Answers For 8

Question 1

C = $1.09

Question 2

C = $2.07

Question 3

P = $3.21

Question 4

S = 51
PV(K) = 49
rf = .05
${\sigma}$ =.2
T = .25 (3 months / 12 months)

(1)
\begin{align} d_1=\frac{ln(\frac{S}{PV(K)})}{\sigma\sqrt{T}}+\frac{\sigma\sqrt{T}}{2} \end{align}
(2)
\begin{align} d_1=\frac{ln\frac{51}{49}}{0.2\sqrt{0.25}}+\frac{0.2\sqrt{0.25}}{2} \end{align}
(3)
\begin{align} d_1=\frac{0.04}{0.1}+\frac{0.05}{2} \end{align}

$d_{1}$ = .45

N($d_{1}$) = N(.45) = .6737 Shares

Question 5

You can buy a call for $3 to protect yourself synthetically.
Sell the stock for $38
This generates a net of $38 - $3 = $35.
Invest the $35 at the risk free rate so it grows to $35 x (1+0.05) = $36.75
At maturity if the call is out of the money, buy the stock for under $35, deliver it against the short and keep your profits.
If the call is in-the-money, exercise the call, pay $35 for the stock and deliver it against your short position. Keep your profits.