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+750 Part VI: Measuring and Trading Volatility 
+of how volatility affects option positions will be in plain English as well as in the more 
+mathematical realm of vega. Having said that, let's define vega so that it is understood 
+for later use in the chapter. 
+Simply stated, vega is the amount by which an option's price changes when 
+volatility changes by one percentage point. 
+Example: XYZ is selling at 50, and the July 50 call is trading at 7.25. Assume that 
+there is no dividend, that short-term interest rates are 5%, and that July expiration is 
+exactly three months away. With this information, one can determine that the implied 
+volatility of the July 50 call is 70%. That's a fairly high number, so one can surmise 
+that XYZ is a volatile stock. What would the option price be if implied volatility were 
+rise to 71 %? Using a model, one can determine that the July 50 call would theoreti­
+cally be worth 7.35 if that happened. Hence, the vega of this option is 0.10 (to two 
+decimal places). That is, the option price increased by 10 cents, from 7.25 to 7.35, 
+when volatility rose by one percentage point. (Note that "percentage point" here 
+means a full point increase in volatility, from 70% to 71 %.) 
+What if implied volatility had decreased instead? Once again, one can use the 
+model to determine the change in the option price. In this case, using an implied 
+volatility of 69% and keeping everything else the same, the option would then theo­
+retically be worth 7.15- again, a 0.10 change in price (this time, a decrease in price). 
+This example points out an interesting and important aspect of how volatility 
+affects a call option: If implied volatility increases, the price of the option will 
+increase, and if implied volatility decreases, the price of the option will decrease. 
+Thus, there is a direct relationship between an option's price and its implied volatili-
+ty. 
+Mathematically speaking, vega is the partial derivative of the Black-Scholes 
+model (or whatever model you're using to price options) with respect to volatility. In 
+the above example, the vega of the July 50 call, with XYZ at 50, can be computed to 
+be 0.098 - very near the value of 0.10 that one arrived at by inspection. 
+Vega also has a direct relationship with the price of a put. That is, as implied 
+volatility rises, the price of a put will rise as well. 
+Example: Using the same criteria as in the last example, suppose that XYZ is trading 
+at 50, that July is three months away, that short-term interest rates are 5%, and that 
+there is no dividend. In that case, the following theoretical put and call prices would 
+apply at the stated implied volatilities: