I have started to work with given two period binomial model S(0)=100 u=1.25 d=0.8 r=0.05 and the market probability of stock going up each period is p=0.55.

I am trying to calculate two probabilities;

  1. P(S(2)>S(0)) -> For this one I thought only Suu (156.25)>100 so I assumed probability being 0.55x0.55.

  2. P(S(2) < S(1),S(1) > S(0)) -> For this I did not know how begin with but I said looks like only up and down gives this so I claimed 0.55x0.45.

So I wanted to ask is this the right way or am I missing something. Any explanation would be appreciated.


1 Answer 1


Answering both questions:

  1. Your answer is correct.
  2. Is the comma (in the probability function) an "And" or a "Or", what is the mathematical notation used? From what you answered, it seems like an "And", and in which case your answer seems correct as well.
  • $\begingroup$ Thank you. Yes that is an and. Appreciate your comment $\endgroup$
    – mva
    Commented Feb 15 at 16:08
  • $\begingroup$ No problem, if you feel my response has helped you, you can accept it as the solution :) $\endgroup$
    – KaiSqDist
    Commented Feb 22 at 14:53
  • $\begingroup$ You got it. I completely forgot to do that my apologies. Thanks again $\endgroup$
    – mva
    Commented Feb 22 at 18:03

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