Question $5[10$ points$].$

A bond has price $$50$ today. In $3$ months it will become either $$60$ or $$40,$ as given in the following single$-$period binomial tree. A $3-$month put option on the bond has a strike price of $$52.$ Assume the risk$-$free rate $($short rate$)$ is constantly $4\%$ over time.

$3$

$[2$ point$]$ Consider a portfolio of longing $$ units of bond and longing $1$ put option. How to set $$ to make the portfolio riskless? What is the value of the portfolio today?

$[2$ point