In this problem you need to determine the numerical values of the payoffs at expiration of certain exotic options that cannot be exercised early. We assume that the stock prices S(t) at time t are given by S(0) = 80, S(1)=90, S(2) = 100, and S(3) = 95, and that all options expire at time t = 3. For those options considered below that are Asian options and hence refer to an average, the average is the arithmetic average of the stock price at times t = 1, t = 2, and t = 3. Determine the payoff at expiration of (and in each case show your work and explain your reasoning; you will lose points, possibly all points, if you only give the numerical answer): (a) an average price call with strike price 90, entered into at time t = 0. (b) an average strike put, entered into at time t = 0. (c) an up-and-in call option with barrier 92 and strike price 90, entered into at time t = 0. (d) a down-and-out put option with barrier 78 and strike price 96, entered into at time t = 0.