Question #$4$: Black$-$Scholes Call$-$Option Valuation $[30$ Points$]$

Current Stock Price $(S_0)=$$$48\mathrm{.}75$

Strike Price $(x)=$$$42$

interest rate $(r)=0\mathrm{.}05$

annual dividend yield $()=0$

Time to expiration $(T)=9$ months years$)$

Standard deviation $()=0\mathrm{.}32$

$[$A standard normal table is provided in Cat Courses under "Other Files" Folder.$]$

$($a$)$ Using the Black$-$Scholes formula, find the value of a call option given the above information. $($Hint:

When calculating $d_1$ and $d_2$ be sure to round to the $2^{nd}$ decimal point$)[10$ Points$]$

$($b$)$ What is the price of the put$-$option, with the same strike price and expiration date as the call, using the

same information? $[$Hint: Use the Put$-$Call Parity relationship$][5$ Points$]$

$($c$)$ Recalculate the value of the call option and the put option if the strike price was $$46($instead of $$42)$

Assume all other variables remain constant $[15$ Points$]$