Sample midterm-法律资料-人文社科-专业资料

Sample Midterm for

Risk Management: Applications to Financial Firms

Multiple Choice

1. No matter what happens, a call option can never be worth more than the stock.

a. True

b. False

c. Not if dividend yield is higher than the risk free rate

2. DeadBeat stock has dropped from $100 to $3 in the last year, since its technology is now obsolete. A

friend is offering to sell you an at the money American put with maturity of 5 years for a premium of $4. Do you:

a. Grab this opportunity and buy the put

b. Pass on this opportunity (and never speak to this ?friend? again)

c. I?m not sure, since the question setup doesn?t talk about dividends at all

3. A forward contract is usually traded

a. Over the counter

b. On the Chicago Mercantile exchange

c. On the NYMEX

4. True or False. A forward is better than a future because it has lower credit risk.

a. True

b. False

5. After a futures transaction the open interest:

a. Increases

b. Decreases

c. Stays the same

d. All of the above are possible

Quantitative Problems

1. The spot price of oil is $80 per barrel and the cost of storing a barrel of oil for one year is $3,

payable at the end of the year. The risk-free interest rate is 5% per annum, continuously

compounded. What is an upper bound for the one-year futures price of oil?

2. A trader owns 55,000 troy oz of silver and decides to hedge with 6-month silver futures contracts.

Each futures contract is on 5,000 troy oz. The standard deviation of the change in the spot price of silver is 0.43. The standard deviation of the change in silver futures prices is 0.40. The coefficient of correlation between the two is 0.95.

3. The LIBOR zero curve is flat at 5% (continuously compounded) out to 1.5 years. Swap rates for

2- and 3-year semiannual pay swaps are 5.4% and 5.6%, respectively. Estimate the LIBOR zero rates for maturities of 2.0, 2.5, and 3.0 years. (Assume that the 2.5-year swap rate is the average

of the 2- and 3-year swap rates and use LIBOR discounting.) 4.

Suppose that a corporate treasurer said: “I will have ￡1 million to sell in six months. If the exchange rate is less than 1.41, I want you to give me 1.41. If it is greater than 1.47 I will accept 1.47. If the exchange rate is between 1.41 and 1.47, I will sell the sterling for the exchange rate.” How could you use options to satisfy the treasurer? 5. Suppose that F1 and F2 are two futures contracts on the same commodity with times to maturity, t1

and t2, where t2>t1. Prove that

21() 21r t t F Fe -≤ where r is the interest rate (assumed constant) and there are no storage costs. For the purposes of this problem, assume that a futures contract is the same as a forward contract.