Suppose that you are valuing an American$-$type put option on non$-$dividend$-$paying stock with a strike price of $95.$ The expiration date of this option is exactly in $2$ years from now. The spot price of the underlying stock is $100.$

Suppose that this is a volatile stock, and its price may either increase by $25\%$ or fall by $25\%$ by the end of year $1$ and, similarly, increase or decrease by $25\%$ by the end of year $2($compared to the end of year $1$ price$).$ Suppose that the annual risk$-$free interest rate is $6\%.$

Use the Two$-$Step Binomial Tree Model by assuming that there are two $1-$year time$-$steps and $...$

a$)$ outline the binomial tree corresponding to the information outlined in the exercise. Identify the stock price and the value of the option at each node $($based on the calculations in part b of this exercise$).$

b$)$ calculate the value of the option described at each node and find the current value of this option.