880 Part VI: Measuring and Trading VolatiRty 
attempting to create a spread that is neutral with respect to both gamma and delta, 
he could attempt it in the following way: 
Example: XYZ is 60. A spreader wants to establish a spread that is neutral with 
respect to both gamma and delta, using the following prices: 
Option 
October 60 call 
October 70 call 
Delta 
0.60 
0.25 
Gamma 
0.050 
0.025 
The secret to determining a spread that is neutral with respect to both risk meas­
ures is to neutralize gamma first, for delta can always be neutralized by taking an off­
setting position in the underlying security, whether it be stock or futures. First, deter­
mine a gamma neutral spread by dividing the two gammas: 
Gamma neutral ratio= 0.050/0.025 = 2-to-l 
So, buying one October 60 and selling two October 70 calls would be a gamma 
neutral spread. Now, the position delta of that spread is computed: 
Position 
Long 1 October 60 call 
Short 2 October 70 calls 
Net position delta: 
Delta 
0.60 
0.25 
Position Delta 
+60 shares 
-50 shares 
+ 10 shares 
Hence, this gamma neutral ratio is making the position delta long by 10 shares 
of stock for each l-by-2 spread that is established. For example, if one bought 100 
October 60 calls and sold 200 October 70 calls, his position delta would be long 1,000 
shares. 
This position delta is easily neutralized by selling short 1,000 shares of the stock. 
The resulting position is both gamma neutral and delta neutral: 
Option Position Option Position 
Position Delta Delta Gamma Gamma 
Short 1,000 XYZ 1.00 -1,000 0 0 
Long 1 00 October 60 calls 0.60 +6,000 0.050 + 500 
Short 200 October 70 calls 0.25 -5,000 0.025 - 500 
Net Position: 0 0