课程名称︰财务工程入门 课程性质︰系选修 课程教师︰石百达 开课学院：管理学院 开课系所︰财务金融学系 考试日期（年月日）︰20100618 考试时限（分钟）：220 是否需发放奖励金：是 （如未明确表示，则不予发放） 试题 : 1.证明Barrier option 的 In-Out parity。 10% 2.在相同的条件下，比较 (a)Asian option和 European plain vanilla option 10% (b)American barrier option 和 European barrier option 10% 3. (a)给定以下的条件，试求VIX指数。 20% 此条件即为讲义上之大表格 The option used in this hypothetical example have 16 days and 44 days to expiration, respectively. The new VIX generally uses put and call option in the two nearset-term expiration months in order to bracket a 30-day calendar period. (b)请导出VIX的公式。 20% 4.考虑real option，举例说明当value σ越大，投资临界值不一定越高。(假设其他参 数不变) 5% 5.You are given the following information: 10% One share of the S&P index currently sells for 1,000. The S&P index does not pay dividends. The effective annual risk-free interest ratw is 5% You want to lock in the ability to buy this index in one year for a price of 1,025. How can you construct a protfolio by buying or selling European put and call option with a strike price of 1,025? (Instead of longing a future contract) And how much does the protfolio cost? 6.Digital option的定义如下： 5% / 1 if S(T) >= K Payoff= { (只能在期末履约) \ 0 if S(T) < K 用以下的资料，用(两期的)二元树方法，计算此Digital option的价格： S(0) = 50, K = 45, T = 2, u = 1.1, d = 1/u, r = 5% (每期的有效利率)。 7.考虑lookback option，在期末时 T Payoff = max{S(T)-M , 0} 0 T 其中M = min{S(t )|i = 0,1,.....N}，t = i* T/N 0 i i 当N变大时，此option的价格会变大还是变小? 10% -- --

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