$8\mathrm{.}1.$ The stock price process for a stock is given by $(S_0,S_1,S_2,S_3)$ in the $3-$period binomial model

with model parameters $r,u,$ and $d$ as given below:

$S_0=32,r=\frac{1}{10},u=\frac{3}{2},d=\frac{1}{2}$

Work out the following for a $3-$period American put on this stock with a strike price of $23.$

The full price process tree $(S_0,S_1,S_2,S_3)$ for this stock.

The full intrinsic value process tree $(G_0,G_1,G_2,G_3)$ for this security.

The full value process tree $(V_0,V_1,V_2,V_3)$ for this security.