Project: American Put Option Valuation Using $4-$Period Binomial Tree Problem Statement You are tasked with valuing an American put option on a non$-$dividend$-$paying stock using a $4$period binomial tree model. The option has the following characteristics: $-$ Current stock price $\backslash (\backslash$left$(\backslash$mathrm$\{$S$\}\_\{\backslash$mathrm$\{$o$\}\}\backslash$right$)$: $\backslash$$ $100\backslash )-$ Strike price $($K$)$: $\backslash (\backslash$$ $100\backslash )-$ Time to maturity: $1$ year $($divided into $4$ equal periods, $\backslash (\backslash$mathrm$\{$h$\}=0\mathrm{.}25\backslash ))-$ Risk$-$free interest rate $($r$)$: $\backslash (1\mathrm{.}25\backslash \%\backslash )$ per period $-$ Volatility of stock price $\backslash ((\backslash$sigma$)$: $20\backslash \%\backslash )$ Tasks $1.$ Construct the complete $4-$period binomial tree showing: $-$ Stock price at each node $($you need to calculate $\backslash ($ u $\backslash )$ and $\backslash ($ d $\backslash )$ first$).-$ Corresponding put option value at each node $($solve from backward$).-$ Clear indication of nodes where early exercise is optimal. $2.$ At each node: $-$ Calculate both the continuation value and the intrinsic value $-$ Continuation value: the value of the option if it is alive, which is computed using risk$-$neutral pricing formula. $-$ Intrinsic value: the value of the option if immediate exercise. $-$ Determine whether early exercise is optimal and highlight the specific node where early exercise is optimal $3.$ Calculate the current value of the American put option and compare it to the value of an equivalent European put option $($which cannot be exercised early$).$ Submission Submit an Excel spreadsheet that contains a visual representation of the complete binomial tree showing all stock prices and option values, with each cell including your formulas for verification. Specifically, highlight and discuss the nodes where early exercise is optimal.