BUS333 DERIVATIVE SECURITIES
FINAL EXAM - PREVIOUS QUESTIONS
SOLUTIONS
1. A European call option and put option on a stock both have a strike price of $10 and an
expiration date in three months. The call option sells for $1.00 and the put has a premium of
$1.50. The risk free rate is 10% per annum (continuously compounded), and the current stock
price is $9.50. Outline the procedure for a trader to exploit any arbitrage opportunity that is
present.
,2. A stock is currently priced at $20. It is known that at the end of four months it will be either
$18 or $22. A four-month European call option on this stock with a strike price of $20.50 is
available, while the risk-free interest rate is 5% p.a. (continuously compounded).
i) What is the composition of the riskless portfolio?
ii) Use no-arbitrage arguments to determine the value of the call option.
3. Explain why Black’s approximation for valuing an American call option on a dividend paying
stock works.
2
, 4. Give an intuitive explanation of why the early exercise of an American put option becomes
more attractive as:
i) the risk-free rate increases
ii) the volatility of the share’s price decreases.
5. A mutual fund (unit trust) announces that the salaries of its fund managers will depend on the
performance of the fund. If the fund loses money, the salaries will be zero. If the fund makes
a profit, the salaries will be proportional to the profit. Describe the salary of a fund manager
as an option. How is a fund manager motivated to behave with this type of remuneration
package?
3
FINAL EXAM - PREVIOUS QUESTIONS
SOLUTIONS
1. A European call option and put option on a stock both have a strike price of $10 and an
expiration date in three months. The call option sells for $1.00 and the put has a premium of
$1.50. The risk free rate is 10% per annum (continuously compounded), and the current stock
price is $9.50. Outline the procedure for a trader to exploit any arbitrage opportunity that is
present.
,2. A stock is currently priced at $20. It is known that at the end of four months it will be either
$18 or $22. A four-month European call option on this stock with a strike price of $20.50 is
available, while the risk-free interest rate is 5% p.a. (continuously compounded).
i) What is the composition of the riskless portfolio?
ii) Use no-arbitrage arguments to determine the value of the call option.
3. Explain why Black’s approximation for valuing an American call option on a dividend paying
stock works.
2
, 4. Give an intuitive explanation of why the early exercise of an American put option becomes
more attractive as:
i) the risk-free rate increases
ii) the volatility of the share’s price decreases.
5. A mutual fund (unit trust) announces that the salaries of its fund managers will depend on the
performance of the fund. If the fund loses money, the salaries will be zero. If the fund makes
a profit, the salaries will be proportional to the profit. Describe the salary of a fund manager
as an option. How is a fund manager motivated to behave with this type of remuneration
package?
3
