Practice problems for homework from chapters 22 and 23; 8
th
and 9
th
editions of the text
1
Practice Problems for chapter 22 (1, 2, 5, 7, 11, 23 in 8
th
edition) and chapter 23 (4 in 8
th
edition)
Plus a practice problem on payoffs and profits, based on my ppt example from WSJ.
Chapter 22, 8
th
edition, # 1, 2, 5, 7, 11, 23
Chapter 22, 9
th
edition, #5, #11
P
ractice problems with payoffs
, see my ppt for ch. 22 – look at the example (below) we did in class from
WSJ.
For a, b, c,
Buy 10 July 135 calls on IBM; pay premium of $4.75.
At expiry, IBM = $138.25.
a.
What is the payoff to the call option buyer?
b.
What is the profit to the call buyer?
c.
What is the profit to the call writer?
d.
What is the profit to a put writer if he/she sells 10 August 135 put contracts on IBM for premium of
$5.50 if at expiry, IBM = $138.25?
e.
What is the time value of one August 135 put?
Answers:
a.
10 call contracts = 1000 shares of stock. Payoff to call buyer = intrinsic value = max (S
T
– E, 0) =
$3.25 X 100 X 10 =
$3,250.00
b.
Profit =Payoff minus premium paid = [$3,250 – ($4.75 X 100 X 10) ] = $3,250- $4,750 = -$1,500.
c.
Profit to call writer = Premium received minus payoff to call buyer =
$1,500.00
d.
Profit to put writer = Premium received minus payoff to put buyer =
($5.50 X 100 X 10) –
max (E-S
T
, 0) = ($5,500) – Max(135-138.25,0) =
$5,500.00
(option expires worthless =>
maximum possible profit to option writer – keeps premium and pays off nothing)
e.
Time value = option premium minus intrinsic value; the August 135 put has zero (0) intrinsic value
when the stock is selling at $138.25; hence the time value of the option is the entire option premium.
th
edition of text:
1.
Two
-State Option Pricing Model
T-bills currently yield 6%. Stock in Nina Manufacturing is
currently selling for $55.00 per share. There is no possibility that the stock will be worth less
than $50 per share in one year.
The options expire in one year from today.
a.
What is the value of a call option with a $45 strike? What is the intrinsic value?
b.
What is the value of a call option with a $35 strike? What is the intrinsic value?
c.
What is the value of a put option with a $45 strike? What is the intrinsic value?
1.
a.
The value of the call is the stock price minus the present value of the strike (exercise price), so:
C
0
= $55 – [$45/1.06] = $12.55
The intrinsic value is the amount by which the stock price exceeds the strike (exercise price) of
the call, so the intrinsic value is $10.
(i.e., $55 - $45 = $10)
b.
The value of the call is the stock price minus the present value of the strike (exercise price), so:
C
0
= $55 – [$35/1.06] = $21.98
Option/Strike
Exp.
Vol.
Last
Vol.
Last
IBM
130
Oct
364
15.25
107
5.25
138.25
130
Jan
112
19.25
420
9.25
138.25
135
Jul
2365
4.75
2431
0.8
138.25
135
Aug
1231
9.25
94
5.5
138.25
140
Jul
1826
1.75
427
2.75
138.25
140
Aug
2193
6.5
58
7.5
--Put--
--Call--