Suppose that a stock is currently trading at $60 per share. Suppose also that the stock price can only take two possible values one year from now: It can either go up by 25% or down by 20%. The annual risk-free rate is 4%. Assume that the stock pays no dividend. Suppose that we are interested in pricing a European put option on this stock. The option has a strike price of $66, and its maturity date is exactly one year from now.
a) What is the payoff on the put option if the stock price goes up by 25%?
b) What is the payoff on the put option if the stock price goes down by 20%?
c) What is the price of the put option? You need to find the replicating portfolio.
It is important that you are proficient in solving this systems of equations quickly.