Modelling skew dependent on vol of vol

[MrMuppet]

The options market is zero sum. My gain is your loss outside of any pnl that is extracted from the cash markets (via delta hedging). So there can be a fair value for every option (the price which no one makes money).

it’s the market makers goal to quote around that fair value while we battle each other (like a poker table at a casino where the dealer is the market maker).

and the delta hedging pnl can be extracted without options as it’s an attempt to synthetically create an option.

100% agree to the fact that two options traders on the opposite side of the trade can win when the trader in the underlying loses to both of them.

However, I don't quite agree to the fair value part since market makers have inventory limits which are the dominant forces in the pricing process. Every MM fits his model to market not to a theoretical statistic made up by using historical data.
That's true for Heston, Vanna-Volga, SABR and what not.
Because it's absolutely impossible to know the return distribution and the path of the underlying during an options lifetime you can only compare two or more instruments with similar payouts to figure out what's expensive.

The risk/reward of a structure determines supply and demand, because if for example the model is telling you to price the 50/25 delta vertical at -20vols some dude might immediately buy that thing for all your size because in strike space it costs 5 cts for a 4.95$ payoff

You are happy because you sold ATM vols that are probably expensive compared to realized and hedged with cheap wings. The other guy is happy because he could hop on a 100 lot vertical plus an extra short call to finance the structure and perhaps even get a credit.

So in options space there are two different definitions of fair value while the sucker is the guy who keeps selling shares to the MM as he hedges his deltas on the way up

 

[destriero]

So this is a bit advanced, I'm not expecting too much. But perhaps there is a whiz-kid on ET who fiddled around with this, too.

Option skew exists because asset prices have fat tails, we all know that. Indices fall faster than they go up, vice versa for NatGas.
So you could go to your trusted excel, calculate a historical return distribution and price your 5 - 25 delta options from there.

For me that's not really practical and also it doesn't make a lot of sense from a trading standpoint.

So I tried to view it from another angle.
Primer: ATM vega is linear, OTM vega is convex (volga). This means that OTM options that have no delta and vega when volatily is low will have delta and vega when volatility is higher.

Let's say implied volatility ranges from 50 - 100% we asume that vol of vol returns are evenly distributed.

This means that you can put a price on ATM IV at 75% ((50+100)/2))
The price of the wings, however, are dependend only on the 100% volatility figure, since they have 0 vega/delta under the 50% volatility regime.

So when I know that volatility can go to 100% why would I sell the wings low when IV is at 50%? Right, I won't.

The question I'm tinkering with is: Since vega is convex in the wings, you can't use a simple average like you can ATM. Intuitively, skew is higher in shorter tenors since vol of vol is higher there.
But how would you go about calculating the wing prices depending on vol level?

I mean, we know that VIX has a min reading of 10 and a max reading of 80.
When at 10, the wings should be really expensive compared to ATM, at 80 there should be no skew at all (IF IV of 80 was a granted maximum...which it isn't)

However, due to supply and demand, skew still gets pumped up heavily once IV picks up....which would provide an opportunity to sell wings that are too expensive.

GME was a good example when it started to run. IMO there was no reason for a 40% put skew when IV was already sky high and selling these was actually the best trade during the dump.

Thoughts?
@taowave @Kevin Schmit @destriero

There was put skew on the GME run to 400+? I was shorting bull synthetic straddles knowing the vol would drop with shares. I recall the 20D RR was something like 40bp C/P, but maybe I am remembering it wrong. My concern was modality so I'd rather accumulate deltas than vols. Synthetic at 350, natural at 375, neutral combo was at 400 (px). It's tough to trade the thing naked but you can't afford to buy upside wings. I had a share fly on for a couple cycles (long spot, short 2x calls, long 1x wing).

 

[jamesbp]

There was put skew on the GME run to 400+? I was shorting bull synthetic straddles knowing the vol would drop with shares. I recall the 20D RR was something like 40bp C/P, but maybe I am remembering it wrong. My concern was modality so I'd rather accumulate deltas than vols. Synthetic at 350, natural at 375, neutral combo was at 400 (px). It's tough to trade the thing naked but you can't afford to buy upside wings. I had a share fly on for a couple cycles (long spot, short 2x calls, long 1x wing).

Des ... a "share fly" ( +1 stock / -2 calls / +1 call ) or similar is one of my preferred trades for covering upside delta's ... synthetically the equivalent of Selling Puts / to finance / Buying Call Flies ... I see as part of a series of similar trades that I usually look at

#1 RiskReversal ... sell OTM put / buy OTM call
#2 Seagull ............ sell OTM put / Buy OTM call vertical
#3 Share Fly ....... sell OTM Put / Buy OTM call fly

 

[spriteork]

I'm talking about fair value/midpoint. Offers are insane in these situations because the MMs already sold all their wings

I would mention that selling too much wings is dangerous,
market too panic in hiking IV on topping of NG prices,
so vega component loss is dramatic.
And it's hard to guess a price top, and when it come down
(it feels that other traders margin calls dragging price higher and higher,
so timing is not predictable)

A lot of deposit should be free for "experiments" with NG.

In opposite crude oil energy market haven't so much panic rising IV
even on record price surge.

 

[destriero]

LVLD in these names is tough as you're looking for vomma only after the thing has hit the social media meth heads/reddit. I typically buy wide/deep LVLD verts as a source of vomma into skew. Derman is usually the driver.

 

[morganpbrown]

Holy crap this stuff is complex.

 

[destriero]

Des ... a "share fly" ( +1 stock / -2 calls / +1 call ) or similar is one of my preferred trades for covering upside delta's ... synthetically the equivalent of Selling Puts / to finance / Buying Call Flies ... I see as part of a series of similar trades that I usually look at

#1 RiskReversal ... sell OTM put / buy OTM call
#2 Seagull ............ sell OTM put / Buy OTM call vertical
#3 Share Fly ....... sell OTM Put / Buy OTM call fly

And a share fly is a short natural straddle + upside call wing (syn-share fly). I prefer to do the natural shares in lieu of the natural straddle (synthetic share fly) as I can overwrite and hedge discretely.

 

[emulimu]

Holy crap this stuff is complex.

Not really, if you know the terminology. Just google all the keywords you come across here. Once you learn them, you can easily follow these guys. It's like an illiterate suddenly being able to read. Your mind will light up.

 

[Overnight]

Not really, if you know the terminology. Just google all the keywords you come across here. Once you learn them, you can easily follow these guys. It's like an illiterate suddenly being able to read. Your mind will light up.

It is not just the terminology, but also the action underlying the greeks. For example, this...

"...Option skew exists because asset prices have fat tails, we all know that. Indices fall faster than they go up, vice versa for NatGas..."

That is a quote from Mr. Muppet, and I can see that in my head. Yes, NG and indices are kinda' inverted in their immediate actions. Indices tend to drop fast and take time to rise back up, yet NG tends to rise fast and take time to drop back down. *waves to James Cordier*

How that all translates into profitable options plays does not come down to a simple understanding of "options terminology". There is so much more to it.

 

[emulimu]

How that all translates into profitable options plays does not come down to a simple understanding of "options terminology".

Whoa, hold it right there! I never said anything about that. I was just saying about understanding their greek language. In your example, learning about "skew" and "fat tails" will certainly put you ahead in understanding their greek language. That's all I meant, not taking anything away from anyone.