The following data are market prices on a given day:

calls calls calls puts puts puts

Stock strike JUL AUG OCT JUL AUG OCT

$165 $155 $10.5 $11.75 $14 $.1875 $1.25 $2.75

$165 $160 $6 $8.125 $11.125 $.75 $2.75 $4.50

$165 $165 $2.6875 $5.25 $8.125 $2.375 $4.75 $6.75

$165 $170 $.8125 $3.25 $6 $5.75 $7.5 $9

The expirations are 41 days for JUL, 72 days for AUG and 163 days for OCT.

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

The annual volatility of the returns on the underlying stock is s = .21.

Every CBOE option is for 100 shares.

Use DerivaGem and calculate the Greeks of the following strategies:

A. Long 100 Butterflies with the 160, 165 and 170, OCT CBOE puts.

B. 100 Bear spreads with the 155, 170 AUG CBOE calls.

C. 100 Bull spreads with the 165, 170 OCT CBOE puts.

D. How many share of the stock you need to hold to Delta neutralize each of the strategies in a; b; c?