Chapter 2 An Introduction
to Forwards and Options
FINA0301 Derivatives
Faculty of Business and Economics
University of Hong Kong
Dr. Huiyan Qiu
1
Chapter Outline
Basic derivatives contracts
• Forward contracts
• Call options
• Put options
Types of positions
• Long / Short position
Graphical representation
• Payoff / Profit diagrams
2
Forward Contracts
Forward contract: a binding agreement
(obligation) to buy/sell an underlying asset in
the future, at a price set today
Today
Expiration
date
3
Forward Contracts
A forward contract specifies
• The features and quantity of the asset to be
delivered
• The delivery logistics, such as time, date, and
place
• The price the buyer will pay at the time of delivery
Futures contracts are the same as forwards in
principle except for some institutional and
pricing differences.
4
Low of the day
High of the day
The open price
Reading Price Quotes
Index futures
Settlement price
Daily change
Open interest
Expiration month
5
Hang Seng Index Futures
Hang Seng Index Futures Daily market report on
January 27, 2012. Source: www.hkex.com.hk
HSI - HANG SENG INDEX FUTURES HK$50 PER INDEX POINT
Contract
Month
Open
Price
Daily Daily Settle- Chg in Contract Contract Volume Open Change
High Low ment
Setl
High
Low
Interest
in OI
Price Price
JAN-12 20,340 20,606 20,340
FEB-12 20,388 20,620 20,381
MAR-12 20,337 20,560 20,337
JUN-12 19,950 20,200 19,950
20,594
20,614
20,558
20,196
+180
+179
+172
+177
20,606
20,620
22,590
20,200
17,780 74,019 33,520 -22,356
18,276 49,911 76,335 +25,553
16,050
1,021 5,884
+2
17,220
179 2,458
+18
All Contracts Total
125,130 118,197 +3,217
6
Payoff and Profit
Payoff for a contract is its value at expiration.
Payoff diagrams show the gross value of a
position at expiration.
Profit for a position in a contract is net value at
expiration of all relevant cash flows.
Forward: (1) zero cash flow at initiation, (2) pay
forward price at expiration, (3) get asset (value
ST) at expiration
For forward contract, payoff = profit
7
Payoff on a Forward Contract
Example: S&R (special and rich) index
Today: Spot price = $1,000
6-month forward price = $1,020
In six months at contract expiration:
Case 1: Spot price = $1,050
• Long position payoff = $1,050 – $1,020 = $30
• Short position payoff = $1,020 – $1,050 = – $30
Case 2: Spot price = $1,000
• Long position payoff = $1,000 – $1,020 = – $20
• Short position payoff = $1,020 – $1,000 = $20
8
Payoff Diagram for Forwards
S&R (special
and rich) index
Today: Spot
price = $1,000
6-month forward
price = $1,020
9
Forward vs. Outright Purchase
Outright purchase:
• Invest $1,000 in index and own the index.
Forward:
• Invest zero, sign the contract
• Invest $1,020 at expiration and own the index.
Same outcome: own the index at expiration.
Why investing $1,000 now results in the same
outcome as investing $1,020 later? Price
indication?
10
Forward vs. Outright Purchase
Forward payoff
Bond payoff
Forward + bond = Spot price at expiration – $1,020 + $1,020
= Spot price at expiration
Figure
Comparison of
payoff after 6
months of a long
position in the
S&R index versus
a forward contract
in the S&R index.
11
Additional Considerations
Type of settlement
• Cash settlement: less costly and more practical
• Physical delivery: often avoided due to
significant costs
Credit risk of the counter party
• Major issue for over-the-counter contracts
• Credit check, collateral, bank letter of credit
• Less severe for exchange-traded contracts
• Exchange guarantees transactions, requires
collateral
12
Call Options
A non-binding agreement (right but not an obligation)
to buy an asset in the future, at a price set today
Preserves the upside potential ( ), while at the same
time eliminating the unpleasant (
) downside (for
the buyer)
The seller of a call option is obligated to deliver
if asked
Today
Expiration date
or
at buyer’s choosing
13
Definition and Terminology
Definition: A call option gives the owner the right
but not the obligation to buy the underlying asset at a
predetermined price during a predetermined time
period
Terminology:
• Strike (or exercise) price: the amount paid by
the option buyer for the asset if he/she decides to
exercise
• Exercise: the act of paying the strike price to buy
the asset
• Expiration: the date by which the option must be
exercised or become worthless
14
Exercise Style
Exercise style: specifies when the option can be
exercised
• European-style: can be exercised only at
expiration date
• American-style: can be exercised at any time
before expiration
• Bermudan-style: Can be exercised during
specified periods
Focus: European-style options.
15
Reading Price Quotes
S&P500 Index options
Expiration
month
Strike price
Option type
“c” for call
“p” for put
16
Hang Seng Index Options
Hang Seng Index Options Daily market report on
top-10 traded options on January 27, 2012.
Source: www.hkex.com.hk
HANG SENG INDEX OPTION HK$ 50 PER INDEX POINT
TOP 10 TRADED (BY VOL) VOLUME O.Q.P. IV%
CLOSE
P JAN-12
20200
3301
17 17
C JAN-12
20600
3145
98 13
