[試題] 101下 石百達 財務工程入門 期中考
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）︰102/4/26
考試時限（分鐘）：160分鐘
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
CA:American call PA:American put PE:European put
1.Prove So-K<=CA-PA<=So-Kexp(-rT)
(小於等於)
2.A call with a strike price of $60 costs $6. A put with the same strike price
and expiration date costs $4. Construct a table shows the profit form a
straddle. For what range of stock prices would be the straddle lead to a
loss?
3.A company's stock price is $50 and 10 million shares are outstanding. The
company is considering giving its employees 3 million at-the-money 5-year
call options. Option exercises will be handled by issuing more shares. The
stock price volatility is 25%, the 5-year risk-free rate is 5%, and the
company does not pay dividends. Estimate the cost to the company of the
employee stock option issue.
4.Suppose that x is the yield to maturity with compounding on a zero-coupon
bond the palys off $1 at timeT. Assume that x follows the process
dx=a(xo-x)dt+sxdz,
where a,x0,and s are positive constants, and dz is Wiener Process
What is the process followed by the bond price?
5."A box spread comprises four options. Two can be combined to create a long
forward position and two can be combined to create a short forward position."
Explain this statement.
6.Assume that a non-dividend-paying stock has an expected return of r and a
volatility of (sigma). An innovative financial institution has just
announced that it will trade a security that pays off a dollar amount
equivalent to lnST at time T.
(a) Use risk-neutral valuation to calculate the price of the security at
time t in terms of the stock price, S, at time t.
(b) Confirm that your price satisfies the differential equation
df/dt+rs(df/ds)+0.5(sigma)^2*S^2*(d^2f/ds^2)=rf
7.不發股利情形下，at-the-money European call 和European put 何者價值較高？
為什麼？
8.用幾何布朗運動描述股價過程有何優缺點？
9.請用package 概念證明put-call parity
10.在不發股利情形下，假設執行價格微函數：K(t)=Kexp(r(t-to))
t0為起始時間、t為現在時間，試證明
(a)PE(t)>=K(t)-S(t)
(b)PE(t)=PA(t)
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◆ From: 140.112.217.22
※ 編輯: her0418 來自: 140.112.217.22 (06/22 17:11)