Rob wishes to buy a European put option on BioLabs, Inc., a non-dividendpaying common stock, with a strike price of $40 and six months until expiration. BioLabs common stock is currently selling for $30 per share, and Rob expects that the stock price will either rise to $60 or fall to $15 in six months. Rob can borrow and lend at the risk-free effective annual rate of 8 percent. (Note: The effective annual rate of 8% is different from the stated annual rate of 8%. The stated annual rate can be divided based on the compounding periods. The effective annual rate cannot be divided.)

a. What should the put option sell for today?

b. If no options currently trade on the stock, is there a way to create a synthetic put option with identical payoffs to the put option just described? If there is, how would you do it?

c. How much does the synthetic put option cost? Is this greater than, less than, or equal to what the actual put option costs? Does this make sense?