Gamma vs Volatility

I wrote like 400 words to express it and it's too deep into the weeds. All decay increases with distance. All convexity increases with distance (static vol). Most of this stuff is a rounding error compared to the first-order exposures (and gamma); i.e., Dd/Dt (ddecay) is useless as you near expiration. All (3rd-ord) are of limited utility in vanilla equity vol.

 

I guess this means TOS is wrong as well?

Platform shows:
Gamma decreases when Vol increases.
AND
Gamma deceases when Vol decreases.

 

"When implied volatility goes higher..."

I was referring to curvature (Dg/Ds). The text is accurate w.r.t. IV. The increase in vola moved the needle. Vol rises -> wings trade from $5 to $6 -> is gamma higher or lower (lower)?

 

All decay excluding theta.

 

empirically it makes sense.. vol props up all the premiums, and the the P/L curve will look on average higher but flatter..

 

Just think about it in a simple example, if you have underlying at $50 and your $52 call has a premium of $5, gamma will be lower (and vol higher) because there is less change in the option premium if the underlying goes up to $55 than, all else equal, if the premium paid were originally $2 rather than $5.

It's a complicated mathematical way to arrive at that conclusion is all.

 

What I'm gathering so far is:

1. Option with 0 extrinsic will have no optionality, so gamma will also be 0.
2. If vol increases and the option gains extrinsic the gamma will increase.
3. If vol continues to increase the profile will flatten and gamma will decrease.



Is this correct?

 

DgammaDvol trades inverse to vega as gamma is to theta; ATM max sensitivity. Long vega = short dg/dv.

 

Isn't there speed in ATM/ITM strikes as well? Isn't zomma largest in the front-month ATM?

 

And it makes sense, color is highest at that max sensitivity ATM. I'm wondering if all these relationships because the greeks is because of the symmetry of gamma.