The current stock price is $45, the European put option with an exercise price of $50 is expiring in a year is selling for $10.60/contract. Suppose that you would like to establish a long position in a one-year European call option written on the stock with a strike price of $50. You could buy the call in the options market, where it is currently trading for $7.90/contract. As you are about to submit your order, it just occur to you that you learned that you could also create the position synthetically by using a replicating portfolio.
a. Describe the replicating portfolio by demonstrating that the payoff from your portfolio is identical to that of the call option no matter what the stock price is on expiration day a year from now. Please use a payoff diagram or payoff table to prove your claim.
b. What is the price of the replicating portfolio? Is the call correctly priced relative to the replicating portfolio?