課程名稱︰財務工程入門 課程性質︰系選修 課程教師︰石百達 開課學院：管理學院 開課系所︰財務金融學系 考試日期（年月日）︰20100618 考試時限（分鐘）：220 是否需發放獎勵金：是 （如未明確表示，則不予發放） 試題 : 1.證明Barrier option 的 In-Out parity。 10% 2.在相同的條件下，比較 (a)Asian option和 European plain vanilla option 10% (b)American barrier option 和 European barrier option 10% 3. (a)給定以下的條件，試求VIX指數。 20% 此條件即為講義上之大表格 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)請導出VIX的公式。 20% 4.考慮real option，舉例說明當value σ越大，投資臨界值不一定越高。(假設其他參 數不變) 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的定義如下： 5% / 1 if S(T) >= K Payoff= { (只能在期末履約) \ 0 if S(T) < K 用以下的資料，用(兩期的)二元樹方法，計算此Digital option的價格： S(0) = 50, K = 45, T = 2, u = 1.1, d = 1/u, r = 5% (每期的有效利率)。 7.考慮lookback option，在期末時 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 當N變大時，此option的價格會變大還是變小? 10% -- --

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