Publishing an option post today that emerged from writing Moontower this week. It's about a qualitative intuition for option behavior esp spot/vol correlations.

Option greeks esp as you get into 2nd order ones like gamma, vanna and volga often cause a listener to slow down...

They say "ok, wait what's gamma again...[start recalling some if...then scenarios]"

I have 2 quick heuristics that can make the effect of a vol change more clear especially if you imagine an extreme change in vol (so if your scenario is "vol down", mentally crank it down to 0)

Heuristic

1. "Further away heuristic"

If vol goes down, all OTM options become "further away". The effect on greeks is obvious. Just imagine the extreme as vol goes to zero. All the greeks go to 0. Deltas and second order greeks.

So if you are running a hedged position...

...say short puts and short stock. As the stock falls your negative gamma makes you longer.

But, if vol is falling, then your short OTM option is getting "further away". Perhaps vol goes so low that the option just goes away...

Now instead of getting longer deltas bc of gamma you are actually getting shorter since the only position your left with is short stock as the vol collapse takes vaporizes the option. So the vol decline reduced the negative gamma and positive delta coming from the option...

Sure, the vanna effect offset the gamma effect, but its easier to visualize what is happening...the option is disappearing or getting further away as the vol falls and your position is reduced to delta 1 instruments (short stock in this case. Also, ITM options if you have any)

The second heuristic

2. An increase in volatility is the same thing as increasing time to expiration. The extreme mental scenario... infinite time to expiration.

Options go to their max arbitrage bounds. These include...

All calls go to the stock price. That means all calls are worth the same which means all calls spread are worth 0.

If call spreads are worth 0 then all put spreads go to the distance between the strikes.

Another way to demonstrate that is imagine all puts at max value...

Puts will all be worth the strike price. So the difference between any 2 puts will be the diff between the strikes.

So cranking up vol (or time to expiry) raises all OTM calls faster than ITM calls since the ITM calls already included the intrinsic portion of the stock price.

If call spreads all go to zero and put spreads go to diff between strikes it looks like the stock went to 0 right?

Well, on an infinite timeline we are all dead and the stock is 0. Makes sense. 0 is an absorbing barrier if time or vol are infinite.

(Geo return lovers nodding)

Anyway, my habit whenever I try to quickly understand the interactions of a vol/stock scenario is to establish the extremes quickly so I can ascertain what hard deltas remain when all the extrinsic comes out.

If vol does X do I "decay longer or shorter deltas? Vol?"