06期权期货试卷A卷

华中科技大学文华学院

2008-2009学年第二学期《期权期货》期末考试试卷A卷

课程性质：必修 使用范围：本科 考试时间：2009年5月5日 考试方式：闭卷

学号______专业_______班级_______学生姓名_______成绩________

1. Describe the profit from the following portfolio: a long forward contract on an asset and a long European put option on the asset with the same maturity as the forward contract and a strike price that is equal to the forward price of the asset at the time the portfolio is set up.(6)

2. Suppose that the risk-free interest rate is 10% per annum with continuous compounding and that the dividend yield on a stock index is 4% per annum. The index is standing at 400，and the futures price for a contract deliverable in four months is 405.What arbitrage opportunities does this create?(8)

3. The spot price of silver is $9 per ounce. The-storage costs are $0.24 per ounce; per year payable quarterly in advance. Assuming that interest rates are 10% per annum for all maturities, calculate the futures price of silver for delivery in 9 months.(8)

4. It’s July 30,1996.The cheapest-to-deliver bond in a September 1996 Treasury bond futures contract is a 13% coupon bond, and delivery is expected to be made on September 30,1996.Coupon payments on the bond are made on February 4 and August 4 each year. The term structure is flat, and the rate of interest with semiannual compounding is 12% per annum. The conversion factor for the bond is 1.5.The current quoted bond price is $110.Calculate the quoted futures price for the contract. (10)

5. Assume that a bank can borrow or lend money at the same interest rate in the LIBOR market. The 90-day rate is 10% per annum, and the 180-day rate is 10.2% per annum both expressed with continuous compounding and actual/actual day count. The Eurodollar futures price for a contract maturing in 90days is quoted as 89.5.What arbitrage opportunities are open to the bank? (12)

6. The price of an American call on a non-dividend-paying stock is $4.The stock price is $31,the strike price is $30,and the expiration date is in 3 months. The risk-free interest rate is 8%.Derive upper and lower bounds for the price of an American put on the same stock with the same strike price and expiration date. Explain carefully the arbitrage opportunities in Problem45 if the American put price is greater than the calculated upper bound.(12)

7.

Call options on a stock are available with strike prices of $15，$17.5，and $20，and expiration dates in 3 months. Their prices are$4，$2，and$0.5，respectively. Explain how the options can be used to create a butterfly spread. Construct a table showing how profit varies with stock price for the butterfly spread.(12)

A stock price is currently $40.It is known that at the end of 3 months it will be either $45 or $35，The risk-free rate of interest with quarterly compounding is 8% Per annum. Calculate the value of a 3-month European put option on the stock with an exercise price of $40.Verify that no-arbitrage arguments and risk-neutral valuation arguments give the same answers.(12)

8.

9.

A stock price is currently $50.over each of the next two 3-month periods it is

expected to go up by 6% or down by 5%.The risk-free interest rate is 5% per annum with continuous compounding. What is the value of a 6-month European call option with a strike price of $51?

For the situation considered in Problem 9，what is the value of a 6-month European put option with a strike price of $51?Verify that the European call and European put prices satisfy put-call parity. If the put option were American，would it ever be optimal to exercise it early at any of the nodes on the tree?(20)

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