課程名稱︰ 財務工程 課程性質︰選修 課程教師︰李志偉 開課學院：管院 試題 : 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.假設12月份天然氣期貨契約於11/1開始交易。 (a) 11/1他當天甲新買進6000口，乙新賣出6000口，則當天總open interest為多少？ (b) 11/2丙新買進2000口、甲賣出持有部位中的2000口，則當天總open interest為多少？ (c) 11/3乙補回持有部位中的2000口，戊新買進1000口，丁新賣出3000口，則當天總open int erest為多少？ 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 (買賣口數)? 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)畫出此currency swap 在期初、期中、期末的cash flow. (b)以債券法來評價此CS, 可視為USD bond （價值Va）與SF bond (價值Vb)的組合，請列 出數學式表達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與Q來表示。 8.下列程式描述waterfall in a securitization 的收取現金方式，其中tranche-1面額 為$20，tranche-2面額為$30，tranche-3面額為$50。 問tranche 1~3，何者券期風險最高？為什麼？ https://i.imgur.com/lrl2QFa.jpg 另外有兩題上機考 --

※ 發信站: 批踢踢實業坊(ptt.cc), 來自: 60.103.218.198 (日本) ※ 文章網址: https://webptt.com/m.aspx?n=bbs/NTU-Exam/M.1637256582.A.5B0.html