Principles of Finance with Excel (Основы финансов c Excel)
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PFE, Chapter 23: Introduction to options page 55
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ABC DE
Investment today in
buying 100 shares
5,000$
Investment today in
buying 1,000 call
options
5,000$
ABC stock price in 3
months, S
T
Dollar profit
from buying 100
shares
Dollar profit from
buying 100 call
options now
Percentage profit
from buying 100
shares
Percentage profit
from buying 1,000
call options now
0
10
20
30
40
50
60
70
80
90
100
10. On 14 February 2002 Microsoft (MSFT) stock is trading at $48.30 per share. The price of a
call option on MSFT expiring March 2003 is $1.45 for options with X = $47.50 and $0.35 for
options with X = $50.
10.a. You think that shares of MSFT will rise in price in the immediate future, and you
want to speculate in the stock. Compare (graphically) the following two alternatives:
purchasing 1,000 MSFT options with an exercise price of $47.5 versus purchasing 1,000
MSFT options with a strike of $50.
10.b. Compare the two strategies. Which is preferable?
Use the following template:
PFE, Chapter 23: Introduction to options page 56
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ABC
Exercise
price
Call price
47.5 1.45
50 0.35
Investment
A: 1000 options, X=47.5 1,450 <-- =B2*1000
B: 1000 options, X=50 350 <-- =B3*1000
Stock price in
3 months, S
T
Percentage
profit on
strate
gy
A
Percentage
profit on
strate
gy
B
0.0
10.0
20.0
30.0
40.0
42.5
45.0
47.5
50.0
55.0
60.0
70.0
80.0
90.0
100.0
11. On 1 September 2004 McDonald’s (MCD) stock is trading at $27.19 per share. The price of
a put option on MCD expiring 17 September 2004 is $0.10 for options with X = $25.00 and
$0.70 for options with X = $27.50.
10.a. You think that shares of MCD will fall in price in the immediate future, and you
want to speculate on the stock. Compare (graphically) the following two alternatives:
purchasing 1,000 MCD options with an exercise price of $25 versus purchasing 1,000
MCD put options with a strike of $27.50.
10.b. Compare the two strategies. Which is preferable?
Use the following template:
PFE, Chapter 23: Introduction to options page 57
Exercise
price
Put price
25 0.1
27.5 0.7
Investment
A: 1000 options, X=25 100 <-- =B3*1000
B: 1000 options, X=27.50 700 <-- =B4*1000
Stock price in
3 months, S
T
Percentage
profit on
strate
gy
A
Percentage
profit on
strate
gy
B
0.0
15.0
20.0
22.0
24.0
25.0
26.0
26.5
27.0
27.5
28.0
30.0
32.5
35.0
40.0
12. A put option written on ENERGY-R-US Corporation’s stock is selling for $2.50. The
option has an exercise price of $20 and 6 months to expiration. The current market price for a
share of ENERGY-R-US is $26. Determine the profit from a strategy of buying the stock and
buying the put; graph these profits. Use the following template.
PFE, Chapter 23: Introduction to options page 58
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ABCD
Energy-R-Us, stock 26.00
Put price, X = 20 2.50
Stock price, S
T
in 6 months
Profit
from put
Profit
from
stock
Total profit
0
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10
15
20
25
30
35
40
45
50
13. Using the data from the previous problem, compare the following three strategies:
•
Purchase one share of stock and one put on the stock.
•
Purchase one share of stock and two puts on the stock.
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Purchase of one share of stock and three puts on the stock.
14. Using the data and the template below: Suppose you bought a GM call with exercise (strike)
price X = 50 and wrote a GM call with exercise price X = 45 Graph the profit of this strategy at
option expiration. Why might this be an attractive strategy?
PFE, Chapter 23: Introduction to options page 59
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ABCD
XPrice
45 4.10
50 1.65
GM stock price, S
T
at option expiration
Profit on
X=45 call
(written)
Profit on
X=50 call
(bought)
Total
profit
20
25
30
35
40
45
50
55
60
65
Call Prices
15. Using the data from the previous problem, compute and graph the profit from a strategy in
which you buy a GM call with exercise price X = 45 and write a calll with exercise price X = 50.
Explain why this strategy might be attractive.
16. The following options are traded on WOW Corporation’s stock. State which property of
option prices is violated and show that you can design a strategy to profit from this mispricing.
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Option Exercise
Price
Expiration
Date
Price
Call 40 1-Jan-04 $13.50
Call 40 1-Jul-04 $12.95
6
Such a strategy is called an arbitrage strategy. Such strategies are discussed at length in the next chapter.
PFE, Chapter 23: Introduction to options page 60
17. The following options are traded on Smow Corporation’s stock. State which property of
option prices is violated and show that you can design a strategy to profit from this mispricing.
