Question: 1. Consider a world in which there are only two periods and three possible states of the world in the second period (a good weather

1. Consider a world in which there are only two periods and three possible states of the world in the second period (a good weather state, a fair weather state, and a bad weather state). Also, apples are the only product produced in this world, and they cannot be stored from one period to the next. The following abbreviations will be used: PA apple in first period (i.e., present apple) GA good weather apple, FA fair weather apple, BA-bad weather apple. Suppose that arn apple tree firm offers for sale a bond and stock. An apple tree produces 80GA, 50 FA, and 25BA The bond pays 20GA, 20FA and 20BA. The stock pays 60GA, 30FA and 5BA. The price of the bond is 18PA, and the price of the stock is 19PA. In addition, a security C is traded for 8PA. The security C pays 45GA, 5 FA, and 0 BA (i) Find the arbitrage-free price of the atomic securities. ii) Calculate the arbitrage-free price of an apple tree (iii) Calculate the discount factor and explain its economic interpretation (iv) An investor wants a security that will pay 30GA, 30FA, and 50BA. Construct such a security and determinets arbitrage-free price (v) Compute the arbitrage-free price of a European call option to buy the stock at a price of 25 in the second period. 1. Consider a world in which there are only two periods and three possible states of the world in the second period (a good weather state, a fair weather state, and a bad weather state). Also, apples are the only product produced in this world, and they cannot be stored from one period to the next. The following abbreviations will be used: PA apple in first period (i.e., present apple) GA good weather apple, FA fair weather apple, BA-bad weather apple. Suppose that arn apple tree firm offers for sale a bond and stock. An apple tree produces 80GA, 50 FA, and 25BA The bond pays 20GA, 20FA and 20BA. The stock pays 60GA, 30FA and 5BA. The price of the bond is 18PA, and the price of the stock is 19PA. In addition, a security C is traded for 8PA. The security C pays 45GA, 5 FA, and 0 BA (i) Find the arbitrage-free price of the atomic securities. ii) Calculate the arbitrage-free price of an apple tree (iii) Calculate the discount factor and explain its economic interpretation (iv) An investor wants a security that will pay 30GA, 30FA, and 50BA. Construct such a security and determinets arbitrage-free price (v) Compute the arbitrage-free price of a European call option to buy the stock at a price of 25 in the second period

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