衍生品定价习题，老师留的作业，求高人解答

florachu

2892

收藏 2010-09-15

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 (&Aacute;, &Atilde;). 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.

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.

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lkylelj

2010-9-15 12:30:31

数学符号太乱了，，看不清楚

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dream03

2010-9-15 20:40:54

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]

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dream03

2010-9-15 20:42:44

其他的类似的做

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