We will derive a two$-$state put option value in this problem. We have the following information:

$100$;$x=110$;$1+$

$1\mathrm{.}10.$ The two possibilities for

$S_T$

$=1\mathrm{.}10.$ The two possibilities for

are $120$ and $80.$

Construct a portfolio of three shares of stock and four puts. What is the $($nonrandom$)$ pay$-$off to this portfolio? What is the present value of the portfolio?

Pay$-$off $=350$ and $PV=318\mathrm{.}18$

Pay$-$off $=350$ and $PV=327\mathrm{.}27$

Pay$-$off $=360$ and PV $=318\mathrm{.}18$

Pav$-$off $=360$ and $PV=327\mathrm{.}27$