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+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?