Structured Products
Spring 2005
Assignment 5
說明一: 上次上課內容 [商品拆解與合成] 的pdf檔 老師已經上傳於授課教材.
說明二: 以下為assignment 5 的內容 同學可以到授課教材 抓取pdf檔.
說明三: 量似乎不少.
1. Assume selling a standard Call option with S = 100, X = 100, T = 90 days, r = 2%,
v = 30%,
With funding cost = 2% (for funds borrowed to purchase underlying stocks for
hedging purpose), calculate the following using Monte Carlo method.
a. The theoretical option premium for this Call.
b. If you use dynamic delta hedging, and hedge frequency (hedge position
adjustment) is one time per day day, calculate the mean and standard
deviation of your hedging result for this Call. (report the mean and standard
deviation of the final value of your hedging position using 100 simulation
run)
c. Repeat part b with hedge frequency of 10 times per day (total of 900 position
adjustments).
d. If each time you adjust (buy or sell) your hedge position, you have to pay
0.1% of the transaction value as the transaction fee, how will that change your
result in part b and part c.
2. 假設券商發行「一觸即發」(商品02) ，標的股價為$48，vol. = 42%，r = 1.2%，
若募集金額為$8,000 萬元，且避險操作以Delta 避險為主。計算：
1) 需建立之避險部位( 標的股數，買或賣)?
2) 假設資金成本為2%，一天的資金利息是多少？
3) 發行後第一天，標的股價下跌至$46，避險部位應如何調整？
4) 發行後第二天，標的股價回漲至至$47.5，避險部位又應如何調整？
3. 針對「前進520」(商品05)，分別對所含之八種商品評價，尋找出是否有哪一
種的投資價值相對上會比較高（也就是你認為最值得購買的）？ 為什麼？
4, 針對「百發百中」(商品07)，由於標的波動率越大，越有可能位於計息範圍
之外。請估計在什麼波動率水準以下，此商品才有價值（值得購買）？假設無風
險利率r = 2%。
Be prepared to discuss your answers in class next time.
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