Gross payoff profile
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.
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.
3. What gross payoff profile do you get if you short a covered call position and go long a
protective put position? Would you pay or receive net premiums on this position? What is the
view taken on the movement of the stock price if you hold this position? What other options
strategy does your portfolio remind you of? Assume a common strike for all options of $100.
4. Suppose that call options on a stock with strike prices $30 and $35 cost $7 and $4,
respectively. How can the options be used to create (a) a bull spread and (b) a bear spread?
Construct a table that shows the profit and payoff for both spreads.
5. A call with a strike price of $60 costs $6. A put with the same strike price and expiration date
costs $4. Construct a table that shows the profit from a straddle. For what range of stock prices
would the straddle lead to a loss?
6. (a) What is a lower bound for the price of a six-month call option on a non-dividend-paying
stock when the stock price is $80, the strike price is $75, and the risk-free interest rate is 10%
per annum?
(b) What is a lower bound for the price of a two-month European put option on a non-dividendpaying stock when the stock price is $58, the strike price is $65, and the risk-free interest rate is
5% per annum?
7. A one-month European put option on a non-dividend-paying stock is currently selling for
$2.50. The stock price is $47, the strike price is $50, and the risk-free interest rate is 6% per
annum. What opportunities are there for an arbitrageur? Explain how you capture an arbitrage
opportunity in details.
8. The price of a European call that expires in six months and has a strike price of $30 is $2. The
underlying stock price is $29, and a dividend of $0.50 is expected in two months and again in
five months. Risk-free interest rates for all maturities are 10%. What is the price of a European
put option that expires in six months and has a strike price of $30?
9. A stock price is currently $50. It is known that at the end of two months it will be either $53 or
$48. The risk-free interest rate is 10% per annum with continuous compounding. What is the
value of a two-month European call option with a strike price of $49? Use no-arbitrage
arguments.
10. A stock price is currently $50. Over each of the next two three-month periods it is expected
to go up by 6% or down by 5%. The risk-free interest rate is 5% per annum with continuous
compounding. What is the value of a six-month European put option with a strike price of $51?
Use no-arbitrage arguments.
11. What is the price of a European call option on a non-dividend-paying stock when the stock
price is $52, the strike price is $50, the risk-free interest rate is 12% per annum, the volatility is
30% per annum, and the time to maturity is three months?
12. What is the price of a European put option on a non-dividend-paying stock when the stock
price is $69, the strike price is $70, the risk-free interest rate is 5% per annum, the volatility is
35% per annum, and the time to maturity is six months?