# Share price probability homework

1. Jan 13, 2014

### motherh

Hi, I'm trying to answer the following question:

In each time period, a certain stock either goes down 1
with probability 0.39, remains the same with probability 0.20, or goes up
1 with probability 0.41. Assuming that the changes in successive time periods
are independent, approximate the probability that, after 700 time
periods, the stock will be up more than 10 from where it started.

I managed to answer a similar question where either the price goes up or it goes down but you are multiplying by a percentage rather than adding/subtracting. Any idea on how I could adapt my solution to this question?

If s(t) is the share price at time t and

X$_{i}$ = -1 (if share goes down), 0 (share stays same), 1 (if share goes up)

then would I be right in saying

s(700) = s(0) + $\sum{X_{i}}$ (sum from 1 to 700) ?

Would I then be looking for the probability

Pr{s(700)-s(0) = $\sum{X_{i}}$ > 10}?

2. Jan 13, 2014

### LCKurtz

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