It's the sensitivity of an option price to
Implied Volatility varaitions.
I - Definition
Option Vega υ is defined as the rate of change of an option price due to implied volatility changes.
Note that it's not a Greek letter at all !
II - How to derive it
If one set
V(σ) as option value for volatility σ
σ(1) and σ(2) two different volatilities
Vega can be written as
υ = [ V(σ1) - V(σ2) ] / (σ(1) - σ(2))
If an option (call or put) is worth 12.37 with an implied volatility set to 31% and the same option is worth 12.765 if implied volatility is 32%,
Vega is then :
υ = ( 12.765 - 12.37 ) / ( 0.32 - 0.31 ) = 0.395 / 0.01 = 39.5
Because volatility is often grasped in % one needs to divide the result by 100.
That is υ = 39.5 / 100 = 0.395
As far as one take a look at small moves for volatility, it's usual to write Vega as :
υ = ( ∂V/∂σ ) / 100
That is the first partial derivative of option price with respect to implied volatility.
III - Graph
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Option Theta θ : A First Attempt
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Option Vega υ : A First Attempt
OPTIONS 101 - INDEX
OPTIONS 101 - CHAPTER I
OPTIONS 101 - CHAPTER II
OPTIONS 101 - CHAPTER III
OPTIONS 101 - CHAPTER IV
OPTIONS 101 - CHAPTER V
OPTIONS 101 - CHAPTER VI Strategies Options