2010期权期货考试.试卷A.docVIP

《中国矿业大学2009～2010学年第 2 学期 《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 一 二 三 四 五 六 七 总分 得分 可能用到的数据： N (0.5444) = 0.7069 , N (0.4628) =0.6782 一、 Explanation（％） ‘In’ options(敲入期权) (5) Forward start options 二、(10%)三、(10%)forward position? 四、(10%) 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、(1%) What is the price of a European call option on the SP500 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%)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 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 ②. Give the definitions of delta, gamma, vega, theta, and rho of the derivative。