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