Option Exercise
Price
Expiration
Date
Price
Put 50 1-Ma
r
-04 $4.25
Put 60 1-Ma
r
-04 $4.00
18. David wants to buy a call option written on RAIDER Corp. stock.
Patrick is willing to sell
David a call option on RAIDER Corp. stock with an exercise price of $50 for $8.20. The option
will mature in exactly one year. The current market price for RAIDER Corp. stock is $50.
18.a. Determine and graph the payoffs of both David and Patrick’s respective positions.
18.b. For what stock price S
T
is the profit of both David and Patrick zero?
Call price 8.20
RAIDER stock
price
at option
expiration, S
T
Patrick's
profit
David's
profit
0
10
20
30
40
50
60
70
80
90
100
19. Portfolio insurance describes a position in which an investor buys put options to insure that
the value of his portfolio does not fall below a certain point. Suppose Jerry has a portfolio that
consists of 100 shares of RTY stock. The current market price of RTY is $35 per share. The
following options are also being traded on RTY stock:
PFE, Chapter 23: Introduction to options page 61
Expiration date
Exercise
price
Call
price
Put
price
1-Jun-04 20 18.00$ 0.10$
1-Jun-04 25 11.35$ 0.45$
1-Jun-04 35 3.50$ 3.20$
1-Jun-04 40 0.75$ 5.65$
19.a. What options must Jerry buy if he wants to insure that the value of his portfolio will
not drop below $2000?
19.b. How much will this cost?
20. A covered call position entails entering into a long position in stock and writing a call option
with a high strike price. The purpose of such a position is to finance a portion of the stock
purchase from the sale of the call option.
Sam thinks that STF Corp. stock, currently priced at $80/share, will go up in price by
about $15 in the next 6 months. He would like to buy 10,000 shares of STF today and cash in on
his bullish sentiment. In order to cut the initial costs of his purchase, he would like to enter into
a covered call position. The following options are being traded on STF Corp:
Expiration
date
Exercise
p
rice
Call
p
rice
1-Aug-04 70$ 18.95$
1-Aug-04 80$ 7.65$
1-Aug-04 90$ 2.70$
1-Aug-04 100$ 0.50$
Suppose Sam writes 10,000 of the $90 calls. Show Sam’s profit. Use the following template:
PFE, Chapter 23: Introduction to options page 62
STF stock price 80$
Number of shares purchased 10,000
Stock price of STF in 6
months, S
T
Profit from
stock
position
Profit from
option position,
10,000 options
with X = $90
Profit from
covered call
strategy
50
60
70
80
90
100
110
120
21. Referring to the facts in the previous problem:
21.a. Compare the profits from a covered call strategy using the $90 calls with one using
the $100 calls.
21.b. Which of the two covered call strategies would you recommend?
22. Given the three calls below, design a butterfly strategy which pays off if the stock does not
make a major move from its current value of $60. Graph the strategy profits. Use the following
template.
PFE, Chapter 23: Introduction to options page 63
Call prices
XPrice
50 22.00
60 15.00
70 10.00
Payoff and profits
Stock price
at option
expiration, S
T
Payoff on
X = 50 call
Payoff on
X = 60 call
Payoff on
X = 70 call Total profit
30.0
35.0
40.0
45.0
50.0
52.5
55.0
57.5
60.0
62.5
65.0
67.5
70.0
72.5
75.0
80.0
85.0
90.0
23. Given the data from the previous problem, design a butterfly strategy which pays off if the
stock price makes a large move from its current price of $60. Graph the strategy profits.
PFE Chapter 23: Facts about option prices page 1
CHAPTER 23: OPTION PRICING FACTS
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This version: September 22, 2002
Chapter contents
Overview......................................................................................................................................... 2
22.1. Fact 1: Call price of an option >
(
)
0
,0Max S PV X
−
..................................................... 3
22.2. Fact 2: It’s never worthwhile to exercise a call early. ......................................................... 8
22.3. Fact 3: Put-call parity
(
)
00 0
Put Call PV X S=+ −.............................................................. 9
22.4. Fact 4: Bound on an American put option price:
[
]
0
,0PMaxXS>−
............................. 12
22.5. Fact 5: Bounds on European put option prices
(
)
0
,0PMaxPVX S
>−
...................... 12
22.6. Fact 6: You might find it optimal to early-exercise an American put on a non-dividend
paying stock .................................................................................................................................. 14
22.7. Fact 7: Option prices are convex ....................................................................................... 14
Summary....................................................................................................................................... 19
*
Notice: This is a preliminary draft of a chapter of Principles of Finance by Simon Benninga
(benninga@wharton.upenn.edu
). Check with the author before distributing this draft (though
you will probably get permission). Make sure the material is updated before distributing it. All
the material is copyright and the rights belong to the author.