Put and Call Options

1
Chapter 11

• Put and Call Options

2
Call Options

• A call option is the right to buy an underlying
  security at an exercise (strike) price during a
  stated time interval.
• C Market value of the call option.
• P Market value of the underlying asset.
• E Exercise price (strike price).

3
Expiration
0
Would like to find value here
But first need to determine value here
4
Value of call option at expiration, E 100 P lt
E P E P gt E e.g., P 90 P 100 P 110 C
0 C 0 C P E e.g., C 10 out-of-the-mone
y at-the-money in-the-money
5
Arbitrage Guarantees That C P E
If C lt P - E at expiration Suppose P 110, E
100, C 6. Arbitrage Buy Call -6 Exercise -10
0 Sell Underlying 110 Arbitrage Profit 4
6
Case of C gt P E
Suppose P 110, E 100, C
17. Arbitrage Write Call 17 Exercised 100 Bu
y Underlying -110 Arbitrage Profit 7
7
Value of call option before expiration, E
100 P lt E P E P gt E e.g., P 90 P 100 P
110 C gt 0 C gt 0 C gt P E e.g., C gt 10
8
Call Option Bounds
C
P
P E
Arbitrage
Feasible call prices
Arbitrage
P
E
9
Arbitrage if C gt P
Time 0 Write Call C Buy Underlying -P C P gt
0 Expiration
P lt E P E P gt E Sell Underlying P P E Call
Exercised E Net P E E
10
Profit Profiles
Expiration
0
Determine Profit or Loss Overlooking Dividends
and Interest
Take a position
Close entire position
11
Expiration
0
Buy or Call-4
Close Exercise if in-money. Let expire if
out-of-money.
12
Profits or Losses for Call Buyer
Price of underlying at expiration 98 100 102 104
Buy call -4 Exercise call at expiration Sell
underlying acquiredfrom exercise Net profit -
C -4 Net profit
C E P -2 0

• -4
• - 4

-4 -100 102
-4 -100 104
13
Profit Profile for Buying a Call

Call in-money
Call out-of-money
Profit
Buy Call
P at Expiration
100
0
E
104
-Loss
-4
14
Profits or Losses for Call Writer
Price of underlying at expiration 98 100 102 104
Write call 4 Sell underlying Buy underlying
Net profit C Net profit C E P
2 0
4 100 -102
4 100 -104

• 4 4

15
Profit Profile for Writing a Call


Call in-money
Call out-of-money
Profit
Profit
4
P at Expiration
P at Expiration
100
0
0
E
104
104
-Loss
-Loss
Write Call
16
Profits or Losses from Writing a Covered Call
Price of underlying at expiration 98 100 102 104
Buy underlying -100 Write call 4 Sell
underlying at exerciseprice when call is
exercised Sell underlying at market 100price Ne
t profit 4
-100 4 100 4
-100 4 100 4

• -100
• 4
• 98
• 2

17
Profit Profile for Writing a Covered Call Option

Buy underlying security
Call in-money
Call out-of-money
Profit
C
?
Write covered call
100
Underlying asset at expiration
0
E
-Loss
18
Profit Profile for Call Option
Profit
Buy underlying security
Call in-money
Call out-of-money
Write call
4
Buy call
100
Underlying asset at expiration
0
E
104
-4
Loss
19
Put Option
A put option is the right to sell the underlying
security at an exercise price during a stated
time interval.
Expiration
0
First, find value at expiration
20
Put Options
Value of put option at expiration, E 100 P lt
E P E P gt E e.g., P 90 P 100 P 110 Put
E P Put 0 Put 0 e.g., Put
10 in-the-money at-the-money out-of-money
21
If P lt E, There is Arbitrage unless Put E P
Case of Put lt E P
Suppose P 90, E 100, Put
6. Arbitrage Buy Put -6 Exercise 100 Buy
Underlying -90 Arbitrage Profit 4
22
Case of Put gt E P
Suppose P 90, E 100, Put
17. Arbitrage Write Put 17 Exercised -100 Sel
l Underlying 90 Arbitrage Profit 7
23
Value of put option before expiration, E 100
P lt E P E P gt E e.g., P 90 P 100 P
110 Put gt E P Put gt 0 Put gt 0 e.g., Put
10 in-the-money at-the-money out-of-money
24
Profits or Losses for Buying a Put Option
Price of underlying at expiration 94 97 100 104
Buy put -3 Buy underlying Exercise put
Net profit Put
-3 -3 Net profit Put E P 3
0
-3
-3 -3 -94 -97 100 100
25
Profit Profile for Put Option
Profit
Put in-money
Put out-of-money
Buy put
100
Underlying asset at expiration
0
E
97
-3
?
Shortsell
Loss
26
Writing a Put
Price of underlying at expiration 94 97 100 104
Write put 3 Sell underlying Put exercised Net
profit Put
3 3 Net profit Put E P
3 97 -100 0
3
3 94 -100 -3
27
Profit Profile for Writing a Put
Profit
Put in-money
Put out-of-money
3
100
Underlying asset at expiration
0
E
97
Loss
28
Put-Call Parity
C Put P E D
0
Expiration
Presentvalue
.98 D E D 98
1 E 100
29
Profit of Put-Call Parity
0
Expiration
Buy call
Cash flows from call
Cash flows from portfolio
Buy portfolio
If cash flows at Expiration are the same for call
as for portfolio, then the Time 0 value must be
the same.
30
Put-Call Parity
P lt E P E P gt E Cash flows at expiration from
buying call Call 0 0 P E Cash flows at
expiration from buying put, buying underlying and
borrowing present value of exercise price Put E
P 0 0 Underlying P P P Loan E E E
31
Implications of Put-Call Parity
C Put P E D Put Levered position in
underlying 5 3 100 98.
32
Leverage
RORon levered
Levered
Unlevered
Higher return from levered
i
Lower return from levered
i
ROR unlevered
i Interest rate
33
If C Put P E D, then C ? P E D
C
P E D
P E
Call
P
E
34
Arbitrage if C lt P ED
Suppose P 110, E 100, D .98. P E 10. P
ED 12.
35
Suppose C 11. Arbitrage Time 0 Buy
Call -11 Short Underlying 110 Lend
ED -98 Arbitrage Profit 1
36
Expiration
P lt E P E P gt E Call 0 0 P E Buy
Underlying -P -P -P Receive E E E E Net E P
gt 0 E P 0 0
37
Factors Affecting the Value of a Call Option
Call--greater value of call 1. P--greater value
of underlying 2. E--lower value of exercise
price 3. Greater time to expiration 4. Higher
volatility of underlying
38
Impact of Longer Remaining Life on the Value of a
Call Option
C
C2 has a longer life than C1 P ? ED is higher for
C2 because D2 lt D1
P ? ED2
P ? ED1
P ? E
C2
C1
P
E
39
Value of a Call
Call Option of Security 1 Prices of
underlying 90 100 110 Value of call option 0
0 10 Probability 1/3 1/3 1/3 Mean value
(0)(1/3) (0)(1/3) (10)(1/3) 3.33 Call
Option of Security 2 Prices of underlying 80 100 1
20 Value of call option 0 0
20 Probability 1/3 1/3 1/3 Mean value (0)(1/3)
(0)(1/3) (20)(1/3) 6.67
40
Impact of the Volatility of the Underlying Asset
on the Value of a Call Option
C
P ? ED
C2 has greater volatility of underlying asset
P ? E
C2
C1
P
E