MANG 6020 Financial Risk Management
Seminar 4
Question 1
Suppose that a European call option to buy a share for $100.00 costs $5.00 and is held until
maturity. Under what circumstances will the holder of the option make a profit? Under what
circumstances will the option be exercised? Draw a diagram illustrating how the profit from a
long position in the option depends on the stock price at maturity of the option.
Solution
Ignoring the time value of money, 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 option
is, in these circumstances, greater than the $5 paid for the option. The option will be exercised if
the stock price at maturity is greater than $100. Note that if the stock price is between $100 and
$105 the option is exercised, but the holder of the option takes a loss overall. The profit from a
long position is as shown in Figure below.
Question 2
Suppose that a European put option to sell a share for $60 costs $8 and is held until maturity.
Under what circumstances will the seller of the option (the party with the short position) make a
profit? Under what circumstances will the option be exercised? Draw a diagram illustrating how
the profit from a short position in the option depends on the stock price at maturity of the option.
Solution:
Ignoring the time value of money, the seller of the option will make a profit if the stock price at
maturity is greater than $52.00. This is because the cost to the seller of the option is in these
circumstances less than the price received for the option. The option will be exercised if the
Seminar 4
Question 1
Suppose that a European call option to buy a share for $100.00 costs $5.00 and is held until
maturity. Under what circumstances will the holder of the option make a profit? Under what
circumstances will the option be exercised? Draw a diagram illustrating how the profit from a
long position in the option depends on the stock price at maturity of the option.
Solution
Ignoring the time value of money, 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 option
is, in these circumstances, greater than the $5 paid for the option. The option will be exercised if
the stock price at maturity is greater than $100. Note that if the stock price is between $100 and
$105 the option is exercised, but the holder of the option takes a loss overall. The profit from a
long position is as shown in Figure below.
Question 2
Suppose that a European put option to sell a share for $60 costs $8 and is held until maturity.
Under what circumstances will the seller of the option (the party with the short position) make a
profit? Under what circumstances will the option be exercised? Draw a diagram illustrating how
the profit from a short position in the option depends on the stock price at maturity of the option.
Solution:
Ignoring the time value of money, the seller of the option will make a profit if the stock price at
maturity is greater than $52.00. This is because the cost to the seller of the option is in these
circumstances less than the price received for the option. The option will be exercised if the
