Consider a stock which is currently selling for $40. Each year you expect that the stock will either increase in value by 40% or decrease in value by 20%. Currently, a one-year pure discount bond with face value $1000 is selling for $980 and the term structure is flat. After analyzing the stock, you believe that its prospects are not good and you believe that there is a 90% chance that it will decrease in value each year. a) What is the price of a European put option with a one-year maturity and a strike price of $40 written on this?

b)Suppose that this option is trading for $5.25. Would you take advantage of this price in some way? If so, describe in detail what you would do.