Problem 4: with the same parameters as in Problem 2, but the additional parameters $n_1 = 4, n_2 =6,$ and $b=66$: price a down and out barrier option, that has payoff at time $T$ of $$ C_T = (S_T...

Python Programming: Option Pricing Using Monte Carlo Simulation

Extracted text: Problem 4: with the same parameters as in Problem 2, but the additional parameters $n_1 = 4, n_2 =6,$ and $b=66$: price a down and out barrier option, that has payoff at time $T$ of $$ C_T = (S_T -K)^+ I\{ S_{n_1} \geq b, S_{n_2} \geq b \}.$$ %3D Use $n=100, n=1000, n=10,000$ id copies of $C_T$ (for averaging). In the above, recall that for any event $A$, $1\{A\}$ denotes the indicator random variable defined by $$ I{{A\} = \left\{ \begin{array}{II} 1 & \mbox{if $A$ occurs,} || 0 & \mbox{if $A$ does not occur.} %3D \end{array} \right. $$ Here, $A = \{S_{n_1} \geq b, S_{n_2} \geq b\}$. %3D In [5]: # write your code here # you may add more cells as needed