Generic Stock Inc. $($GS$)$ is trading at $$100.$ A call option with a strike price of $$102,$ which

expires in $6$ months, costs $$9\mathrm{.}52($assuming a risk$-$free rate of $5\%$ and a volatility of $0\mathrm{.}33).$

What is the Delta of this option?

b$.$ Using your answer from above, assuming you want to write $12$ call options $($you are

obligated to buy $1,200$ shares$),$ how many shares must you purchase today in order for

your position to be Delta Neutral?

c$.$ Assuming your portfolio now has a Gamma of $-12,$ and the option has a Gamma of

$1\mathrm{.}3333,$ how many more options must you buy to make your portfolio Gamma Neutral?

d$.$ After making your portfolio Gamma Neutral, it is no longer Delta Neutral. How many

more shares must you buy or sell in order to be both Gamma and Delta Neutral