ST_path_f<-function(S,r,T,n,sigma){
    delta_T<-T/n
    ST<-seq(1:n)*0
    ST[1]<-S
    for (i in 2:n){
       temp1<-r-0.5*sigma*sigma*delta_T
       temp2<-sigma*rnorm(1)*sqrt(delta_T)
       ST[i]<-ST[i-1]*exp(temp1+temp2)
   }
   return(ST)
}