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Option Vega υ
Issued on December 01 2011 par Strategies Options

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



Next : Option Theta θ : A First Attempt
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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

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