Lecture Note
Currency Futures and Options
-
University:
California State University, Northridge -
Course:
FIN 639 | Seminar in Financial Problems Academic year:
2024
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Views:
178
Pages:
28
Author:
Fennaumg
Currency Futures and
Options
(chapter 7) The following sections in chapter 7 are not
required for the exam:
- American option-pricing relationships
- European option-pricing relationships
- Binomial option-pricing model
- European option-pricing formula
- Empirical tests of currency options
2 International Financial Management
Futures Contracts: Preliminaries
A futures contract is like a forward contract:
- It 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
3 International Financial Management
Futures Contracts: Preliminaries
Standardizing Features:
- Contract Size
- Delivery Month
- Daily resettlement
Initial Margin (about 4% of contract value, cash or T-bills
held in a street name at your brokers).
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Daily Resettlement: An Example
Consider a long position in the CME
Euro/U.S. Dollar contract.
It is written on €125,000 and quoted in $ per €.
The futures price is $1.30 per € the maturity is
3 months.
At initiation of the contract, the long has in the
margin account $20,000.
5 International Financial Management
Daily Resettlement: An Example
The futures price is $1.30 per €
If tomorrow, the futures rate closes at $1.2 per €., then your
position’s value drops.
Your original agreement was to buy €125,000 and pay
125,000 x1.3=$162,500
Now €125,000 is worth € 125,000 x1.2=$150,000
You have lost $12,500 = € 125,000 x (1.20-1.3)
The $12,500 comes out of your $20,000 margin account
6 International Financial Management
Daily Resettlement: An Example
With futures contracts, we have daily
resettlement of gains and losses rather than one
big settlement at maturity.
Every trading day:
- If the price goes down, the long pays the short.
- If the price goes up, the short pays the long.
After the daily resettlement, each party has a
new contract at the new price with one-dayshorter maturity.
7 International Financial Management
Toting Up
At
the end of his adventure, our investor has three ways of
computing his gains and losses:
1. Sum of daily gains and losses.
– $7,500 = $1,250 – $1,250 – $3,750 – $1,250 – $2,500
2. Contract size times the difference between initial contract
price and last settlement price.
– $7,500 = ($1.24/€ – $1.30/€) × €125,000
3. Ending balance on the account minus beginning balance on
the account, adjusted for deposits or withdrawals.
– $7,500 = $2,750 – ($6,500 + $3,750)
8 International Financial Management
Forward vs. Futures Contracts
Basic differences:
- Trading Locations
- Contractual size
- Settlement
- Expiration date
- Delivery
9 International Financial Management
Interest Rate Parity Carefully Defined
No matter how you quote the exchange rate ($
per ¥ or ¥ per $) to find a forward rate, increase
the dollars by the dollar rate and the foreign
currency by the foreign currency rate:
1 + i¥
F¥/$ = S¥/$ ×
1 + i$
or
10
1 + i$
F$/¥ = S$/¥ × 1 + i
¥ International Financial Management
Currency Futures Markets
The CME Group (formerly Chicago Mercantile Exchange) is by
far the largest currency futures market.
CME hours are 7:20 a.m. to 2:00 p.m. CST Monday-Friday.
Extended-hours trading takes place Sunday through Thursday
(local) on GLOBEX i.e. from 5:00 p.m. to 4:00 p.m. CST the next
day.
The Singapore Exchange offers interchangeable contracts.
There are other markets, but none are close to CME and SIMEX
trading volume.
Expiry cycle: March, June, September, December.
The delivery date is the third Wednesday of delivery month.
The last trading day is the second business day preceding the
delivery day.
11 International Financial Management
Options Contracts: Preliminaries
An option gives the holder the right, but not the
obligation, to buy or sell a given quantity of an asset in the
future, at prices agreed upon today.
Calls vs. Puts
- Call options gives the holder the right, but not the
obligation, to buy a given quantity of some asset at
some time in the future, at prices agreed upon today.
- Put options gives the holder the right, but not the
obligation, to sell a given quantity of some asset at
some time in the future, at prices agreed upon today.
12 International Financial Management
Options Contracts: Preliminaries
The premium: the price of an option that the writer charges
the buyer.
For currency options the strike price is the exchange rate at which
the option holder can buy or sell the contracted currency
13 International Financial Management
Options Contracts: Preliminaries
Contract features:
- strike/exercise price
- size of the contract
- delivery month
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.
