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