[試題] 101下 石百達 財務工程入門 小考1
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）︰2013/05/09
考試時限（分鐘）：1hr，點名用
是否需發放獎勵金：是
（如未明確表示，則不予發放）
試題 :
Consider the following options are all European style and without paying
dividend.
1.(20%)Please derive the Delta of a long straddle portfolio, and a short
straddle portfolio, respectively.
2.(20%)What are the Gamma of the 2 portfolios mentioned above?
3.(10%)The stock price is at 110. Consider a butterfly made from options:
long 1 call with K=100, short 2 calls with K=110, and long 1 call with K=120.
Maturities of these options are the same. Will the Gamma of this portfolio
be positive or negative?
4.(20%)
(i )Will the Theta and Gamma be positive or negative if holding a call option
with delta-hedged position?
(ii)Will the Theta and Gamma be positive or negative if holding a long
straddle with delta-hedged position?
5.(10%)A company use delta hedging to hedge a potfolio of long positions in put
and call options on a currency. Which of the following would give the most
favorite result?
(a) a virtually constant spot rate
(b) wild movement in the spot rate
6.(20%)Proof:
(a) Under no arbitrage, Futures F0=S0exp(rT)
(b) While holding a stock option portfolio, will the hedge position be the
same if hedging with futures rather than stock?
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06/22 23:54, , 1F
06/22 23:54, 1F