Options and Speculative Markets
2004-2005
Introduction
Professor André Farber
Solvay Business School
Université Libre de Bruxelles
1.Introduction
•
Outline of this session
1. Course outline
2. Derivatives
3. Forward contracts
4. Options contracts
5. The derivatives markets
6. Futures contracts
August 23, 2004
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• Reference:
John HULL Options, Futures and Other Derivatives, Fifth edition,
Prentice Hall 2003
• Copies of my slides will be available on my website:
www.ulb.ac.be/cours/solvay/farber
• Grades:
– Cases: 20%
– Final exam: 80%
August 23, 2004
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Course outline
Introduction
Case 2
Pricing Forwards and Futures
IR Options 2
Using Futures
IR Options 1
IR Derivatives
Using Options
Swaps
Inside Black Scholes
Case 1
Pricing Options
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Derivatives
• A derivative is an instrument whose value depends on the value of other
more basic underlying variables
• 2 main families:
• Forward, Futures, Swaps
• Options
• = DERIVATIVE INSTRUMENTS
• value depends on some underlying asset
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Forward contract: Definition
• Contract whereby parties are committed:
– to buy (sell)
– an underlying asset
– at some future date (maturity)
– at a delivery price (forward price) set in advance
•
•
The forward price for a contract is the delivery price that would be applicable to the contract
if were negotiated today (i.e., it is the delivery price that would make the contract worth
exactly zero)
The forward price may be different for contracts of different maturities
•
•
•
•
Buying forward = "LONG" position
Selling forward = "SHORT" position
When contract initiated: No cash flow
Obligation to transact
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Forward contract: example
•
•
•
•
•
Underlying asset:
Gold
Spot price:
$380 / troy ounce
Maturity:
6-month
Size of contract:
100 troy ounces (2,835 grams)
Forward price: $390 / troy ounce
Profit/Loss at maturity
Spot price
350
370
390
410
430
Buyer (long)
-4,000
-2,000
0
+2,000
+4,000
Seller (short)
+4,000
+2,000
0
-2,000
-4,000
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Forward contract: Gains and losses
LONG
Gain
SHORT
Gain
0
0
F
Loss
August 23, 2004
S
F
T
S
T
Loss
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Options contracts: Definition
•
•
•
•
•
A call (put) contract gives to the owner
- the right :
- to buy (sell)
- an underlying asset
- on or before some future date (maturity)
• on : "European" option
• before: "American" option
• - at a price set in advance (the exercise price or striking price)
• Buyer pays a premium to the seller (writer)
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Option contracts: example
•
•
•
•
•
•
Underlying asset:
Spot price:
Maturity:
Size of contract:
Exercise price:
Premium
Gold
$380 / troy ounce
6-month
100 troy ounces (2,835 grams)
$390 / troy ounce
Call $30 / troy ounce
Put $34 / troy ounce
Spot price
350
370
390
410
430
Long call
-3,000
-3,000
-3,000
-1,000
+1,000
Seller (short)
+3,000
+3,000
+3,000
+1,000
-1,000
Long put
+600
-1,400
-3,400
-3,400
-3,400
Short put
-600
+1,400
+3,400
+3,400
+3,400
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European call option: Terminal payoff
•
•
•
•
Exercise option if, at maturity,
ST > K
then : CT = ST - K
otherwise: CT = 0
•
CT = MAX(0, ST - K)
Value at maturity
ST
K
Striking
price
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Stock
price
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European call option: Profit at maturity
Profit at maturity
Profit at maturity
Premium
K
K
- Premium
August 23, 2004
Striking
price
S
ST
Stock
price
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T
European put option
•
•
•
Exercise option if, at maturity, ST <
K
then PT = K - ST
otherwise PT = 0
•
Value / profit at maturity
Value
PT = MAX(0, K - ST )
Profit
K
ST
Premium
Stock
price
Striking
price
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Put, call and forwards: put call parity
Profit
Long call
Long forward
K
Short put
ST
+ Call – Put = + Forward
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Derivatives Markets
• Exchange traded
– Traditionally exchanges have used the open-outcry system, but
increasingly they are switching to electronic trading
– Contracts are standard there is virtually no credit risk
• Over-the-counter (OTC)
– A computer- and telephone-linked network of dealers at financial
institutions, corporations, and fund managers
– Contracts can be non-standard and there is some small amount of credit
risk
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Global Market Size
Notional amount billions US$
Dec. 2002
Dec. 2003
OTC Derivatives
141,679
197,177
- Foreign exchanges contracts
18,460
24,484
- Interest rate contracts
121,799
141,991
2,799
3,787
923
1,040
-Other
21,952
25,510
Organized Exchanges
23,675
46,733
- IR Futures
9,956
13,123
- IR Options
11,759
20,793
- Currency Futures
47
80
- Currency Options
27
38
- Equity Index Futures
326
502
- Equity Index Options
1,700
2,197
- Equity-linked contracts
- Commodity contracts
August
23, 2004
Source:
BIS Quarterly Review, June 2004 – www.bis.org
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Evolution of global market
250,000
Principal Amount USD Billions
200,000
150,000
100,000
50,000
0
1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003
Markets
August 23, 2004
OTC
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Main Derivative markets
•
Europe
•
United States
Eurex:http://www.eurexchange.com/
Liffe: http://www.liffe.com
Matif : http://www.matif.fr
Chicago Board of Tradehttp: //www.cbot.com
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Why use derivatives?
