So I recently came back from Lunar New Years holiday and had some general thoughts on market dynamics and how shifts in volatility regime can occur due to the interaction between two interacting factors - Forced transactions and liquidity profiles.

I decided to write this out and post it in full here, where I hope it might be able to help other people in their thinking and understanding of markets:

https://keypaganrush.medium.com/forced-transactions-liquidity-profiles-and-market-ecology-4e0625f85b7e

I post this on the RV exchange to ask the following:

Is this already obvious to everyone and I was the only one who took ages to learn it?

Have there been other people who have written/vocalised the same ideas?

Any criticism/feedback? (Even "Duh, obviously, how did you not know that?" is an acceptable comment)

# A thought on a generalised principle underlying volatility in markets

A thought on a generalised principle underlying volatility in markets

### Where am I?

In The Exchange you can ask and answer questions and share your experience with others!

Regarding the Gaussian assumption,

I think this has been debunkedand that most people do not assume this probability distribution unless you are a very lazy finance professor that never left academia or ever traded? Also, I guess it depends on what your timeframe is, although again seems wild to assume normality when things look like this ⬇I remember reading about the Variance Gamma distribution being used for Daily stock prices. But I wonder if this is something @Moritz Heiden or @Christopher Denruyter use?

Other things I have seen people use or try to use are the Log-Normal and the Cauchy (although I wonder how useful the Cauchy is in practice (I have seen it being used in insurance models for earthquakes as an example).

Example of VG & Apple:

This could simply be due to the mixing of both Guassian and pathological distributions (Such as Cauchy) over long enough time frames.

It was my contention that in "normal" markets, price movements look rather Gaussian but in "volatile" markets, they look rather Cauchy.

Over a long enough time frame, you would expect both Normal and Volatile regimes, thus mixing the 2 probabilities.

It then follows: Parametric Distribution + Pathological Distribution = Pathological Distribution.

I'm not too deep into modelling anymore (been there, done that) as I'm not a pricing quant. However I agree with @Seahyung Park, it's quite common to use a mixture (even mixture of gaussians is quite useful). Alternatively I usually used to fit something from the class of skewed generalized error distributions. I think variance gamma is a subset of that class.

Pricing will involve simulation which try to overcome many of the simplified assumptions. There's a lot of other stuff like stochastic vol, jumps and vol skew that has to be taken care of.

In general very interesting thoughts regarding the disappearance of alpha from a liquidity perspective. Another thing is also the demand for certain strategies and return profiles that is driving certain market characteristics. Investors are looking for premium oriented strategies with a steady return profile (negative skew, positive average return) and herd into that. This is further driven by low to negative yields on gov debt and drives investors into "cash equivalent" strategies. Carry and short vol is even sometimes pitched as that....

Regarding your last point; Yes, even in retail I have seen carry being pitched as an alternative to cash.

Yeah, so things like selling calls (Covered calls) offer a liquidity profile in the options space of placing sell offers for calls. This initially works well in markets that are willing to buy calls. As the market becomes more skewed to this strategy, there are less buy offers below to absorb the flows, thus necessitating that the price of a call gets compressed over time and reducing the premium that covered calls can yield as the liquidity profile of the market becomes dominated by more and more covered callers.

People who aren't getting enough yield on their covered calls can respond by increasing leverage and doing covered calls in more size thus exacerbating the distortion in liquidity profile; eventually the thing self destructs when a forced transaction occurs in sufficient volume to buy calls and spiking IV/premiums on calls. This huge wave of call buying is also probably gonna shift the underlying up, due to MM delta hedging, so covered callers suffer from both gamma and vega.

This triggers forced transactions (Margin calls) from the covered callers themselves and we shift into a volatile regime.

The point on negative yields pushing investors into this strategy is well noted.

I don't know if what I wrote on that post is already plainly obvious to everyone already, but it seemed like a eureka moment to me lol.

Every model is wrong. Reality is unfathomable.

Some models are useful.

In physics, the basic Newton law F = m*a is an approximation in absence of air viscosity and at human scale. It's useful within limits.

Finance adds another layer of 'noise'. Markets are social phenomena, it's absurd to hope to find any kind of permanent equation of their dynamics, because the 'governing laws' can change over time, contrary to laws of physics which will outlive all of us. The idea of reflexivity developed by Soros is an example of the impermanence of market laws.

Now to log normality within the contexts of investing and of hedging:

When looking at real world dynamics, log returns are useful to investors in at least two respects: trade sizing (Kelly criterion) and ergodicity (https://www.nature.com/articles/s41567-019-0732-0 ). In short: how to size your bets so that your wealth doesnt vanish over time,... even when the odds are in your favour.

When hedging derivatives, you don't care where prices are going (because you hedge the market), typically you care about how fast some price moves (volatility). Assuming a level of vol, Log normality considerably simplifies calculations of prices and hedges. It makes things tractable cheaply that's why it's ubiquitous. It also provides a good intuitive way to communicate product characteristics. But using normal log returns and ignoring tail risk is plain wrong, so you start from logN and you adjust for dislocations.