金融工程试题

六、 计算题(15分) 35. Suppose the continuously compounded risk-free interest rate is r per annum and stock price St follows geometric Brownian motion, i.e., dSt = µSt dt + σSt dzt, √ where z is standard Brownian motion, µ is a constant and σ = 2r. We also assume the initial stock price S0 = x > 0. Please calculate the price at t = 0 of a security which pays 1 at time T if ST > x, and 0 otherwise.
B. highest price in a trading day D. lowest price in a trading day
15. In Merton’s jump-diffusion model, the jump time is determined by a ( )
A. Brownian motion C. square root process
D. 1 − N (d1)
14. In a futures contracts, which price is used for calculating daily gains and losses
and margin requirements?
()
A. opening price C. settlement price
7. A company has a $20 million portfolio with a beta of 1.5. It would like to
use futures contracts on the S&P 500 to hedge its risk. The index is currently
mation.
()
四、 名词解释(每小题5分，共15分)
31. Futures
32. Implied volatility
33. Exotic options
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五、 简答题(10分) 34. Describe the differences between forward contracts and futures contracts.
()
22. A position in the underlying asset itself can be used to change the gamma of
a portfolio.
()
23. A position in a forward contract on the underlying asset itself cannot be used
云南财经大学 2010 至 2011 学年 下 学期 金融工程 课程期中考试试卷
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专业：
班 级：
得 一 二 三 四 五 六 七 八 总分 复 核
分
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阅 卷 人
一、 填空题(每空2分，共20分)
1. The delta of a forward contract on one share of a non-dividend-paying stock
0.86σn2−1. Then the long-run average variance implied this model is
.
4. The delta of an at-the-money 6-month European call option on a non-dividend-
paying stock when the risk-free interest rate is 10% per annum and the stock
A. normal distribution C. exponential distribution
B. lognormal distribution D. Poisson distribution
12. The delta of a European call option on a non-dividend-paying stock is ( )
9. A
is a portfolio consisting of standard European call, standard Eu-
ropean puts, forward contracts, cash, and the underlying asset itself.
10. Options that will start at some time in the future are called
B. Poisson process D. geometric Brownian motion
16. It is March 1. A U.S. company expects to receive 50 million Japanese yen at
the end of July. Yen futures contracts on the CME have delivery months of
options.
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姓 名：
学 号：
二、 单选题(在每小题的四个备选答案中选择一个正确的答案代码填入题后括号 内，每小题2分，共20分)
11. When stock price follows a geometric Brownian motion, the stock return is a ()
standing at 1080, and each contract is for delivery of $250 times the index. It
should short
contracts to minimizes risk.
8. A position with a delta of
is referred to as delta neutral.
17. GARCH model is proposed by
A. Engle
B. Bollerslev
C. Nelson
() D. Scholes
18. Which of the following options is path dependent?
A. European call options C. Asian options
it.
()
27. A short hedge is appropriate when the hedger already owns an asset and
expects to sell it at some time in the future.
()
28. On a practical level, a company may find that it is increasing rather than
decreasing risk by hedging if none of its competitors does so.
()
29. Volatility skew is a pattern for foreign currency options
()
30. The usual method for estimating GARCH model is maximum likelihood esti-
price volatility is 25% per annum is
.
5. Options on options are called
options.
6. Suppose that the stand deviation of quarterly changes in the prices of a commodity is $0.65, the standard deviation of quarterly changes in a futures price on the prices of a commodity is $0.81, and the coefficient of correlation between the two changes is 0.8. The optimal hedge ratio for a three-month contract is .
()
20. Which of the following stock market indexes is price weighted?
()
A. Dow Jones Industrial Average C. Shanghai Composite Index
B. S&P500 D. FTSE 100 Index
三、 判断题(在正确的题后括号内划”√”，错误的题后括号内划”×”，每小题2分， 共20分)
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21. During the delivery period of a futures contract, the decision on when to deliver
is made by the party with the long position.
to change the gamma of a portfolio.
()
24. If a hedger requires a portfolio to be both gamma and vega neutral, at least two traded derivatives dependent on the underlying asset must usually be used. ()
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25. The basis in a hedging situation using futures can not be negative. ( )
26. The position necessary to create an option synthetically is the same as to hedge
March, June, September, and December. What is the delivery month of the
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futures contract that the company should use for hedging?
()
A. March
B. June
C. September D. December
B. Binary option D. Exchange options
()
19. Which of the following option’s vega can be negative ?
A. European call options C. Binary option
B. European put options D. Barrier options
is
.
2. The gamma of a forward contract on one share of a non-dividend-paying stock
is
.
3. Suppose a GARCH(1,1) model is estimated as σn2 = 0.000002 + 0.13u2n−1 +
A. N (d1)
B. N (d2)
C. N (d1) − 1
D. 1 − N (d1)
13. The delta of a European put option on a non-dividend-paying stock is ( )
A. N (d1)
B. N (d2)
C. N (d1) − 1