Chapter 40: Advanced Concepts 887 
will necessarily be used to make these projections. As was shown earlier, if there is a 
distortion in the current implied volatilities of the options involved in the position, 
the strategist should use the current implieds as input to the model for future option 
price projections. If he does not, the position may look overly attractive if expensive 
options are being sold or cheap ones are being bought. A truer profit picture is 
obtained by propagating the current implied volatility structure into the near future. 
Using an example similar to the previous one a ratio spread using short stock 
to make it delta neutral - the concepts will be described. 
Initial Position. XYZ is at 60. The January 70 calls, which have three months 
until expiration, are expensive with respect to the January 60 calls. A strategist 
expects this discrepancy to disappear when the implied volatility of XYZ options 
decreases. He therefore established the following position, which is both gamma 
and delta neutral. 
Position Delta Gamma 
Long 100 January 60 calls 0.57 0.0723 
Short 240 January 70 calls 0.20 0.0298 
Short 800 XYZ 
The risk measures for the entire position are: 
Position delta: -38 shares (virtually delta neutral) 
Position gamma: + 7 shares (gamma neutral) 
Position theta: + $263 
Position vega: -$827 
Theta Vega 
-0.020 0.109 
-0.019 0.080 
Thus, the position is both gamma and delta neutral. Moreover, it has the attrac­
tive feature of making $263 per day because of the positive theta. Finally, as was the 
intention of the spreader, it will make money if the volatility of XYZ declines: $827 
for each percentage point decrease in implied volatility. Two equations in two 
unknowns (gamma and vega) were solved to obtain the quantities to buy and sell. The 
resulting position delta was neutralized by selling 800 XYZ. 
The following analyses will assume that the relative expensiveness of the April 
70 calls persists. These are the calls that were sold in the position. If that overpricing 
should disappear, the spread would look more favorable, but there is no guarantee 
that they will cheapen - especially over a short time period such as one or two weeks. 
How would the position look in 7 days at the stock prices determined above?