14 International Financial Management
Call Option
In-the-money
- The exercise price is less than the spot price of the
underlying asset.
At-the-money
- The exercise price is equal to the spot price of the
underlying asset.
Out-of-the-money
- The exercise price is more than the spot price of the
underlying asset.
15 International Financial Management
Put Option
In-the-money
- The exercise price is greater than the spot price of the
underlying asset.
At-the-money
- The exercise price is equal to the spot price of the
underlying asset.
Out-of-the-money
- The exercise price is lower than the spot price of the
underlying asset.
16 International Financial Management
Basic Option Pricing
Relationships at Expiration
At expiration, 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 ST – 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 - ST.
If the put is out-of-the-money, it is worthless.
PaT = PeT = Max[E - ST, 0]
17 International Financial Management
EXAMPLE
You buy a call on one € at $1, expiring on June
30th. You are long the call.
The counter party is the writer of the call; he has
the potential obligation to deliver one Euro to you
at $1 if you want him to (i.e. if you exercise the
option)
If ST = $1.05 or $1.1, you will exercise your right
and buy € at $1, and make 5 or 10¢, respectively.
If ST < $1you will not exercise.
18 International Financial Management
Basic Option Profit Profiles
CaT = CeT = Max[ST - E, 0]
profit
-C
E
loss
19
E+C
ST International Financial Management
Basic Option Profit Profiles
CaT = CeT = Max[ST - E, 0]
profit
C
E
loss
20
E+C
ST International Financial Management
Basic Option Profit Profiles
PaT = PeT = Max[E - ST, 0]
profit
E-p
loss
21
ST
E
-p International Financial Management
Basic Option Profit Profiles
PaT = PeT = Max[E-ST , 0]
profit
p
E-p
loss
22
E
ST International Financial Management
Option premium
Intrinsic Value
- The difference between the exercise price of the option
and the spot price of the underlying asset or zero.
Speculative Value
- The difference between the option premium and the
intrinsic value of the option.
Option
Premium
=
Intrinsic
Value
23
+
Speculative
Value International Financial Management
The determinants of time value
of option prices
a.
value rises with longer time to expiration.
b.
value rises when greater volatility in the exchange rate.
c.
Value is complicated by both the home and foreign interest
rates.
24 International Financial Management
Example
For a call on Euro with strike price k = US¢/€ 91.5.
The intrinsic value is 5¢ if the spot rate is 96.5¢.
Time value is 1¢ if the market price is 6¢.
The intrinsic value is 0 if the spot rate is 88¢ (or any other
price equal to or below 91.5¢). Time value is 2¢ if market
price is 2.
For put with strike price k = US¢/€ 91.5.
The intrinsic value is 0 if the spot rate is 96.5¢.
Time value is 2 if the market price is 2¢.
The intrinsic value is 3.5¢ if the spot rate is 88¢. Time
value is 1.5¢ if market price is 5.
25 International Financial Management
Example
The call premium per British pound on February 1 is $0.011; the
expiration date is June, and the strike price is $1.6. You anticipates that
the spot rate will increase to $1.7 by May1. If your expectation proves
correct, what should be your dollar profit from speculating one pound
call option (31,250 units per contract)?
Buy one call option on February 1
Exercise the option on May 1
Sell the pound on May 1
Net profit per pound
-$0.011 per pound
-$1.60 per pound
+$1.70 per pound
+$0.089
Net profit per contract: £31,250x $0.089=$2,781.25
26 International Financial Management
Black–Scholes Pricing Formulae
The Black-Scholes formulae for the price of a European
call and a put written on currency are:
c = S0e
− riT
× N(d1 ) − Ee
− r$T
× N(d 2 )
p = [ E × N(−d 2 ) − FT × N(−d1 )]e
− r$T
1 2
+ σ T
2
σ T
FT
ln
E
d1 =
d 2 = d1 − σ T
N(d) = Probability that a standardized, normally distributed,
random variable will be less than or equal to d.
27 International Financial Management
Learning outcomes
• Discuss the similarities and differences between forward and futures.
• Define the call and put options; the obligations or/and options of the buyers and
sellers
• Explain the differences between European and American options
• Know the basic option pricing relationships at expiration
• Basic option profit profiles (all four of them)
• Know how to calculate the intrinsic value and time value of the options
• Know how to calculate the profit/loss of long/short call and put speculative positions
(for example, see the numerical examples done in class)
•
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