υ = δV/δσ
V  option price
σ  implied option volatility
The value of the option price also changes when the implied volatility rises or falls. The sensitivity of the option price to changes in volatility is called vega. Vega indicates a potential change in the price of an option if the volatility changes by 1%, all other factors being equal.
For example, if the call option price is $5.58 and its vega is $0.53, then if the implied volatility rises by 1 percentage point, the option price will increase to
$5.58 + $0.53 = $6.11.
However, if the implied volatility falls by one point, the call price will fall to
$5.58  $0.53 = $5.05.
Buying an option, call or put, involves buying volatility and a long vega position. The owner of the option will earn if the volatility increases and will incur losses if the volatility drops. A trader who has sold options expects the implied volatility to fall as he has a short vega position. Decrease in implied volatility will lead to cheaper option value, and the trader will be able to close the short option position with profit.
Figure 1 shows the relationship between atthemoney call option price and implied volatility. As the volatility increases, the option price increases approximately in a linear proportion.
Fig. 1. Option price
Mathematically, vega is the first derivative of the option price with respect to volatility. Implied volatility is traded through vega, and options with a long expiry date are generally used for this purpose. Options with a long expiry date have a higher vega, i.e. the value of the vega decreases as the time goes by.
Fig. 2. Option vega

Delta 
Gamma 
Theta 
Vega 
Rho 
Long Call 
+ 
+ 
Pay 
+ 
+ 
Short Call 
– 
– 
Receive 
– 
– 
Long Put 
– 
+ 
Pay 
+ 
– 
Short Put 
+ 
– 
Receive 
– 
+ 