Variance and Vega notional relation

CFA Level III Derivatives
#1

Hi,

I understand the need for adjustment to go from Vega notional to Variance notional in a variance swap but I don’t understand why we multiply Variance notional by 2K to get the vega notional.

Thank you.

#2

Hi,

The formula of Variance Notional =Vega notional/ (2 X Strike)

Therefore, Vega Notional = Variance Notional X (2 X Strike)?

Not sure if how do you get 2,000 aka 2k from?

#3

I understand this simple equation. I just wonder why we multiply by 2 times the strike

#4

Apparently, the objective of the vega notional is to approximate the payoff when the realized volatility is 1% higher than the strike volatility. (No: I have no idea why they picked 1% as the all-important change.) The payoff is the change in the variance times the variance notional. The change in variance is:

\left(X + 1\right)^2 - X^2 = X^2 + 2X + 1 - X^2 = 2X + 1

So the vega notional should be the variance notional times \left(2X + 1\right). They simplified it to 2X.

(Note: for a 1% decrease in the volatility, dividing by \left(2X - 1\right) is appropriate. So the simplification of dividing by 2X is an average of the correct up and down divisors. Whatever.)

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#5

I got it! Thank you very much :+1:

#6

My pleasure.

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