(30%) Suppose you buy a call option of a firm’s stock. The current price of the stock is $60, but the price will change next period, with a probability 70% of increasing to $120, and with a probability 30% of decreasing to $30. The exercise price for this call option is $70 at expiration (next period). Assume the interest rate is 5%. a) What is the present value of your expected profit? (Remember that is the price of the call option in today’s dollars) b) Now consider a three-period case: Suppose the stock price in the first period is still $60. In the second period, the stock price will increase to $120 with a probability 70%, and this price will continue to change in the third period, with a probability 40% of increasing to $150 and a probability 60% of decreasing to $100; in the second period, the stock price will go down to $30 with a probability 30%, and this price will also continue to change in the third period, with a probability 40% of going up to $65 and a probability 60% of going down to $20. The call option you buy will expire in the third period and the exercise price is still $70. The interest rate is still assumed to be 5%. Calculate the present value of your expected profit