894 Part VI: Measuring and Trading Volatility 
quick changes in volatility. In order to quantify the statement that he "wants to be 
gamma long," let us assume that he wants to be gamma long 1,000 shares or 10 con­
tracts. 
It is known that delta can always be neutralized last, so let us concentrate on the 
other two variables first. The two equations below are used to determine the quanti­
ties to buy in order to make gamma long and vega neutral: 
0.0510x + 0.0306y = 10 (gamma, expressed in# of contracts) 
0.089x + 0.147y = 0 (vega) 
The solution to these equations is: 
X = 308, y = -186 
Thus, one would buy 308 March 60 calls and would sell 186 June 60 calls. This is the 
reverse calendar spread that was discussed: Near-term calls are bought and longer­
term calls are sold. 
Finally, the delta must be neutralized. To do this, calculate the position delta 
using the quantities just determined: 
Position delta= 0.54 x 308 - 0.57 x 186 = 60.30 
So, the position is long 60 contracts, or 6,000 shares. It can be made delta neutral by 
selling short 6,000 shares of XYZ. 
The overall position would look like this: 
Position 
Short 6,000 XYZ 
Long 308 March 60 calls 
Short 186 June 60 calls 
Its risk measurements are: 
Delta 
1.00 
0.54 
0.57 
Position delta: long 30 shares (neutral) 
Position vega: $7 (neutral) 
Position gamma: long 1,001 shares 
Gamma 
0 
0.0510 
0.0306 
Vega 
0 
0.089 
0.147 
This position then satisfies the initial objectives of wanting to be gamma long 
1,000 shares, but delta and vega neutral. 
Finally, note that theta = -$625. The position will lose $625 per day from time 
decay. 
The strategist must go further than this analysis, especially if one is dealing with 
positions that are not simple constructions. He should calculate a profit picture as