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tutorial2 - buy 1GA for 0.75BA Dealer III sell 1PA for 2BA...

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TUTORIAL 2– WEEK 3 ECON3107/ECON5106 – Economics of Finance All the questions this week refer to a world in which there are only two periods and two possible states of the world in the second period (a good 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, BA = bad weather apple. 1. Dealer I is willing to trade 0.3PA for 1GA (or vice versa), and dealer II is willing to trade 1GA for 0.6BA (or vice versa). What is the arbitrage-free price of a BA in terms of PA? 2. In addition dealer III is willing to trade 0.6PA for 1BA (or vice versa). Are there arbitrage opportunities? If so, design a profitable arbitrage strategy. 3. Suppose now there are transaction costs. The three dealers have the following bid-ask spreads: Dealer I: sell 1PA for 2.5GA buy 1PA for 2GA Dealer II: sell 1GA for 1BA
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Unformatted text preview: buy 1GA for 0.75BA Dealer III: sell 1PA for 2BA buy 1PA for 1.5BA. Are there arbitrage opportunities now? Explain. 4. Suppose there are no dealers, but now instead, an apple tree firm offers for sale a bond and stock. An apple tree produces 70GA and 45BA. The bond pays 20GA and 20BA. The stock pays 50GA and 25BA. The price of the bond is 18PA, and the price of the stock is 30PA. (i) Find the arbitrage-free price of the atomic securities (i.e., a security that pays 1GA, and another security that pays 1BA). (ii) Calculate the arbitrage-free price of an apple tree. (iii) Construct a profitable arbitrage strategy if the price of an apple tree is lower than its arbitrage-free level. (iv) Calculate the discount factor and explain its economic interpretation. (v) An investor wants a security that will pay 80GA and 100BA. Construct such a security and determine its arbitrage-free price. Note: • Do not submit this tutorial assignment, since it will not be marked. 1...
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