$(7\%)$ The following information is given for the European call option on Schlumberger $($SLB$).S=67\mathrm{.}44,$

$x=65,r_c=1\mathrm{.}0\%($continuously compounded interest rate$),T=\frac{32}{365}=0\mathrm{.}08767123,$ actual call option price $=$

$4\mathrm{.}15$ and no cash dividend is expected by option expiration.

$($a$)(1\%)$ When we select an initial implied volatility $()$ of $0\mathrm{.}30,$ what value does the Black$-$Scholes model

predict for the call option on SLB$?$

$($b$)(1\%)$ If an adjustment to the initial guess of implied volatility would be needed, should we increase or

decrease our initial guess?

$($c$)(1\%)$ Calculate the vega $(\frac{\text{d}\text{e}\text{l}\text{C}}{\text{d}\text{e}\text{l}}=\frac{S\sqrt[\phantom{2}]{T}{e}^{-\frac{1}{2}{d}_1^2}}{\sqrt[\phantom{2}]{2}})$ using the initial selected volatility of $0\mathrm{.}30.$

$($d$)(1\%)$ Based on ${}_{n+1}={}_n-\frac{C({}_n)-\text{C}\text{m}\text{a}\text{r}\text{k}\text{e}\text{t}}{C^{\text{'}}({}_n)},$ what is our new guess for the implied volatility?

$($e$)(1\%)$ Calculate the implied volatility using EXCEL.

$($f$)(2\%)$ Calculate the price of European put option on SLB based on the Black$-$Scholes model using the

implied volatility found in part $($e$)$ and the same other parameters.