Problem 1.1. An arbitrage free forward contract written on a dividend paying stock which mature at time T is values as For = Soep-5T 1. Prove that For = Svetsis the arbitrage free price by showing if Foz * Soet-5T then arbitrage opportunity erist. 2. Show that long and short forward positions can be create synthetically using stocks and cash. 3. Explain cash and carry and reverse cash and carry arbitrage strategies with appropriate eramples, charts. 4. Suppose 7 180 days, 8 = 0, r = 4.75% and For = 50.25 and you are long in forward contracts (to buy the stock). After 90 days (that mean today), you decided you want to close out the forward contract position. Thus enter into another forward contract to sell the stock, which mature in 90 days with current stock price price 45. Assume 365 days per year. (a) What is the second forward contract price? (b) What is the combine payoff (both long and short) at maturity? (c) What is the present value (as of today) of combine position? Problem 1.1. An arbitrage free forward contract written on a dividend paying stock which mature at time T is values as For = Soep-5T 1. Prove that For = Svetsis the arbitrage free price by showing if Foz * Soet-5T then arbitrage opportunity erist. 2. Show that long and short forward positions can be create synthetically using stocks and cash. 3. Explain cash and carry and reverse cash and carry arbitrage strategies with appropriate eramples, charts. 4. Suppose 7 180 days, 8 = 0, r = 4.75% and For = 50.25 and you are long in forward contracts (to buy the stock). After 90 days (that mean today), you decided you want to close out the forward contract position. Thus enter into another forward contract to sell the stock, which mature in 90 days with current stock price price 45. Assume 365 days per year. (a) What is the second forward contract price? (b) What is the combine payoff (both long and short) at maturity? (c) What is the present value (as of today) of combine position