FIN5401 Investments
Assignment 6 Solutions
Fei Fang
Spring 2021
SOM
Clark University
Question I (15 points)
An investor buys a European put on a share for $3. The current stock price is $42 and the
strike price is $40.
(a) Under what circumstances does the investor make a profit (have positive profit) on the
expiration date?
(b) Under what circumstances will the option be exercised on the expiration date?
(c) Please draw a diagram showing how the investor’s profit depends on the stock price
on the expiration date. To put it another, draw a diagram showing the relationship
between the investor’s profit and the stock price on the expiration date.
Solution:
(a) The profit function for buying European put is max(0, K − ST ) − put premium. The
investor makes a profit if max(0, K − ST ) − put premium > 0, i.e., max(0, K − ST ) >
put premium. Put it another way, the payoff from exercising the put option should be
greater than the put premium. Therefore, the investor makes a profit if the price
of the stock on the expiration date is less than $37. In these circumstances the
payoff from exercising the option is greater than $3, the put premium.
(b) The option will be exercised if the stock price is less than $40 at the maturity
of the option. In these circumstances, the options will be in the money and exercising
it can provide positive payoff to the investor.
(c) Please refer to Figure 1.
Figure 1: Profit from Buying a European Put
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Question II (15 points)
An investor sells a European call on a share for $4. The current stock price is $47 and the
strike price is $50.
(a) Under what circumstances does the investor make a profit (have positive profit) on the
expiration date?
(b) Under what circumstances will the option be exercised on the expiration date?
(c) Please draw a diagram showing how the investor’s profit depends on the stock price
on the expiration date. To put it another, draw a diagram showing the relationship
between the investor’s profit and the stock price on the expiration date.
Solution:
(a) The profit function for selling European call is −max(0, ST − K) + call premium. The
investor makes a profit if −max(0, ST − K) + call premium > 0, i.e., put premium >
max(0, ST −K). Put it another way, the call option should expire worthless or the payoff
from exercising it should be less than the call premium. Therefore, the investor
makes a profit if the price of the stock is below $54 on the expiration date.
If the stock price is below $50, the option will not be exercised, and the investor makes
a profit of $4. If the stock price is between $50 and $54, the option is exercised and the
investor makes a profit between $0 and $4.
(b) The option will be exercised if the stock price is greater $50 at the maturity
of the option. In these circumstances, the options will be in the money and exercising
it can provide positive payoff to the investor.
(c) Please refer to Figure 2.
Figure 2: Profit from Selling a European Call
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Question III (15 points)
An investor buys a European call on a share for $5. The current stock price is $102 and the
strike price is $100.
(a) Under what circumstances will the investor make a profit (have positive profit) on the
expiration date?
(b) Under what circumstances will the option be exercised on the expiration date?
(c) Please draw a diagram showing how the investor’s profit depends on the stock price
on the expiration date. To put it another, draw a diagram showing the relationship
between the investor’s profit and the stock price on the expiration date.
Solution:
(a) The profit function from buying a European call is max(0, ST − K) − call premium. The
holder of the European call option will make a profit if max(0, ST −K)−call premium >
0, i.e., max(0, ST − K) > call premium. Put it another way, the payoff from exercising
the call option should be greater than the call premium. Therefore, the holder of
the option will make a profit if the stock price at maturity of the option is
greater than $105. This is because the payoff to the holder of the call option is, in
these circumstances, greater than the $5 paid for the option.
(b) The option will be exercised if the stock price is greater $100 at the maturity
of the option. In these circumstances, the call options will be in the money and
exercising it can provide positive payoff to the holder.
(c) The profit of the holder of a European call option is as shown Figure 3 below.
Figure 3: Profit from Buying a European Call
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Question IV (15 points)
An investor sells a European put on a share for $8. The current stock price is $57 and the
strike price is $60.
(a) Under what circumstances will the investor make a profit (have positive profit) on the
expiration date?
(b) Under what circumstances will the option be exercised on the expiration date?
(c) Please draw a diagram showing how the investor’s profit depends on the stock price
on the expiration date. To put it another, draw a diagram showing the relationship
between the investor’s profit and the stock price on the expiration date.
Solution:
(a) The profit function from selling a European put is −max(0, K −ST )+put premium. The
writer of the European put option will make a profit if −max(0, K−ST )+put premium >
0, i.e., put premium > max(0, K − ST ). Put it another way, the payoff from exercising
the put option should be less than the put premium. Therefore, the seller of the
put option will make a profit if the stock price at maturity is greater than
$52. If the stock price is greater $60, the option will not be exercised, and the put
option writer makes a profit of $8. If the stock price is between $52 and $60, the option
is exercised and the put option writer makes a profit between $0 and $8.
(b) The option will be exercised if the stock price at maturity is less than $60. In
these circumstances, the put options will be in the money and exercising it can provide
positive payoff to the holder.
(c) The profit from a short European put position is as shown Figure 4 below.
Figure 4: Profit from Selling a European Put
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