IBM stock currently sells for $64$ dollars per share. The implied volatility equals $40\mathrm{.}0.$ The risk$-$free rate of interest is $5\mathrm{.}5$ percent continuously compounded. If you shorted an option on $100$ shares of IBM stock with strike price $69$ and maturity $9$ months, how many shares of stock would you have to buy $($sell$)$ to create a delta$-$neutral hedge?

$47\mathrm{.}02$

$188\mathrm{.}01$

$53\mathrm{.}19$

$25\mathrm{.}74$