I asked this question yesterday: Suppose that, in each period, the cost of a security either goes up

I asked this question yesterday:

Suppose that, in each period, the cost of a security either goes up by a factor of 2 or goes down by a factor of 1/2 (i.e. u=2, d=1/2).  If the initial price of the security is 100, determine the no-arbitrage cost of a call option to purchase the security at the end of two periods for a price of 150.

In the answer I got today the first step said:  “We assume that the probability of moving up and moving down be 50% each, which means equal chances for both the movements. “

I had learned that the risk neutral probability for the stock price to go up is:

p=(1+r-d)/(u-d).  In this particular problem, we'd have

p=(1+0-.5)/(2-.5)=1/3.  And so the probability going down would be 1-p or 2/3.  

Thus, my question is why weren't these probabilities used in the solution previously sent?  And if they should be, what would be the new solution to the problem?  Thank you for your help.  I'm new to learning all of this and some of it is hard for me to understand.

 

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