Shares of Opto$-$Binocular Company stock currently trade at $$66.$ The annual

standard deviation of the underlying stock returns is $20\%$ per year, and the risk$-$free

interest rate is $9\%,$ annual rate, compounded quarterly. The stock will pay no

dividends or undertake any other capital distributions.

Consider a put option on a share of Opto$-$Binocular with an exercise price of $$64.$

This option can only be exercised at expiration, in $90$ days. Use the binomial option

pricing model with $2$ sub$-$periods to value this option. Please use excel to answer.