Modelling skew dependent on vol of vol

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

 

You seem to use a lot of heuristics / back of the napkin calculations, I'd simply use a market model which considers the vol of vol, like the Heston model: https://en.wikipedia.org/wiki/Heston_model

Then you don't have to reinvent the wheel since you already have a pricing formula, so you can also infer the greeks numerically.

I tinkered with Heston and the pure version can't fit the high skew one observes in the market implied volatility. But you get a perfect fit if you consider the vol of vol isn't constant but itself a ... skew. So for Heston you compute the 2'nd level implied vol of vol, like for Black-Sholes you have 1'st level implied vol.

Anywayz, that was a long time ago and I lost the code. Tried recently to resurrect the Heston model calculation but it's convoluted enough that I lost motivation, particularly since I don't believe it'll give me an edge.

 

Thanks for the input. I try heuristics more than models and I decided to do so a long time ago for my day to day business especially when it comes to modelling forward curves.
Callibrating a model is for me nothing else than an overfitted backtest which might be nice to understand the dynamics but don't give edge in any way.

So the only models I use are no arbitrage criteria, which also exist for skew. But times where I got a calendar spread or verticals for free are almost non existent, in fact I witnessed them only during the crash of 2008.

But on the other hand, when I see wing vol of 200 when the maximum implied ATM vol ever recorded is 140% I'm getting interested. Of course you have to pay a premium for volga but for me it's rather how much is too much. On the other hand, when you look at NG skew, the question is if call wings are too cheap compared to ATM.

 

I suppose you mean wings with BID prices, so someone's buying at that price (vol). Because ASK price can be any ridiculously high amount but if there's no bid as well, it doesn't seem very reliable to me.

 

It's tough to value wings. Like you say, it's a blend between what the vol will be local to the strike, but still also a function of ATM vol. Because even if VIX is floored at 10, sometimes it sits there for a long time. So the breakeven IV for a two year period of 10 rvol concluded by a subsequent crash might be 14 vol for short-dated wings or something.

In rapid regime changes or on a big jump, even wing strikes become pure intrinsic. So in certain scenarios, we are paying/collecting carry vs. being on the hook for the jump. The ceiling realized vol almost becomes less relevant in that scenario, at least for shorter tenors.

Trying to separate out fair skew and supply/demand pressures is a question I also run into; so I am interested in the discussion. In a market flooded with infinite capital, would every possible vertical be priced fractionally above breakeven? Because gamma is higher ATM wouldn't that naturally create some skew even if realized vol didn't change as spot moved through strike space?

 

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

 

In the end, all comes down to surface for me, not so much about vol at strike touch. Since I'm hoarding wings whenever I can get them for cheap, the only question I have is how much carry I can get ATM to finance them.

On the other hand the scenario is a bet on a tail event where you want to buy cheap volga and hope for an outlier. But this is a static position that you don't want/need to adjust as market visits different strikes.

When skew is ridiculous, however, it is worth it to buy teenies, sell 25 deltas and buy ATM to use skew deltas as your P/L driver. However, the question still remains: How do you evaluate wings

 

Hard to answer succinctly. I think it is interesting that when we are talking about wings we automatically bring up things in relation to them. ATM vol; skew of the rest of the surface, etc. I think evaluating them in light of something is key.

If ATM is very rich a higher skew can be justified because combos will still carry. Or if vol is near the floor it should steepen like we see commonly. Dependent on a lot of variables. If anyone has a better idea how to view them in complete isolation that would be interesting to hear. I also share your question.

I was trying to imagine what a perfectly priced, nearly risk-neutral surface would look like. Understanding what the fair skew should be in a scenario would be useful; because then it would be more obvious when market conditions distort prices away from that.

 

The fun thing with options is the fact that basically two sides of the trade can be winners. While one guy is trading vs realized vol, the other guy trades vs other options and the next one builds a trade by taking the surface at market to bet on delta.

So a fair priced surface doesn't exist IMHO because you have to ask the question fair compared to what? To realized vol, to vol of vol, to historical IV levels, to other skews in the same sector, to basket correlation? That's why trading vol is so interesting because the deeper you dive into the rabbit hole the more edge you can find...and the more difficult it is to realize the edge

 

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.