The following data are market prices on a given day:

The expirations are: $41$ days for JUL; $72$ days for AUG; $163$ days for OCT.

The respective simple annual risk$-$free rates for each expiration period are: $\mathrm{.}0503,\mathrm{.}0535$ and $\mathrm{.}0571.$

The annual volatility of the returns on the underlying stock is $=\mathrm{.}21.$

Use DerivaGem and calculate the Greeks of the following strategies:

Q$1.$ Short a Butterfly with the $160,165$ and $170,$ OCT puts.

Q$2.$ Short a Bear spread with $100$ CBOE of the $155,170$ AUG calls.

Q$3.$ Short a Bull spread with $100$ CBOE of the $165,170$ OCT puts.

Q$4.$ Calculate the number of shares of the underlying stock that will Delta neutralize the strategy in:

$4\mathrm{.}1$ Q$2.$

$4\mathrm{.}2$ Q$3.$

Q$5.$ A financial institution just sold $1,000$ CBOE of the $170,$ AUG calls. Explain how to create a Delta $-$

neutral position with these short calls and shares of the underlying asset.