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Homework answers / question archive / FIN5DER Tutorial 8 Questions Problem 11
FIN5DER Tutorial 8 Questions
Problem 11.1.
List the six factors affecting stock option prices.
Problem 11.2.
What is a lower bound for the price of a four-month call option on a non-dividend-paying stock when the stock price is $28, the strike price is $25, and the risk-free interest rate is 8% per annum?
Problem 11.3.
What is a lower bound for the price of a one-month European put option on a non-dividend-paying stock when the stock price is $12, the strike price is $15, and the risk-free interest rate is 6% per annum?
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 11.8.
Explain why the arguments leading to put–call parity for European options cannot be used to give a similar result for American options.
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 11.10.
What is a lower bound for the price of a two-month European put option on a non-dividend-paying stock when the stock price is $58, the strike price is $65, and the risk-free interest rate is 5% per annum?
Problem 11.11.
A four-month European call option on a dividend-paying stock is currently selling for $5. The stock price is $64, the strike price is $60, and a dividend of $0.80 is expected in one month. The risk-free interest rate is 12% per annum for all maturities. What opportunities are there for an arbitrageur?
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. What opportunities are there for an arbitrager?
Problem 11.14.
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 (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?
Problem 11.15.
Explain the arbitrage opportunities in Problem 11.14 if the European put price is $3.
FIN5DER Tutorial 8 Questions
Problem 11.1.
List the six factors affecting stock option prices.
Problem 11.2.
What is a lower bound for the price of a four-month call option on a non-dividend-paying stock when the stock price is $28, the strike price is $25, and the risk-free interest rate is 8% per annum?
Problem 11.3.
What is a lower bound for the price of a one-month European put option on a non-dividend-paying stock when the stock price is $12, the strike price is $15, and the risk-free interest rate is 6% per annum?
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 11.8.
Explain why the arguments leading to put–call parity for European options cannot be used to give a similar result for American options.
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 11.10.
What is a lower bound for the price of a two-month European put option on a non-dividend-paying stock when the stock price is $58, the strike price is $65, and the risk-free interest rate is 5% per annum?
Problem 11.11.
A four-month European call option on a dividend-paying stock is currently selling for $5. The stock price is $64, the strike price is $60, and a dividend of $0.80 is expected in one month. The risk-free interest rate is 12% per annum for all maturities. What opportunities are there for an arbitrageur?
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. What opportunities are there for an arbitrager?
Problem 11.14.
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 (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?
Problem 11.15.
Explain the arbitrage opportunities in Problem 11.14 if the European put price is $3.
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