Currency Derivatives
(or chapter 7)
1
Agenda
 How forex futures quoted & used for speculation?
 Futures vs. forwards?
 How forex options are quoted?
 Speculate w/ forex options.
 Distinction b/n buying & writing options?
 How forex options are valued?
2


Forex Futures
Future delivery of standard amount of currency @ fixed time &
price. Traded @ Chicago Mercantile Exchange (CME).
Specifications:
•
•
•
•
•
Size –notional principal, in even multiple.
Method of stating exchange rates – “American terms” used.
Maturity date –mature on 3rd Wed/ 01, 03, 04, 06, 07, 09, 10, or 12.
Last trading day – contracts may trade through 2nd business day
prior to maturity.
Collateral & maintenance margins –purchaser/trader must deposit
initial margin or collateral.
– Daily marked-to-market
• Settlement
– round turn fee.
• Use of a clearing house as a counterparty
3
Futures Speculation
500,000 New Mexican pesos.
Maturity
Open
High
Low
Settle
Change
High
Low
Open
Interest
Mar
.10953
.10988
.10930
.10958
---
.11000
.09770
34,481
June
.10790
.10795
.10778
.10773
---
.10800
.09730
3,405
Sept
.10615
.10615
.10610
.10573
---
.10615
.09930
1,4181
Source: Wall Street Journal, February 22, 2002, p.C13
Short Position – believes that the value of the Peso will fall
Long Position - believes that the value of the Peso will rise
Value at maturity (Short) = - Principal  (Spot – Future)
= -PS 500,000  ($0.09500/ PS - $.10958/ PS) = $7,290,
assuming spot rate of $.09500/Ps @ maturity.
Value at maturity (Long) = Principal  (Spot – Forward)
= PS 500,000  ($0.11000/ PS - $.10958/ PS) = $210,
assuming spot rate of $.11000/Ps @ maturity.
4
Forex Futures vs. Forwards
Characteristic
Foreign Currency Futures
Forward
Contract Size
Standardized
any size desired
Maturity
fixed maturities
Location
organized exchange
any maturity up
up to a year
b/n individuals &
banks
Pricing
open outcry
bid/ask quotes
Margin/Collateral
daily marked to market
no collateral
Settlement
rarely delivered, settlement
through offsetting
contract delivered,
can offset position
Fees
single commission for purchase& sell
bid/ask spread
Trading hours
exchange hours
24 hours
Counterparties
through clearing house
direct contact
Liquidity
very liquid
liquid, relatively
5
large market
Initial Margin Requirements
 Held as collateral by broker.
 Usually 2-4% of contract value.
 Margin amount same for short & long positions.
 Buyer holds a long position (seller – short).
 If settlement price higher than yesterday, buyer has a


positive settlement for the day.
Long position now worth more.
Exact opposite for seller (zero-sum game).
6
Open Interest
•Open Interest refers to the
number of contracts
outstanding for a particular
delivery month.
•Initially open interest is zero.
•Increases over time, until
positions are liquidated.
•Total open interest is the total
number of outstanding
positions in all the delivery
months of a futures market.
http://www.activetradermag.com/futuresbasics.htm
•Liquidity = at least 5,000
outstanding contracts.
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Reversing Trades
 Rare in forward markets –90% of all contracts lead to

delivery.
Common in futures markets – only 1% of contracts
lead to delivery!
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Forex Option

Gives right but not obligation to buy/sell amount of currency
@ fixed price for given time period
• Call – buyer has right to purchase
• Put – buyer has right to sell
• Buyer = holder & seller = writer.

