =Profit = - (1+i) = 0- (1+i) = 0

Uncovered parity suggests that you shouldn’t EXPECTEXPECT to make money this way!

This is the expectedexpected future exchange rate

i – i* = Expected Change in the Exchange Rate

6% – 4% = 2% (An expected 2% dollar depreciation)

Expected e’ = $1.35/E (1.02) = $1.38

CoveredCovered Interest Parity Interest Parity

You could eliminate all your risk by “locking in” your future exchange rate with a futures contract

Borrow $1,000 in the US, Buy a futures contract for $1,078 at $1.40/E

E741 (1.04) = E770i = 6% e = $1.35/E

i* = 4% FF = $1.40/E

$10001.35 =

(E770.31)(1.40) = $1,078

E741

Profit = $1,078 - $1,000(1.06) = $18

CoveredCovered Interest Parity Interest Parity

(1+i*)(1+i*)FF

eeProfit =Profit = - (1+i) = 0- (1+i) = 0

Covered parity is a zero arbitrage condition between spot and forward rates

This is the futures/forward rate

i – i* = Forward Premium/Discount

Given the 2% interest differential, Forward/Futures Given the 2% interest differential, Forward/Futures should be selling at a 2% premium (= $1.38)should be selling at a 2% premium (= $1.38)

Forward rates as Predictors of Forward rates as Predictors of the Future?the Future?

Forward Premium/Discount = i – i* =

Covered Interest Parity

Expected Percentage Change in Spot Rate

Uncovered Interest Parity

Forward Premium/Discount = Expected Percentage Change in Spot Rate

Currency OptionsCurrency Options With options, you have the right to buy/sell With options, you have the right to buy/sell

currency, but not the requirementcurrency, but not the requirement Call: The right to buy at a specific “strike price”Call: The right to buy at a specific “strike price” Put: The right to sell at a specific “strike price”Put: The right to sell at a specific “strike price”

The option belongs to the buyer of the contract. If The option belongs to the buyer of the contract. If you sell a put, you are REQUIRED to buy if the you sell a put, you are REQUIRED to buy if the holder of the put chooses to exercise the option.holder of the put chooses to exercise the option.

The buyer must pay an up front price for the The buyer must pay an up front price for the contract contract

Reading Options Quotes Reading Options Quotes (Call Option)(Call Option)

Date/Date/

StrikeStrikeOpenOpen HighHigh LowLow SettleSettle Pt Pt

ChgeChgeVolumVolumee

InterestInterest

Feb05Feb05

76007600.0008.0008 .0012.0012 .0006.0006 .0007.0007 +3+3 1212 5050

Mar05Mar05

77007700.0003.0003 .0005.0005 .0002.0002 .0003.0003 -5-5 33 1010

CAD 100,000

Settlement Date and Strike Price

Daily Price Movements (per CAD): .0001 = $10 per contract

Change From Previous Day (in Pips)

Contracts Traded/ Outstanding (000s)

Payout from a CallPayout from a Call

0

0.05

0.1

0.15

0.2

0.9

5 1

1.0

5

1.1

1.1

5

1.2

1.2

5

1.3

1.3

5

1.4

Exchange Rate ($/ E)

Pro

fit per

Euro

Suppose you buy a 30 Suppose you buy a 30 day call on 125,000 day call on 125,000 Euros at a strike price of Euros at a strike price of $1.20$1.20

For spot rates less than For spot rates less than $1.20, the option is $1.20, the option is worthless (“out of the worthless (“out of the money”)money”)

If the spot rate is $1.25, If the spot rate is $1.25, your profit is your profit is

($.05)*($125,000) = ($.05)*($125,000) = $6,250$6,250

Pricing a Call OptionPricing a Call Option

If the future price of a Euro is $1.25 at expiration If the future price of a Euro is $1.25 at expiration (30 days from now) with certainty, the contract (30 days from now) with certainty, the contract guarantees a $6,250 payout in 30 days ($.05 per guarantees a $6,250 payout in 30 days ($.05 per Euro). Suppose the interest rate is currently 5%Euro). Suppose the interest rate is currently 5%

Call Price = Present Value of $6,250 in one Call Price = Present Value of $6,250 in one monthmonth

= $6,250/(1.05) = $5,952.38 (.047 = $6,250/(1.05) = $5,952.38 (.047 per Euro)per Euro)A call option price should be positively related to the (expected) A call option price should be positively related to the (expected)

future exchange rate and negatively related to the interest ratefuture exchange rate and negatively related to the interest rate.

Pricing a Call OptionPricing a Call Option If the future price of a Euro has a 50% chance of If the future price of a Euro has a 50% chance of

decreasing to $1 and a 50% chance of increasing to $1.50 decreasing to $1 and a 50% chance of increasing to $1.50 at expiration (30 days from now). Suppose the interest rate at expiration (30 days from now). Suppose the interest rate is currently 5%is currently 5%

Expected Payout = (.5)($0) + (.5)($.30*125,000) = Expected Payout = (.5)($0) + (.5)($.30*125,000) = $18,750$18,750

Call Price = Present Value of $18,750 in one monthCall Price = Present Value of $18,750 in one month

= $18,750/(1.05) = $17,857.14 (.143 per Euro)= $18,750/(1.05) = $17,857.14 (.143 per Euro)A call option price should be positively related to the variance of A call option price should be positively related to the variance of the exchange rate.the exchange rate.

