衍生品定价习题，老师留的作业，求高人解答

是 否 +2 论坛币

k人 参与回答

经管之家送您一份

应届毕业生专属福利!

求职就业群

赵安豆老师微信：zhaoandou666

经管之家联合CDA

送您一个全额奖学金名额~ !

立即领取

感谢您参与论坛问题回答

经管之家送您两个论坛币！

+2 论坛币

1。Consider a simple binomial one-step model with one riskless asset (bond) and one risky asset (stock):

Bt = er t

St = St−1 uXt d1−Xt where P(Xt = 1) = p = 1 − P(Xt = 0)

Furthermore, we consider a European put option with strike price e 10.00 that expires

after T = 1 period. We assume that the initial value of the stock is e 10.0 and that

u = 1.5, d = 0.5, r = 0.09531, and p = 0.7.

(a) Determine the replicating portfolio (Á, Ã). What is the price of the portfolio at

time t = 0?

(b) Determine the price of the option by risk-neutral pricing and compare it with the

price of the replicating portfolio.

(c) Show explicitly how to use the available instruments to make an arbitrage profit if

the observed market price for the above European put option is e 2.00.

e=euro

2。 Arbitrage pricing of a European swap

Consider a (European) swap contract:

(a) The buyer pays the seller an amount P0 to enter into the contract at time t = 0.

(b) The seller agrees to exchange one unit of asset A1 for one unit of asset A2 at time

t = T.

Suppose the market consists of one riskless asset B with interest rate r and the two

assets A1 and A2, and let Bt, A1t

, and A2t

be the corresponding prices at times t with

0 · t · T.

(a) Use the law of one price to determine the fair price P0 of the contract.

(b) Show that any deviation from the price found in (1) indeed leads to an arbitrage

opportunity by constructing suitable arbitrage portfolios.

扫码加我 拉你入群

请注明：姓名-公司-职位

以便审核进群资格，未注明则拒绝

分享0 收藏0 回帖

关键词：衍生品定价 高人解答 衍生品 Constructing replicating initial simple period option 衍生品

数学符号太乱了，，看不清楚

1.（a）构造资产A：它包括a单位股票和b单位债券，在t=0时刻，该组合的价值为A0=a*S0+b*B0（其中S0=10，B0=1），在t=1时刻，资产组合两个未来价值：上升状态：A1=a*Su+b*exp(r),下降状态：A1=a*Sd+b*exp(r),其中：Su=u*S0，Sd=d*S0，

令，a*Su+b*exp(r)=U， a*Sd+b*exp(r)=D，这样该资产组合复制了看跌期权，U=max{ X- Su，0}= max{10-15，0}=0，D= max{ X- Sd，0}= max{10-5，0}=5，Su=15,Sd=5

[img][/img]

其他的类似的做