The stock price is currently $$130.$ Over each of the next two $2-$month periods, it is expected to go up by $3\%$ or down by $4\%.$ The risk$-$free interest rate is $1\mathrm{.}5\%$ per annum with continuous compounding. What is the value of a $4-$month European put option with a strike price of $$120?$ Use a binomial tree model, and round the result to three decimal places.

$1.$ $$1\mathrm{.}019$

$2.$ $$2\mathrm{.}602$

$3.$ $$0\mathrm{.}029$

$4.$ $$0\mathrm{.}0$

$5.$ $$6\mathrm{.}645$