课程名称︰ 财务工程 课程性质︰选修 课程教师︰李志伟 开课学院：管院 试题 : 1. The price of gold is currently $1000 per ounce. The forward price for delivery in one year is $1200. An arbitrageur can borrow money at 10% per annum. How m uch could the arbitrageur gain? Assume that the cost of storing gold is zero a nd that gold provides no income. 2.假设12月份天然气期货契约於11/1开始交易。 (a) 11/1他当天甲新买进6000口，乙新卖出6000口，则当天总open interest为多少？ (b) 11/2丙新买进2000口、甲卖出持有部位中的2000口，则当天总open interest为多少？ (c) 11/3乙补回持有部位中的2000口，戊新买进1000口，丁新卖出3000口，则当天总open int erest为多少？ 3. On July 1 , an investor holds 50000 shares of a certain stock. The market pric e is $30 per share. The investor is interested in hedging against movements in the market over the next month and decides to use the September Mini S&P 500 futures contract. The index is currently 1500 and one contract is for delivery of $50 times the index. The beta of the stock is 1.3. What strategy should th e investor follow (买卖口数)? Under the circumstances will it be profitable? 4. Suppose that the forward LIBOR rate for the period between time 1.5 years and time 2 years in the future in 5% (with semiannual compounding) and that some time ago a company entered into an FRA where it will receive 5.8% (with semian nual compounding) and pay LIBOR on a principal of $100 million for the period . The 2-year risk -free rate is 4%(with continuous compounding .) What is the value of the FRA？ 5. It is July 30,2015. The cheapest-to-deliver bond in a September 2015 Treasury bond future contract is a 13% coupon bond, and delivery is expected to be made on September 30,2015. Coupon payments on the bond are made on February 4 and August 4 each year. The term conversion factor for the bond is 1.5. The current quoted bond price is $110. There are 176 days between February 4 and July 30 and 181 days between F ebruary 4 and August 4. (a) Calculate the cash price of the CTD bond. (b) Calculate the cash futures price of the CTD bond. 6. On August 1 a portfolio manager has a bond portfolio worth $10 million. The du ration of the portfolio in October will be 7.1 years.The December Treasury bon d futures priceis currently 91-12 and the cheapest-to-deliver bond will have a duration of 8.8 years at maturity. How should the portfolio manager immunize the portfolio against changes in interest rates over the next two months? 7. A financial institution has entered into a 10-year currency swap with compa ny Y. Under the terms of the swap , the financial institution receives interes t at 3% per annum in Swiss francs and pays interest at 8% per annum in U.S. do llars. (a)画出此currency swap 在期初、期中、期末的cash flow. (b)以债券法来评价此CS, 可视为USD bond （价值Va）与SF bond (价值Vb)的组合，请列 出数学式表达Va,Vb，不用算出。 (c) If Q is the current exchange rate (number of units of currency SF per unit of currency USD)，what is the value of the swap in currency USD? 用Va,Vb与Q来表示。 8.下列程式描述waterfall in a securitization 的收取现金方式，其中tranche-1面额 为$20，tranche-2面额为$30，tranche-3面额为$50。 问tranche 1~3，何者券期风险最高？为什麽？ https://i.imgur.com/lrl2QFa.jpg 另外有两题上机考 --

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