•
•
•
•
•
To hedge risks
To speculate (take a view on the future direction of the market)
To lock in an arbitrage profit
To change the nature of a liability
To change the nature of an investment without incurring the costs of selling
one portfolio and buying another
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Forward contract: Cash flows
• Notations
ST Price of underlying asset at maturity
Ft Forward price (delivery price) set at time t<T
Initiation
Maturity T
Long
0
ST - Ft
Short
0
Ft - ST
• Initial cash flow = 0 :delivery price equals forward price.
• Credit risk during the whole life of forward contract.
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Forward contract: Locking in the result before
maturity
• Enter a new forward contract in opposite direction.
• Ex: at time t1 : long forward at forward price F1
• At time t2 (<T): short forward at new forward price F2
• Gain/loss at maturity :
• (ST - F1) + (F2 - ST ) = F2 - F1 no remaining uncertainty
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Futures contract: Definition
• Institutionalized forward contract with daily settlement of gains and losses
• Forward contract
– Buy  long
sell 
short
• Standardized
– Maturity, Face value of contract
• Traded on an organized exchange
– Clearing house
• Daily settlement of gains and losses (Marked to market)
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Example : Gold Futures (Comex – Nymex.com)
• Trading unit: 100 troy ounces (2,835 grams)
• July 3, 2002
July
Aug
Oct
Dec
Fb03
June
Aug
Settle
312.80
313.20
314.30
315.20
316.00
317.70
318.70
Open interest
21
96,313
5,937
31,110
7,566
5,457
4,014
Source: Wall Street Journal
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Gold futures: contract specifications
•
Trading Months
Futures: Trading is conducted for delivery during the current calendar month, the next two calendar months, any February,
April, August, and October thereafter falling within a 23-month period, and any June and December falling within a 60month period beginning with the current month.
Options: The nearest six of the following contract months: February, April, June, August, October, and December. Additional
contract months - January, March, May, July, September, and November - will be listed for trading for a period of two
months. A 24-month option is added on a June/December cycle.
The options are American-style and can be exercised at any time up to expiration.
On the first day of trading for any options contract month, there will be 13 strike prices each for puts and calls.
Price Quotation
Futures and Options: Dollars and cents per troy ounce. For example: $301.70 per troy ounce.
Minimum Price Fluctuation
Futures and Options: Price changes are registered in multiples of 10¢ ($0.10) per troy ounce, equivalent to $10 per contract. A
fluctuation of $1 is, therefore, equivalent to $100 per contract.
Maximum Daily Price Fluctuation
Futures: Initial price limit, based upon the preceding day’s settlement price is $75 per ounce. Two minutes after either of the
two most active months trades at the limit, trades in all months of futures and options will cease for a 15-minute period.
Trading will also cease if either of the two active months is bid at the upper limit or offered at the lower limit for two minutes
without trading.
Trading will not cease if the limit is reached during the final 20 minutes of a day’s trading. If the limit is reached during the
final half hour of trading, trading will resume no later than 10 minutes before the normal closing time.
When trading resumes after a cessation of trading, the price limits will be expanded by increments of 100%.
Options: No price limits.
Last Trading Day
Futures: Trading terminates at the close of business on the third to last business day of the maturing delivery month.
Options: Expiration occurs on the second Friday of the month prior to the delivery month of the underlying futures contract.
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Futures: Daily settlement and the clearing house
• In a forward contract:
– Buyer and seller face each other during the life of the contract
– Gains and losses are realized when the contract expires
– Credit risk
BUYER

SELLER
• In a futures contract
– Gains and losses are realized daily (Marking to market)
– The clearinghouse garantees contract performance : steps in to take a
position opposite each party
BUYER  CH
 SELLER
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Futures: Margin requirements
• INITIAL MARGIN : deposit to put up in a margin account by a person
entering a futures contract
• MAINTENANCE MARGIN : minimum level of the margin account
• MARKING TO MARKET : balance in margin account adjusted daily
LONG(buyer)
+ Size x (Ft+1 -Ft)
SHORT(seller)
-Size x (Ft+1 -Ft)
• Equivalent to writing a new futures contract every day at the new futures
price
• (Remember how to close of position on a forward)
• Note: timing of cash flows different
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Example of a Futures Trade
• An investor takes a long position in 2 December gold futures
contracts on June 5
–
–
–
–
contract size is 100 oz.
futures price is US$400
margin requirement is US$2,000/contract (US$4,000 in total)
maintenance margin is US$1,500/contract (US$3,000 in total)
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A Possible Outcome
Day
Futures
Price
(US$)
Daily
Gain
(Loss)
(US$)
Cumulative
Gain
(Loss)
(US$)
400.00
August 23, 2004
Margin
Account Margin
Balance
Call
(US$)
(US$)
4,000
5-Jun 397.00
.
.
.
.
.
.
(600)
.
.
.
(600)
.
.
.
3,400
.
.
.
13-Jun 393.30
.
.
.
.
.
.
(420)
.
.
.
(1,340)
.
.
.
2,660 + 1,340 = 4,000
.
.
.
.
.
< 3,000
19-Jun 387.00
.
.
.
.
.
.
(1,140)
.
.
.
(2,600)
.
.
.
2,740 + 1,260 = 4,000
.
.
.
.
.
.
26-Jun 392.30
260
(1,540)
5,060
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0
.
.
.
0
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Futures Contracts Example: Barings
•
•
•
•
Long position on 20,000 Nikkei 225 Futures
1 index pt = Yen 1,000 = $ 10
If Nikkei 225 = 20,000
Size of contract = $ 200,000  position =$ 4,000 mio
• Date
• 30.12.94
• 25.02.95
Nikkei 225
19,723
17,473  F = - 2,250
• Loss =  F  $/pt  # contracts
•
= (-2,250)  ($ 10)  (20,000) = $ 450,000,000
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