Problem 1. (15 Points) You take a long position in a one-year forward contract on a stock whose price you expect to increase in the future. The current price of the stock is $100 per share. The interest rate is 10% continuously compounded and the stock pays dividends of $2 in both 4 months and 8 months from now. (a) (2 Points) What is the (no-arbitrage) forward price at time 0, for this one-year forward contract? What is the value of this one-year forward contract at time 0? (b) Six months later, the price of the stock is $110 per share. You decide now to take a second long position, in a six-months forward contract on the stock; observe that both contracts have the same delivery date. i) (2 Points) What is the forward price of your second contract at t = 1/2? (ii) (2 Points) What is the value at time t= 1/2 of the long position you made at time t = 0? (c) Four months later, i.e., at t = 10 months, you need to sell your long positions in the two forward contracts. i) (4 Points) If the current price of the stock is $120 per share, how much money will you receive from selling your two long positions? (i) (2 Points) How much money did you invest in total? Did you take advantage of an arbitrage opportunity? Explain your answer (why or why not). (d) (3 Points) At t = 10 months compute the minimum price of the stock such that you receive $20 from selling your two long positions.