搞不懂性别~

Problem1:

The formular for call at t is C(t) = e^r(T-t)*E_Q[(S(T)-E)+|Ft],

where S(t) follows binomial distribution, i.e. we split time interal[0,T] into n pieces, then the time step is T/n

at t we have S(t+1) will be either S(t)*e^(u*T/n) or  S(t)*e^(d*T/n), with probability p and 1-p. By means of risk neutral prob, p = (e^r-1)/(u-d).

Next we need to decide the condition of exercise the call, i.e. how manp up jumps will be required for S(T)>E?

assume we need k up-jumps, i.e. S(T) = S(t)*[(e^(u*T/n))^k]*[(e^(d*T/n))^（n-k)]>E, by inverting this inequality, we can have the minimum number of ups. Take the integer part of k+1 if k is not a interger, denotes it as k. 

Finaly we need to solve the expectation under risk neutral probability Q, E_Q[(S(T)-E)+|Ft]= sum _j from k to n ( S(t)*combination(j,n)*[(p*e^(u*T/n))^j]*[((1-p)*e^(d*T/n))^(n-j)]  -   sum _j from k to n ( E*combination(j,n)*[p^j]*[((1-p)*(n-j)].

As to the hedging, we need find out every point's call price, and take the portfolio of delta(t) number of shares and psi(t) amount of risk free asset. where delta(t) is the ratio of the difference of C(t+1) and the diff of S(t+1). Psi(t) = C（t)-delta(t)*S(t).

   2:　cannot understand you question?

先算风险中性概率：(R-D)/(s-d),美式和欧式不一样，欧式简单，利用中性概率求出T其价格然后贴现就可以了。保值的话是用股指期货+股票，做一个PORTFOLIO，匹配度我忘了，实在想要给我站内信，可以保证获得无风险利率。

关于第二个题目，可以从期权组合角度考虑（例如蝶式什么的当然这个题目不是蝶式），具体看一下HULL的书，应该是最基本的熊市组合，书上应该有

[此贴子已经被作者于2008-7-17 13:17:06编辑过]