With the relevant data from Part $1,$ use the Black$-$Scholes formula to calculate and report the value of an otherwise$-$similar European$-$style Call option. From this value, use the European Put$-$Call Parity relationship $($provided on Page $3)$ to find the value of a European$-$style Put option with the same terms. Calculate the difference between your put value here and the put value found in Part $1,$ and provide two explanations of any difference that you find.

The Black$-$Scholes Model

$C(S,)=SN(d_1)-PV(K)N(d_2)$

where:

$d_1=\frac{ln(\frac{S}{PV(K)})+\frac{1}{2}{}^2}{\sqrt[\phantom{2}]{}},d_2=d_1-\sqrt[\phantom{2}]{}$

and:

$PV(K)=K{r}^{-}$

when:

$S-=$ the current stock price

$K-=$ the striKe $($exercise$)$ price

$-=$ the time$-$to$-$expiration $($in years$)$

$r-=$ the risk free annual factor, $=(1+i)$

$-=$ the standard deviation of the stock's returns $(\%/$year$)$

$N(*)-=$ the cumulative standard normal probability distribution.

$2$

European$-$Style Put$-$Call Parity Relationship

$P=C-S+PV(K)$

$($For a non$-$dividend$-$paying stock.$)$

Useful Excel Functions

$e^z,=$ExP$(z)$

$\sqrt[\phantom{2}]{z},\frac{?}{S}=QRT(z)$

max$\{y,z\},=$MAx$(y,z)$

$ln(z),=LN(z)$

$N(z),=$ NORM.$S.$DIST $(z,$TRUE$)$

The symbol $z$ indicates a required argument for the function, and the Excel function includes the $"="$ sign.

Note that the NORM.S$.$DIST function with the logical value of TRUE is for the cumulative standard normal distribution $($the special case of a mean of zero and standard deviation of one$)$ and only requires two arguments. The Excel function NORM.DIST is more general and requires you to specify values for the mean and standard deviation, and the logical value of TRUE for the cumulative distribution. The NORM.DIST function can be used in your Black$-$Scholes calculation instead of NORM.S$.$DIST but then you will need to input the extra arguments, i$.$e$.$ NORM.S$.$DIST $(z,$TRUE$)=$NORM.DIST$(z,0,1,$TRUE$)$