Let S$0,\backslash$mu $,\backslash$sigma be constants, S$0>0,\backslash$sigma $>0.$ Assume that

dS$($t$)=$ S$($t$)(\backslash$mu dt $+\backslash$sigma dW $($t$)),$ S$(0)=$ S$0.$

Given that we approximate S$($T $)$ by

S$($ti$+1)$ :$=$ S$($ti$)+$S$($ti$)(\backslash$mu $($ti$+1$ti$)+\backslash$sigma $($W$($ti$+1)$W$($ti$))),$

$[12$ Points$]$

S$($t$0)$:$=$S$0$

Name and explain four $($possible$)$ sources of the numerical error of the Monte$-$Carlo approxi$-$

whereT $=$tm $>>$t$0=0.$ mation

of the expectation E$($S$($T$)).$