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Homework answers / question archive / FIN5DER SEM 2 Tutorial 7 Questions and Solutions Problem 10
FIN5DER SEM 2
Tutorial 7 Questions and Solutions
Problem 10.1.
An investor buys a European put on a share for $3. The stock price is $42 and the strike price is $40. Under what circumstances does the investor make a profit? Under what circumstances will the option be exercised? Draw a diagram showing the variation of the investor’s profit with the stock price at the maturity of the option.
Problem 10.2.
An investor sells a European call on a share for $4. The stock price is $47 and the strike price is $50. Under what circumstances does the investor make a profit? Under what circumstances will the option be exercised? Draw a diagram showing the variation of the investor’s profit with the stock price at the maturity of the option.
Problem 10.3.
An investor sells a European call option with strike price of K and maturity T and buys a put with the same strike price and maturity. Describe the investor’s position.
Notations for European Options:
c: European call option price
p: European put option price
S0 : Stock price today
K: Strike price
T: Life of option
s : Volatility of stock price
Problem 10.9.
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.
Problem 10.10.
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.
Problem 10.13.
Explain why an American option is always worth at least as much as a European option on the same asset with the same strike price and exercise date.
Problem 10.15.
Explain carefully the difference between writing a put option and buying a call option.
Problem 11.4.
Give two reasons that the early exercise of an American call option on a non-dividend-paying stock is not optimal. The first reason should involve the time value of money. The second reason should apply even if interest rates are zero.
Problem 11.5.
“The early exercise of an American put is a trade-off between the time value of money and the insurance value of a put." Explain this statement.
Problem 11.7.
The price of a non-dividend paying stock is $19 and the price of a three-month European call option on the stock with a strike price of $20 is $1. The risk-free rate is 4% per annum. According to the put-call parity, what is the price of a three-month European put option with a strike price of $20?
Problem 11.9.
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?
Problem 11.12.
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.
a. What is a lower bound for this option?
b. Which transactions should an arbitrageur take?
