[試題] 101下 石百達 財務工程入門 期末考
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）︰102/06/22
考試時限（分鐘）：3hr
是否需發放獎勵金：是
（如未明確表示，則不予發放）
試題 :
(每題10分)
1.Please derive the put-call parity for European currency options.
2.Suppose that a one-year futures price is currently 35. A one-year European
call option and a one-year European put option on the futures with a strike
price of 34 are both priced at 2 in the market. The risk-free rate is 10% per
annum. Identify an arbitrage opportunity.
3.Use the put-call praity relationship to derive, for a non-dividend-paying
stock, the relationship between:
(a) the gamma of a European call and the gamma of the European put (5%)
(b) the vega of a European call and the vega of a European put (5%)
4.Derive the equations corresponding to equation:
Ft + rSFs + 0.5(sigma*S)^2Fss = r*pi
for a portfolio of derivatives on a futures price
5.A European call and put option have the same strike price and time to
maturity. The call has an implied volatility of 30% and the put has an
implied volatitlity of 25%. What trades would you do?
6.Use a three-time-step tree to value a 9-month American call option on wheat
futures. The current futures price is 400 cents, the strike price is 420
cents, the risk-free is 6%, and the volatility is 35% per annum. Estimate
the delta of the option from your tree.
7.Please state the advantages and disadvantages of implicit finite difference
method and explicit finite difference method, respectively.
8.Suppose that the stock price follows geometric Brownian motion:
dS = uSdt + (sigma)Sdw, what is the process followed by S^n?
9.Construct a table showing the payoff from a bull spread when puts with strike
prices K1 and K2 with K2 > K1, are used.
10.What is an expression for the value fo a derivative that pays off $100 if
the price of a stock at time T is greater than the strike price K?
PS：除了第七題是從筆記裡出的之外，其他題目都從助教勾選題目出的，一模一樣
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06/22 17:52, , 1F
06/22 17:52, 1F