2010期权期货考试.试卷A

《Options, Futures and other Derivatives》试卷（A）卷

考试时间：100分钟 考试方式：闭 卷

学院 班级 姓名 学号 题号 得分 阅卷人 可能用到的数据：

N (0.5444) = 0.7069 , N (0.4628) =0.6782 一、 Explanation（30％） (1) Short selling

(2) Factors affecting stock option pricing

(3) risk-neutral valuation

一 二 三 四 五 六 七 总分 (4) ‘In’ options(敲入期权)

(5) Forward start options

二、(10%) The price of gold is currently $500 per ounce. The forward price for delivery in one year is $700. An arbitrageur can borrow money at 10% per annum. What should the arbitrageur do? Assume that the cost of storing gold is zero.

三、(10%) What is the difference between a long forward position and a short forward position?

四、(10%) One call option with a strike price of $65 costs $2. Another call option with a strike price of $50 costs $4。 Both the options have the same expiration date T.

① Explain how a bull spread can be created from these two options. ② Construct a table that shows the payoff and profit from the bull spreads.

③ For what range of stock prices would the bull spread lead to a loss?

五、(10%) What is the price of a European call option on the S&P500 that is two months from maturity, the current value of the index is 930, the exercise price is 900, the risk-free interest rate is 8% per annum, the volatility of the index is 20% per annum., Continuous dividend yields is 3% per annum? （计算精确至四位小数）

六、(15%) Consider one year American put option on a non-dividend-paying stock when the stock price is $50, the strike price is $50, the risk-free interest rate is 10% per annum, and the volatility is 40% per annum. Divide the year into three 4-month time intervals and use the tree approach to estimate the value of the option. （计算精确至四位

小数）

七、(15%) The stock price process assumed satisfies

dSSdtSdW

Suppose that f is the price of a call option or other derivative contingent on S.

①. Using no arbitrage opportunity to derive the Black-Scholes Differential Equation

ff1222frSSrf 2tS2S②. Give the definitions of delta, gamma, vega, theta, and rho of the derivative。