The following information is given for the European call option on

Schlumberger $($SLB$).$ S$=86\mathrm{.}89,$ X$=90,$ rc$=1\mathrm{.}0\%($continuously compounded interest rate$),$ T$=19/365=0\mathrm{.}0521,$

actual call option price $=1\mathrm{.}21$ and no cash dividend is expected by option expiration.

$($a$)$ When we select an initial implied volatility $()$ of $0\mathrm{.}40,$ what value does the Black$-$Scholes model

predict for the call option on SLB$?$

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

decrease our initial guess?

$($c$)$ Calculate the vega $($

$2$

$2$

$1$

$2$

$1$ d

eTSC $$

$=$

$$

$)$ using the initial selected volatility of $0\mathrm{.}40.$

$($d$)$ Based on$)(\text{'}$

$)($

$1$

n

n

nn C

CmarketC

$$

$$

$$

$=+,$ what is our new guess for the implied volatility?

$($e$)$ Calculate the implied volatility using EXCEL.