请教一个MFE ASM的问题

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For a stock, you are given:
(i) current price is 40
(ii) no dividents
(iii) continuously compounded risk-free rate is 0

A 1-year American call option on the stock with strike price 45 is modeled with a 1-period binomial tree. The replicating portfolio consists of a long position in 0.2625 shares of stock and a loan of 8.715.

Determine the ratio of the stock price at the upper node to the original stock price.

(A) 1.19 (B) 1.2 (C) 1.21 (D) 1.22 (E) 1.23





Thanks for any comments.









The answer given is (E).

ANS:

The value of the option at the end of the year is 40u-45 at the upper node.
The value of the replicating portfolio at the upper node is 0.2625(40u)-8.715. (why so? I think the replicating should be for current time. How come the replicating portfolio is for upper node?)
Equating two, solve to get u=1.23

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关键词：ASM MFE replicating Continuous Portfolio original position current option price

because the dividents is 0,the interest-free is 0,so at time 1, replicating portfolio at the upper node is 0.2625(40uexp(0))-8.715exp(0),it is the option payoff at the upper node,that is 40u-45 ,solve for u=1.23

I agree with the 2 floor

replicating portfolio can for any node in the binomial tree.

If u review charpter 3, u can find the way which calculate the delta(share of stock) and B(loan), and then u will understand.

I am preparing for MFE too...so despaired....average wrong questions for every Practice exam is above 10....

谢谢大家了哈