There is a European put option on a stock that expires in two months. The stock price is $$93,$ and the standard deviation of the stock returns is $68$ percent. The option has a strike price of $$101,$ and the risk$-$free interest rate is an annual percentage rate of $7$ percent.

What is the price of the put option today using one$-$month steps? Use a two$-$state model with one$-$month steps.

What is the Put value?