Vega Notional / Variance Notional

The notional for a variance swap can be expressed either as a variance notional or a vega notional.

The variance notional represents the P&L per point difference between the strike squared (implied variance) and the subsequent realised variance.

 

Since most market participants are used to thinking in terms of volatility, trade size is typically expressed in vega notional. 

The vega notional represents the average P&L for a 1% change in volatility. 

The vega notional = variance notional * 2K 

 

The P&L of a long variance swap can be calculated as:  Vs formula

When RV is close to the strike, the P&L is close to the difference between IV and RV multiplied by the vega notional. 

The variance swap payout, expressed in vega notional, is locally linear around the strike. 

 

Vega and variance notionals

 

The P&L of a variance swap is often expressed in terms of vega notional.

For a vega notional of €100k, a gain of €500k is expressed as a profit of 5 vegas (i.e. 5 times the vega notional).  

Comments (2)

Campuzan
  • 1. Campuzan (link) | 29/05/2022
Hi,

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

Thank you.
maxxman100
  • maxxman100 | 11/06/2022
Bonjour Florian, C'est simplement la dérivée première de la fonction x^2 (passage de la volatilité à la variance). Cette formule de P&L est une approximation qui sera cohérente lorsque la volatilité réalisée sera relativement proche du strike (puisqu'on approxime une fonction convexe par une droite). A l'initiation du swap, expected(RV) = K --> RV = K dans la formule et le swap vaut 0 quand l'investisseur rentre dedans. Ensuite, tu peux partir de la formule du P&L sur base du vega notionnel. Imagine un mouvement de RV vers (RV + dRV). Comment sera impacté RV^2? Une bonne approximation est de que RV^2 passera à RV^2 + 2*RV. Prenons un exemple chiffré très simpliste (je grossis un peu le trait en ne parlant pas directement en % pour faciliter la compréhension). Swap en T0, RV = K = 22. Vega notionnel = 100K. Grosso modo pour un passage de la vol de 22 à 23, le VS gagne 100K. Ce passage de RV de 22 à 23 entraine un passage de RV^2 de 484 à 529. Cette modification pouvait être approximée initialement par 22^2 + 2*22 (2x étant la dérivée de X^2) = 484 + 44 = 528. Alors que RV a augmenté de 1, RV^2 approximé a augmenté de 44 (2*K puisque RV = K à la conception du produit). Le P&L du VS étant évidemment le même, l'ajustement est fait au niveau du Notionnel qui est divisé par ce 44 (2K).

Add a comment

 

The NEW website is OUT! 

Go have a look at https://www.derivativesacademy.com.

You will find the content in the 'Derivatives Academy' section in a book format. 
The full content is not yet available as I am rewriting it and improving it.

You can try the Exotic Derivatives pricer under the 'Derivatives Pricer' section (
https://www.derivativesacademy.com/derivatives-pricer/). I will speed up the page soon as I forgot to compress some images.
Each application allows you to price differents products and contains links towards the correct section of the book. 
You will then be able to get practical and theoretical knowledge quite easily.

I teach quite often using the pricer. You can get so much information and answers to your questions thanks to it.

Take advantage of it as much as you can to hone your knowledge!

If you are looking for junior opportunities in the field of market finance. Register yourself on the website. It's free!

If you have any questions, do not hesitate to contact me on info@derivativesacademy.com.