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

$S_{0}100$;$x=110$;$1+r_f=1\mathrm{.}10.$ The two possibilities for $S_T$ are $120$ and $80.$

a$)$ What is the hedge ratio of the put?

Options:

$-0\mathrm{.}75$

$0\mathrm{.}50$

$0\mathrm{.}75$

$-0\mathrm{.}50$

b$)$ 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?

Options:

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

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

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

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

c$)$ Given that the stock currently is selling at $100,$ what is the value of this put option?

Options:

$6\mathrm{.}82$

$6\mathrm{.}24$

$5\mathrm{.}24$

$5\mathrm{.}82$