C JAN-12
21000
3142
14 16
P JAN-12
20400
2820
43 15
P FEB-12
19600
2570
185 23
C JAN-12
20800
2386
38 14
C JAN-12
20400
2076
231 14
C FEB-12
21400
1893
196 19
P JAN-12
20000
1816
7 19
C FEB-12
21200
1325
256 20
DAILY
HIGH
46
119
15
123
227
45
237
199
44
261
DAILY
OPEN
O.Q.P.
LOW INTEREST CHANGE
11
2069
-42
37
2438
+36
3
2922
+7
22
1322
-78
180
2974
-45
10
2467
+16
99
2022
+91
152
2517
+25
6
2043
-21
202
1550
+37
17
Example: S&R Index
Today:
• call buyer acquires the right to pay $1,000 in six
months for the index, but is not obligated to do so
• call seller is obligated to sell the index for $1,000
in six months, if asked to do so
In six months at contract expiration:
Spot price
$1,100
$900
Buyer’s payoff
$1,100 – $1,000 = $100
$0
Seller’s payoff
$1,000 – $1,100 = ($100)
$0
18
Example: S&R Index (cont’d)
In six months at contract expiration,
• If the spot price is higher than $1,000, the option will
be exercised.
• If the spot price is lower than $1,000, the option
buyer will walk away and do nothing.
• Payoff for buyer = Max [0, spot price – strike price]
Why would anyone agree to be on the seller side?
• The option buyer must pay the seller an initial
premium of $93.81 (option pricing)
• For a forward contract, the initial premium is zero
19
Payoff and Profit for the Buyer
Payoff = Max [0, spot price at expiration – strike price]
Profit = Payoff – future value of option premium
Suppose 6-month risk-free rate is 2%
• If index value in six months = $1,100
• Payoff = max [0, $1,100 – $1,000] = $100
• Profit = $100 – ($93.81 x 1.02) = $4.32
• If index value in six months = $900
• Payoff = max [0, $900 – $1,000] = $0
• Profit = $0 – ($93.81 x 1.02) = – $95.68
20
Diagrams for Purchased Call
Payoff at expiration
Profit at expiration
21
Payoff/Profit of a Written Call
Call writer: the option seller
• To receive the premium for option sold
• To have the obligation to sell if requested
Seller’s payoff and profit is opposite to the buyer
• Payoff = - max [0, spot price at expiration – strike price]
• Profit = Payoff + future value of option premium
The payoff and profit diagram of a written call is the
mirror image of a purchased call, symmetric with
regard to the X-axis
22
Profit Diagram for a Written Call
Figure:
Profit for writer
of 6-month
S&R call with
strike of $1000
versus profit for
short S&R
forward.
23
Put Options
A put option gives the owner the right but not
the obligation to sell the underlying asset at a
predetermined price during a predetermined
time period
The seller of a put option is obligated to buy if asked
Payoff/profit of a purchased (i.e., long) put
• Payoff = max [0, strike price – spot price at expiration]
• Profit = Payoff – future value of option premium
Payoff/profit of a written (i.e., short) put
• Payoff = – max [0, strike price – spot price at expiration]
• Profit = Payoff + future value of option premium
24
Put Option Examples
S&R Index 6-month Put Option
• Strike price = $1,000, Premium = $74.20, 6month risk-free rate = 2%
If index value in six months = $1,100
• Payoff = max [0, $1,000 – $1,100] = $0
• Profit = $0 – ($74.20 x 1.02) = – $75.68
If index value in six months = $900
• Payoff = max [0, $1,000 – $900] = $100
• Profit = $100 – ($74.20 x 1.02) = $24.32
25
Profit Table for Long Put Position
Table: Profit after
6 months from a
purchased 1000strike S&R put
option with a
future value of
premium of $75.68.
26
Profit Diagram for a Long Put Position
Figure:
Profit on a
purchased S&R
index put with
strike price of
$1000 versus a
short S&R index
forward.
27
A Few Items to Note
A call option becomes more profitable when the
underlying asset appreciates in value
A put option becomes more profitable when the
underlying asset depreciates in value
Moneyness of option:
• In-the-money: positive payoff if exercised
immediately
• At-the-money: zero payoff if exercised immediately
• Out-of-the money: negative payoff if exercised
immediately
28
Summary on Forward & Option
Table: Maximum possible profit and loss at maturity
for long and short forwards and purchased and
written calls and puts.
29
Summary on Forward & Option
Figure:
Profit diagrams
for the three basic
long positions:
long forward,
purchased call,
and written put.
(Long w.r.t. the
underlying asset.)
30
Summary on Forward & Option
Figure:
Profit diagrams
for the three
basic short
positions: short
forward, written
call, and
purchased put.
(Short w.r.t. the
underlying
asset.)
31
Summary on Forward & Option
Table: Forwards, calls, and puts at a glance: a
summary of forward and option positions.
32
Options and Insurance
Homeowner’s insurance as a put option
Figure:
Profit from
insurance
policy on a
$200,000
house.
$25,000
deductible.
33
Example: Equity Linked CDs
The 5.5-year CD promises to repay initial invested
amount and 70% of the gain in S&P 500 index
• Assume $10,000 invested when S&P 500 = 1300
• Final payoff =

$ 10 , 000   1  0 . 7  max


 S final

 1 
0,

 1300

• Where S final = value of the
S&P 500 after 5.5 years
34
End of the Notes!
35