Two option types

Price elements
• American: may exercise during life of option.
• European: may not exercise until maturity.
• Strike (exercise price): exchange rate @ which foreign currency
•
•
can be purchased/ sold.
Premium, price of option
Spot rate
9
Forex Options
 May be classified as:
• At-the-money (ATM): exercise price = spot rate.
• In-the-money (ITM) options profitable, excluding
premium, if exercised immediately.
• Out-of-the-money (OTM) options not profitable,
excluding premium, if exercised immediately.
 Markets for derivatives:
• OTC Market
• Organized exchanges - Chicago Mercantile and the
Philadelphia Stock Exchange
– Option Clearinghouse Corporation
10
Futures Contracts vs. Options
 Futures Contract – you’ve agreed to
purchase/sell the contract. No backing out. Can
offset/ exit by buying/selling to someone else.
• Buy = long; sell = short.
 Option – contract that gives you the right but not
the obligation to purchase/sell something at prespecified terms. No commitment.
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Forex Options Markets
 Swiss Franc options (WSJ)
Each option = 62,500 Swiss francs.
Calls - Last
Options &
Underlying
58.51
58.51
58.51
58.51
58.51
58.51
58.51
Strike Price
56
56 1/2
57
57 1/2
58
58 1/2
59
Aug
--1.13
0.75
0.71
0.50
0.30
Sep
----1.05
-0.66
Puts - Last
Dec
2.76
-1.74
-1.28
-1.21
Aug
0.04
0.06
0.10
0.17
0.27
0.50
0.90
Sep
0.22
0.30
0.38
0.55
0.89
0.99
1.36
Dec
1.16
-1.27
-1.81
---
 Call premium: SF 62,500 x $0.0050/SF = $312.50.
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Speculation
 Assume spot rate: $0.5851/SF, 6m forward: $0.5760/SF.
 Spot market
• $100,000. Expect six month spot SF $0.6000/SF.
• Step 1: purchase SF 170,910.96 @ spot $0.5851/SF.
• Step 2: sell at target spot rate of $0.60/SF.
 Forward market
• Step 1: Buy forward SF173,611.11 x $0.576/SF=
$100,000.
• Step 2: In 6m, fulfill forward & sell proceeds in spot
market Sfr173,611.11 x $0.6000/Sfr = $104,166.67.
 Options market
• Long Call, Short Call, Long Put, Short Put.
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For Example…
 Suppose that:
• you have $10 m.
• Wish to speculate on Euro
• S = $ 0.885/ EUR, F30 = $ 0.900/ EUR.
– You expect S30 = $ 0.844/ EUR (EUR depreciates).
– Arbitrage strategy?
– You expect S30 = $ 0.944/ EUR (EUR appreciates).
– Arbitrage strategy?
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Profit & Loss Buyer of Call (Long Call)
ATM
Strike price
Profit
(US cents/SF)
CeT = Max[ST - E, 0]
OTM
ITM
+ 1.00
+ 0.50
0
- 0.50
Unlimited profit
57.5
58.0
58.5
59.0
59.5
Spot price
(US cents/SF)
Limited loss
Break-even price
- 1.00
Loss
Profit = Spot rate – (Strike price + Premium)
Profit = ? if Spot = $ 0.595/ SF.
15
Profit & Loss Writer of Call (Short Call)
ATM
Strike price
Profit
(US cents/SF)
CeT = Max[ST - E, 0]
+ 1.00
+ 0.50
0
Break-even price
Limited profit
57.5
58.0
58.5
- 0.50
59.0
59.5
Spot price
(US cents/SF)
Unlimited loss
- 1.00
Loss
Profit = Premium – (Spot rate - Strike price).
Profit = ? if Spot = $ 0.595/ SF.
16
Profit & Loss for Buyer of Put (Long Put)
“At the money”
Strike price
Profit
(US cents/SF)
“In the money”
PaT=PeT=Max[E - ST, 0]
“Out of the money”
+ 1.00
+ 0.50
0
Profit up
to 58.0
57.5
58.0
58.5
59.5
Spot price
(US cents/SF)
Limited loss
- 0.50
- 1.00
59.0
Break-even
price
Loss
Profit = Strike price – (Spot rate + Premium)
Profit = ? if Spot = $ 0.575/ SF.
17
Profit & Loss for Writer of Put (Short Put)
“At the money”
Profit
(US cents/SF)
Strike price
PaT=PeT=Max[E - ST, 0]
+ 1.00
+ 0.50
Break-even
price
Limited profit
0
57.5
58.0
58.5
59.0
59.5
Spot price
(US cents/SF)
- 0.50
- 1.00
Unlimited loss
up to 58.0
Loss
Profit = Premium – (Strike price - Spot rate)
Profit = ? if Spot = $ 0.575/ SF.
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For Example…

Suppose that:
•
•
•
•
•
You wish to speculate on fall of Yen vs. $.
Current S = Yen 120/ $ (or $.00833/Yen).
Maturity: 90 days.
Expected S90 = Yen 140/$ (or $.00714).
Two options available:
Call on Yen
Put on Yen
– Strike:
– Premium:
Yen 125/$
(or $.008/ Yen)
$.00046
Yen 125/$.
(or $.008/ Yen)
$.00003
1. What option to buy?
2. Break even price on option of choice?
3. If S= Yen 140/ $, what is net profit?
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Option Pricing
 Market value = Time value + Intrinsic Value
 Intrinsic Value –gain if option exercised

immediately. Will reach zero when the option is
OTM. At maturity, option value = intrinsic value.
Time Value – reflects a gamble that the option might
be more profitable (more in-the-money) as time
passes (i.e. before time of expiry).
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Market-, Time- & Intrinsic Value
Option Premium
(US cents/£)
Strike Price of $1.70/£
-- Valuation on first day of 90-day maturity --
6.0
5.67
Total value
5.0
4.00
4.0
3.30
3.0
2.0
1.67
Time value
Intrinsic
value
1.0
0.0
1.66
1.67
1.68
1.69
1.70
1.71
1.72
1.73
1.74
Spot rate ($/£)
European Call on Brit Pound
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Option Volatility
 Standard deviation of daily % changes in underlying
exchange rate, usually stated per annum, e.g. 12.6 %.
• Can obtain daily volatility 12.6%  12.6%  0.66%
365
19.105
 Volatility estimates:
• Historic.
• Forward-looking.
• Implied.
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Replicating Portfolio Evaluation







Suppose US$-EUR rate is S0($/EUR) = $1.
S1($/ EUR) is $1.10 or $0.90.
Consider call w/ K=$1/EUR (exercise price).
Can replicate payoffs of call w/ levered position in EUR.
Borrow PV $.90 today & buy1 EUR.
Net payoff: $0.20 or $0.
1
$.90 
$.
90

Portfolio value: $1 
so option value:C0   $1 
2 
(1  i$ )
S0($/EUR) S1($/EUR) C1($/EUR)
(1  i$ ) 
Debt
Portfolio
$1.10
$0.10
-$0.90
$0.20
$0.90
$0
-$0.90
$0.00
$1
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Rogue Trading: Good Fellas…
 Nick Leeson @ Barings.
• 1995, managed to bankrupt Barings Brothers (UK).
 John Rusnak @ Allied Irish Bank.
• 2002, lost $691 m on behalf of Allied Irish Bank
(Baltimore office).
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Things to remember
 Futures terminology.
 Futures vs. Forwards.
 Speculation
• In spot & forward markets.
• In option markets.
 How forex options are quoted?
 Distinction b/n buying & writing options.
 How forex options are valued?
25