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Assignment 3

Course: Risk Management and Derivatives

Question 1 [25 marks]:

i.       List the six factors affecting stock option prices. [12.5 marks]

ii.       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? [12.5 marks]

Question 2 [25 marks]:

“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. [12.5 marks]

Question 3 [25 marks]:

i.       Why an American call option on a dividend-paying stock is always worth at least as much as its intrinsic value. Is the same true of a European call option? Explain your answer. [12.5 marks]

ii.       Give two reasons that the early exercise of an American call option on anon-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. [12.5 marks]

Question 4 [25 marks]:

You are considering a stock A that pays a dividend of $1. The beta coefficient of A is 1.3. The risk free return is 6%, while the market average return is 13%.

i.       The price of anon-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. What is the price of a three-month European put option with a strike price of $20? [12.5 marks]

ii.       What is a lower bound for the price of a six-month call option on anon-dividend-paying stock when the stock price is $80, the strike price is $75, and the risk-free interest rate is 10% per annum? [12.5 marks]