Problem $16-8($Algo$)$

We will derive a two$-$state put option value in this problem. Data: $S_e=$$$140$;$x=$$$150$;$1+r=1\mathrm{.}10.$ The two possibilities for $S_T$ are $$170$

and $$70.$

Required:

a$.$ The range of $S$ is $$100$ while that of $P$ is $$80$ across the two states. What is the hedge ratio of the put? $($Negative value should be

indicated by a minus sign. Round your answer to $2$ decimal places.$)$

Answer is complete and correct.

Hedge ratio

$(0\mathrm{.}80)$

b$.$ Form a portfolio of four shares of stock and five puts. What is the $($nonrandom$)$ payoff to this portfolio? $($Round your answer to $2$

decimal places.$)$

Answer is complete and correct.

c$.$ What is the present value of the portfolio? $($Round your answer to $2$ decimal places.$)$

Answer is not complete.

d$.$ Given that the stock currently is selling at $$140,$ calculate the put value. $($Do not round intermediate calculations and round your

answer to $2$ decimal places.$)$

Put value