Thread by @LilyWrites4

So, a brief thread since I haven't done one in a while about volatility. Unlike all my other threads, this will probably be wrong or something, I'll wait until someone who does vol chimes in or go ask like, Benn Eifert. Volatility in short, is a function of variance and time.

Or in even simpler terms, we have some variable we're looking at - usually price, or more formally spot price. We're looking at how it evolves over time. The wider the distribution of spot prices that occur in a given time range, the more volatility we say is occurring.

This is usually expressed as a function of the spot price itself, but depends on the context. In general the way stock prices move is naturally expressed as a % of the given stock price - we say stocks went 1% down today, vs let's say $3 down. This holds empirically too.

One of the most basic observations of volatility is it isn't really constant over time. The cornerstone of basic options theory, the Black-Scholes model, assumes volatility is constant over time and space (both stock price and for the same tenor). This is trivially incorrect.

There's a couple of obvious reasons why volatility isn't constant over time (the most obvious being - why should it be?). In general, one of the best coincident models of volatility is simply volume. It's not a linear relationship - if you look at spot price, it shows higher

volatility both at the low ends of trading volume (a fairly illiquid asset) as well as the high ends (a crash). The reasons for the volatility however are quite different, and behave differently too. An illiquid asset trivially has high volatility because of the granularity

of price information expressed, as well as the difficulty of making a sale. Depending on the demand for capital, a super illiquid asset (like let's say a house vs stocks) may sell for well above or below its perceived value depending on simple time-dependent supply & demand.

On the high end of course, trading volume picks up when everyone wants to get out. So you see a pretty obvious relationship on, for example, SPY trading volume and daily volatility. Higher the volume, the more we move. Simple.

What's more interesting is understanding how volatility moves. Options, despite how most retail investors use them, are really a function of two things) - realized volatility vs implied volatility. There's other input variables of course, but those are known with clarity to

all market participants (time to expiry, current spot, etc). The only ones which are fuzzy are realized vol (rvol) vs implied volatility (ivol). These terms sound fancy but aren't terribly difficult to grok. Realized volatility is simply how much volatility ACTUALLY

will occur from now til an option expires. Implied volatility, conversely, is how much volatility the market ESTIMATES will happen. However, ivol is interesting because it also largely acts as a supply and demand operator for the option price, which is largely intuitive.

If we think about it logically, if there's high demand for a given option (over-demand), that means the market expects significant movement. Conversely, if everyone is selling the option (over-supply), that means the market expects muted movement.

That, uncoincidentally, tends to be one of the primary ways people assign "sign" for option trades - a buy (in the sense of a non-MM) we expect to increase the ivol for a given option contract; a sell, we expect to decrease the ivol. However, importantly it acts as the market

determined forecast (or more likely in illiquid chains, the forecast of the primary supplier - the MM).
What's interesting now is forecasting rvol, since there's an obvious relationship of rvol and ivol.

If we expect rvol to go up in the future, no matter what the demand is, we should sell for higher ivol. This doesn't exactly hold the opposite way for the seller, but the same rationale holds for the buyer (if we expect lower rvol, we shouldn't pay for high ivol).

It's exactly why most vol folks will tell you an option isn't a buy if it's cheap historically or a sell if it's expensive; it's forward looking, and really depends on the expectation of actual future volatility. Now let's talk briefly about vol forecasting.

Many of the earliest practitioners in the space noted two critical observations:
- Vol tends to revert to a historic (or more realistically, a regime) long term average
- Vol events tend to cluster (if there's high vol now, we expect high vol in the near future, and vice versa).

In a stable vol time (like now), you can get away with almost assuming the most trivial future estimator - that future volatility will equal currently volatility. It works a lot! But vol we consider, unlike stock prices over time, both mean-reverting and (mostly) stationary.

These are more formal expressions of the above statement - if we see VIX at 80, we expect there to be a high vol period right after, but we expect it eventually to decline back to 'normal'. Similarly, if we see VIX at 10, we expect it eventually to go back to a higher long term

average. This is uncoincidentally why VIX options do not behave like spot VIX - if vol spikes today and my European option on VIX does not settle until next week, do not expect today's vol to equal the vol a week from now. There is of course some impact on current vol on future

forecasts, and that's why you see two things on volatility spikes:
- Forward-looking volatility increases (the price of VX contracts)
- Demand for shorter term VX increases more than longer-out VX (since we expect vol to revert over time).

In general, like most futures, VX (which settles according to spot VIX at expiry + some special rules) is in a state of contango - people will pay more for a longer out contract, since we expect more variability in vol to occur (and more chance to profit) the longer out we look.

However, when vol spikes, there's an obvious reason to demand SHORTER contracts - when vol spikes, time is your enemy to profit on increased volatility (due to the reversion tendency). This causes backwardation - people will pay more for a shorter expiry than a longer term one.

Anyway, there's a few models I could bore people with details on including GARCH, ARIMA, Heston, etc. but that's a story for another time. Hope you enjoyed this brief intro/thread.