Black - ScholesBlack - Scholes

Payout from a PutPayout from a Put Suppose you buy a put Suppose you buy a put

on 125,000 Euros at a on 125,000 Euros at a strike price of $1.20strike price of $1.20

For spot rates greater For spot rates greater than $1.20, the option is than $1.20, the option is worthless (“out of the worthless (“out of the money”)money”)

For example, if the spot For example, if the spot rate is $1.15, your profit rate is $1.15, your profit is is

($.05)*($125,000) = ($.05)*($125,000) = $6,250$6,250

0

0.05

0.1

0.15

0.2

0.25

0.9

5

1.0

5

1.1

5

1.2

5

1.3

5

Pricing PutsPricing Puts Consider two investment portfoliosConsider two investment portfolios

Portfolio #1

•Buy a call option for E100 at a strike price of $1.20 (expiration in 1 year)

•Buy a 1 year Treasury with a face value of $120

Portfolio #2

Buy a Put option on E100 at a strike price of $1.20 (expiration of 1 year)

Hold E100 in cash

These two portfolios will generate the same 1 year profit (in $s) These two portfolios will generate the same 1 year profit (in $s) for every possible value of the exchange rate!!for every possible value of the exchange rate!!

Suppose the exchange rate is $1.25/ESuppose the exchange rate is $1.25/E

Portfolio #1



Portfolio #2


Hold E100 in cash

Payout = ($.05)(100) + $120 Payout = $0 + $125

Call Payout

Bond Payout

Put Payout

Value of Euros

Suppose the exchange rate is $1.10/ESuppose the exchange rate is $1.10/E

Portfolio #1



Portfolio #2


Hold E100 in cash

Payout = $0 + $120 Payout = ($.10)(100) + $110

Call Payout

Bond Payout

Put Payout

Value of Euros

Two portfolios with equal returns should have equal costTwo portfolios with equal returns should have equal cost

Portfolio #1



Portfolio #2


Hold E100 in cash

Cost (per Euro)

= Put Price + exchange rate= Call Price +

Strike Price(1+i)

Cost (per Euro)

Put/Call ParityPut/Call Parity

Call Call PricePrice + +

Strike PriceStrike Price(1+i)(1+i)

= Put Price + exchange rate= Put Price + exchange rate

Given the price of a call option, the current exchange rate and the current interest rate, we can price a put.

Currency SwapsCurrency Swaps

Currency swaps are contracts to convert Currency swaps are contracts to convert known income/payment streams from one known income/payment streams from one currency to another – think of them as a currency to another – think of them as a portfolio of forwards with varying portfolio of forwards with varying maturities/strikesmaturities/strikes

As with forward contracts, swaps are As with forward contracts, swaps are individualized and not traded.individualized and not traded.


Suppose that IBM wishes to raise funds Suppose that IBM wishes to raise funds by issuing a 5 year Swiss Franc by issuing a 5 year Swiss Franc denominated Eurobond with a face denominated Eurobond with a face value of CHF 100,000 and fixed annual value of CHF 100,000 and fixed annual coupon payments of 6%. Up front, IBM coupon payments of 6%. Up front, IBM receives CHF 100,000. IBM plans on receives CHF 100,000. IBM plans on using the proceeds to finance domestic using the proceeds to finance domestic operationsoperations


0 Yrs0 Yrs 5 Yrs5 Yrs1 Yrs1 Yrs 2 Yrs2 Yrs 3 Yrs3 Yrs 4 Yrs4 Yrs

IBM Collects CHF 100,000

IBM owes CHF 106,000

IBM owesIBM owesCHF 6,000CHF 6,000

IBM owesIBM owesCHF CHF 6,0006,000



IBM Wishes to hedge IBM Wishes to hedge its currency exposureits currency exposure


0 Yrs0 Yrs 5 Yrs5 Yrs1 Yrs1 Yrs 2 Yrs2 Yrs 3 Yrs3 Yrs 4 Yrs4 Yrs

IBM Sells IBM Sells CHF 100,000 CHF 100,000 @ .844@ .844

IBM buys IBM buys CHF 106,000CHF 106,000@ .836@ .836

IBM buysIBM buysCHF 6,000CHF 6,000@ .845@ .845

IBM buysIBM buysCHF CHF 6,0006,000@ .830@ .830



IBM enters into a swap IBM enters into a swap agreement withagreement with

This swap is very similar to buying/selling six separate futures This swap is very similar to buying/selling six separate futures contracts and is priced in a similar fashioncontracts and is priced in a similar fashion

currency futures and options. spot exchange rates spot transactions are done immediately. a spot...

Documents