Problem 3. The price of a certain security follows a geometric Brownian motion with drift parameter u = .05 and volatility parameter o = 0.3. The present price of the security is 90. Suppose that the interest rate is r = 4%. (a) Find the no-arbitrage cost of a call option that erpires in three months and has erercise price 100. (6) What is the probability that the call option in part (a) is worthless at the time of erpiration? (c) Suppose that a new type of investment on the security is being traded. This investment returns 100 at the end of one year if the price six months after purchasing the investment is at least 90 and the price one year after purchase is at most twice as much as the price was after six months. Determine the no-arbitrage cost of this investment