Use the binomial valuation method for $N=4$ periods to determine the value of an American$-$style Put option with a striKe price of $$40$ that expires in $60$ days. Note that $=\frac{60}{365}$ years, and $h=\frac{}{N}$ is the amount of time $($in years$)$ covered by one period. The other relevant data are:

Current stock price: $S=$$$36\mathrm{.}75(no$ dividends$)$

Annual riskless interest rate: $i=4\mathrm{.}50\%$

Annual volatility: $=28\%$

The values of the parameters $u,d,$hat$(r),$ and $$ can be found from the equations:

$u=e^{\sqrt[\phantom{2}]{h}},d=\frac{1}{u},$hat$(r)=r^h=(1+i{)}^h,=\frac{(hat(r))-d}{u-d}$

Prominently list on your spreadsheet the values for these parameters displayed to four decimal places.$*$

Using the values for the parameters $u$ and $d,$ build the binomial "tree" showing all of the possible realizations for the stock price. Next, for each node in the binomial tree, calculate the corresponding put option value. Specifically, for each of the five possible stock prices at $t=4($expiration$)$:

$P_t=$max$\{0,K-S_t\}$

And then for all of the ten possible stock prices at $t=0,1,2,3$ :

$P_t^f=\frac{1}{(hat(r))}[P_{u,t+1}+(1-)P_{d,t+1}]$

$P_t=$max$\{P_t^f,K-S_t\}$

where the last step is the check for early exercise. Clearly display the price of the stock and the value of the put at each node, displayed to four decimal places.