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: