Aggregating Option Vega Across Strikes, Maturities, and Underlyings

# Option Vega for a portfolio of Options


# Option Vega for a portfolio of Options












I am given a list of `Options` positions consisting of various combinations of `Underlying` and `Strikes`. I am also given the `Vega` values for each go these positions.

Now, given this information, I want to calculate total `Vega` exposure of this portfolio. Should I just add up the individual `Vegas` and report that as total `Vega` (without considering the sign ofcourse)?

Is that approach correct at least approximately? If not, what can be the correct approach given the information I have?

## Answer by Frido (score 2)

https://quant.stackexchange.com/a/81142

It has been pointed out in the comments (@Hans and @Kermittfrog) that unless you make the strong and fallacious assumption that the IV surface moves in parallel, you'd need to bucket the Black-Scholes vegas by strike and tenor.

My sole addition over the comments is to point out a fairly recent article by Francois and Stentoft in which they propose an in my opinion interesting new definition of vega.

Since in a flat volatility Black-Scholes world vega and gamma are related as follows: $$ v^{BS}(K,\sigma) = T\sigma S^2 \Gamma^{BS}(K,\sigma), $$ Francois and Stentoft propose to define vega in the presence of a skew analogously by $$ v^{SI}(K,I(K)) = T I(K) S^2 \Gamma^{SI}(K,I(K)), $$ where the subscript SI stands for ``smile implied'', $I(K)$ is the implied volatility corresponding to the strike $K$, and $\Gamma^{SI}(K,I(K))$ is the smile implied gamma which can be deduced/computed from market price $C^{mkt}(K)$ of options: $$ \Gamma^{SI}(K,I(K)) = \frac{ \partial^2 C^{mkt}}{ \partial S^2} (K). $$ In stochastic volatility models $\frac{ \partial^2 C^{mkt}}{ \partial S^2} (K)$ can be implied from the skew in a parameter-free manner. For other models, some additional assumptions are required.

Notice, though, that this definition does not circumvent the issue of having to specify how the IVs are correlated to each other across strike and time to maturity in order to arrive at an aggregate dollar vega of the portfolio.

It's clear that it's high time a smart person writes a paper titled "Oi guv, wots me vega?!", as this is obviously an important question without a clear and robust answer thus far.

## Answer by Anurakt Saxena (score 0)

https://quant.stackexchange.com/a/80874

First try to calculate the Correlation among vega of different underlying . This exercise can be done by historical data ( year ). Calculate the Vega of portfolio by multiplying correlation and arriving at ONE short or Long Vega Number . If not Significant it is also Known as " Square Vega " . Even though you have a Square Vega the portfolio will move the next day . If OTM options are purchased in large qty , best approach is to do scenario analysis and calculating lock delta . Regards