A particular call is the option to buy stock at $25. It expires in six months an

Question

A particular call is the option to buy stock at $25. It expires in six months and currently sells for $4 when the price of the stock is $26.

a) What is the intrinsic value of the call? What is the time premium paid for the call?
b) What will the value of this call be after six months if the price is $20? $25? $30? $40?
c) If the price of the stock rises to $40 at the expiration date of the call, what is the percentage increase in the value of the call? Does his example illustrate favorable leverage?
d) If an individual buys the stock and sells this call, what is the cash outflow (i.e, net cost) and what will the profit on the position be after six months if the price of the stock is $10? $15? $20? $25? $26? $30? $40?
e) If an individual sells this call naked, what will the profit or loss be on the position after six months if the price of the stock is $20? $26? $40?

Please show all work.

Explanation / Answer

a) Intrinsic value of the call = 26 - 25 = $1
Time premium = Premium - Intrinsic value = 4 - 1 = $3

b) Value of the call if price is:
$20 : Value = 20 - 25 = 0 (Since, can't be negative)
$25 : Value = 25-25 = 0
$30 : Value = 30 - 25 = $5
$40 : Value = 40 - 25 = $15

c) Value of the call = 40 - 25 = $15
%Increase = (15 - 4) * 100/4 = 275%

d) Cash Outflow = 26 - 4 = $22

Profit if the price is:
$10: Option Buyer will not exercise the option
Loss = (26 - 10) - 4 = -$12

$15: Option Buyer will not exercise the option
Loss = (26 - 15) - 4 = -$7

$20: Option Buyer will not exercise the option
Loss = (26 - 20) - 4 = -$2

$25: Exercise of option is irrelevant
Profit = (25 - 26) + 4 = $3

$26: Option Buyer will exercise the option
Profit = (26 - 26) + (25 - 26) + 4 = $3

$30: Option Buyer will exercise the option
Profit = (30 - 26) + (25 - 30) + 4 = $3

$40: Option Buyer will exercise the option
Profit = (40 - 26) + (25 - 40) + 4 = $3

e) If sell the call naked

$20: Option Buyer will not exercise the option
Loss = $4(Premium Amount)

$26: Option Buyer will exercise the option
Profit = (25 - 26) + 4 = $3

$40: Option Buyer will exercise the option
Profit = (25 - 40) + 4 = $11

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.