Chapter 40: Advanced Concepts 883 
One other point should be made: The fact that gamma and delta are neutral to 
begin with does not mean that they will remain neutral indefinitely as the stock 
moves (or even as volatility changes). However, there will be little or no effect of 
stock price movements on the position in the short run. 
In summary, then, one can always create a position that is neutral with respect 
to both gamma and delta by first choosing a ratio that makes the gamma zero, and 
then using a position in the underlying security to neutralize the delta that is created 
by the chosen ratio. This type of position would always involve two options and some 
stock. The resulting position will not necessarily be neutral with respect to the other 
risk factors. 
THE MATHEMATICAL APPROACH 
The strategist should be aware that the process of determining neutrality in several 
of the risk variables can be handled quite easily by a computer. All that is required is 
to solve a series of simultaneous equations. 
In the preceding example, the resulting vega was negative: -$238. For each 
decline of 1 percentage point in volatility from .the current level of 35%, one could 
expect to make $238. This result could have been reached by another method, as 
long as one were willing to spell out in advance the amount of vega risk he wants to 
accept. Then, he can also assume the gamma is zero and solve for the quantity of 
options to trade in the spread. The delta would be neutralized, as above, by using the 
common stock. 
Example: Prices are the same as in the preceding example. XYZ is 48. There are 
three months to expiration, and the volatility of XYZ and its options is 35%. The fol­
lowing information is also the same: 
Option 
April 50 call 
April 60 call 
Price 
2.50 
1.01 
Delta 
0.47 
0.17 
Gamma 
0.045 
0.026 
Vega 
0.08 
0.06 
A spreader expects volatility to decline and is willing to set up a position where­
by he will profit by $250 for each one percentage decrease in volatility. Moreover, he 
wants to be gamma and delta neutral. He knows that he can eventually neutralize any 
delta by using XYZ common stock, as in the previous example. How many options 
should be spread to achieve the desired result?