Create an GBM function that takes the following parameters:

$n$:$=$ number of paths to be simulated

$m$:$=$ number of discretization points per path

SO :$=$ initial starting point

$d[ln(S_r)]=(-\frac{{}^2}{2})dt+d{W}_r$

Then convert it to

$S_t$

Program the function by using two nested "for loops"

$1$

def

$(n,m,s,,,dt$

arr$=n$

arr$[]=,$

for $1$ in

for $1$ in :

arr$[1,j]=$

convert ins$\_$t into S$\_$t

return arr

part b$)$

run GBM function with the following parameters and plot the results

$)=1000,m=20,SO=100,=0,$ sigma $=0\mathrm{.}001,dt=(1$

the result sould look like a bell shape centerd around $y=S0$ line