Question 5

Consider a stock that is trading at $100 a share. The annual volatility of the stock is 20 percent, and the 3-month nominal risk-free interest rate is 8 percent.

(a)Find the value of a 3-month European call option on the stock with an exercise or strike price equal to $100.

(b)Find the value of a 3-month European put option with an exercise price equal to $95.

(c)Consider a derivative security that pays, in three months, the square of the stock price that will prevail in 3 months. In other words, this security will pay where denotes the stock price in 3 months. Find the value of this derivative security today.