Extrinsic value actual representation

Usually extrinsic value is represented as the image below, a bell shape curve




My simple question is:

Shouldn't the actual representation be a lognormal?

(Please excuse the crudity of this GRAPH. I didn't have time to build it to scale)

And so:
all the typical representations of first and second order greeks are unfaithful?

How much it can be misleading to think in terms of normal istead of lognormal?

I hope I made it clear.

Thanks

 

P.s. I switched ITM-OTM positions

 

Why not just observe? Here is Extrinsic value of SPX PUTs for the 17JUN expiry for reference.

 

I guess that the representation comes from the bsm model and does not account for observed IV/skew

 

The plot was the Extrinsic value at the time I produced that plot. IV skew IS included, as this was real-time data, not some "model"!. Don't take my word for it, plot it yourself!

 

Yes.
That's my point. In theory the extrinsic value graph should be a lognormal. That's also the reason why ATM delta isn't 0,5, and other consequences in terms of probability of touch, etc etc.
'Cause the foundation of Black Scholes model is geometric brownian motion and not simple brownian motion.

 

My comment was about OP's graph, not yours

 

I know shit about high level math so take my comment as an uneducated guess.. however I think that neither lognormal nor normal are an accurate representation of what you see in reality.

And my guess on the "why" is that while textbooks are based on BSM, market makers use different models to price volatility.

 

From a user of another forum who made the actual calculation.

 

The extrinsic value must be non-smooth ATM. Because it’s the difference of overall value and intrinsic value. The former is smooth and the latter is non-smooth. So the ATM kink is expected.