# Math Help - Binomial Lattace Model

1. ## Binomial Lattace Model

I need to calculate the pdf for X_i after one year given:
This assumes there is a move in the stock market, either up or down each week.
up=1.012
down=.99
p=.52
n=52 weeks

i
Do I use S_n = S_0 *u^n-i * d^i ?

Not sure how to show this.

Thanks

2. Originally Posted by taypez
I need to calculate the pdf for X_i after one year given:
This assumes there is a move in the stock market, either up or down each week.
up=1.012
down=.99
p=.52
n=52 weeks

i
Do I use S_n = S_0 *u^n-i * d^i ?

Not sure how to show this.

Thanks
The probability of $n$ upward movements and $52-n$ downward movements is:

$p(n.52-n)=b(n;52,0.52)$

so the $p(X=1.012^n 0.99^{52-n})=b(n;52,0.52)$

RonL