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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