Question B $(7$ to $10)$

The SPX is $5431\mathrm{.}6.$ Use the $5440-$ call strike. Assume you have a $10,000-$ share portfolio.

The call delta is $\mathrm{.}495,$ gamma is $\mathrm{.}005,$ theta is $11\mathrm{.}68.$

How many calls are needed to have a covered call?

How many calls are needed to be delta neutral?

What will happen to the delta neutral hedge$-$calls if the change in stock price is large?

a$.$ It will work perfectly.

b$.$ The hedge will be inadequate due to the gamma effect.

c$.$ A non$-$ zero gamma will ensure that the hedge will work perfectly.

If the stock rises by $$20,$ calculate the value of the $5440-$ call using the delta, gamma, and

$3-$day theta.