Thread by @kerberos007

below chart intrigued me BIGLY

prompted me to dig into more about $VIX behavior pre-crisis

I took this oppor to get all of my prevous notes/studies/programs on $VIX modeling/prediction to compare results for detecting VIX anomalies before crisis to improve my market-top ind's

https://twitter.com/kerberos007/status/1420773861004619779

https://twitter.com/kerberos007/status/1420842557920186370

several famous Realized Volatility (RV) esti theories out there since 1980's, all involving vol esti using daily hi-lo, opening gap & intraday spike to improve est

0 standard close-close std() est
1 Parkingson
2 Garman-Klass
3 Roger-Satchell
4 Garman-Klass_Yang-Zhang
5 GARCH

0- standard std() available from Excel and Python only requiring close-to close SPX daily returns ( % change ) for SPX RV estimation.

it does not need the Open-Hi-Lo information.

It has been used to confirm the $VIX estimation (using options) for the SPX future price volatility

I should also include $VIX as an volatility estimation & predictions for future SPX return voaltility.

VIX is the only estimator for SPX ret volatility using options market "greed/fear" & "supply/demand", involving human emotions during market boom & bust cycles. Put/Call only

this study was to summarize my findings on the esti of daily return Volatilty for $SPX

1 $VIX (using $SPX options) - CBOE

below esti using $SPX Hi-Lo-Close & % returns

2 standard close-close std()
3 Parkingson
4 Garman-Klass
5 Roger-Satchell
6 Garman-Klass_Yang-Zhang
7 GARCH

Below is the chart of SPX daily Log returns (red line) that all volatility estimation algos trying to estimate.

obs:
A. log return vol exhibiting clustering bahavior, a period of high-vol & low vol-regimes would cluster together

B. log return vol exhibiting "mean-reverting"

$VIX
standard close-close std()
Parkingson
Garman-Klass
Roger-Satchell
Garman-Klass_Yang-Zhang
GARCH

GARCH family of model
only one on the list trying to model the log-ret-volatility employing the stochastic nature of Vol clustering & mean-reversion behavior
hence most accurate

re-cap

$VIX - vol-pred using SPX put/call prem (IV)

$GARCH - Generalized AutoRegressive Conditional Heteroskedasticity: taking advantage of Vol-clusting & vol-mean-reversion

all other models are realized vol (RV) estimaor algos using SPX daily hi-lo-close & log-returns only

HMM
Hidden Markov Model for Financial Time Series & Application to S&P 500 Index
also becoming very popular in reseach
HMM shold provide more insight into the vol prediction in the future

I also have my own ML-based Vol prediction algos that i might share one of these at the end

GARCH family: Generalized AutoRegressive Conditional Heteroskedasticity

the only vol-modeling algo being able to do some near-term volatility prediction due to its "stochastic" modeling nature

Google😉
Heteroskedasticity🧐

fancy word for
'Varying error Variance" process

Parkinson volatility is a volatility measure:
uses the stock's hi & lo price of the day. The main difference between regular volatility and Parkinson volatility is that the latter uses high and low prices for a day, rather than only the closing price

the calm before the storm

Since both VIX & all models are used to est the future log-return-vol of SPX prices

so, we can not conclude that VIX is the correct esti

But, VIX is tradable instrument, if we can predict SPX return-vol with better accuracy than VIX, then we can make tons of money, right?🧐

we can see from below chart. VIX aslmost always over-estimate the SPX return-vol;
VIX > RV;
VIX always higher than RV, due to human emotions in the options market after the "1987" market crash

options market pricing the left tail "crash" risk much higher than SPX price action

VIX > RV fo all models

due to 1987 crash.

all long-only funds using SPX (or index) options to buy "crash protection" puts for left-tail risks, hence the put premium is always higher than the "log-normal" distribution implied by the SPX price action & Black Scholes options model

short-vol folks might think:
this is the best time to short-vols & selling premium if VIX > RV

but, from below chart, short-vol has not been a good strategy; almost all VIX spikes since 1998 came after
VIX>RV spread (>10 pts) after "calm before the storm" RV suppresion periods

a myth

if VIX>RV, volatility risk premium is too high & short-vol funds would make tons of money by shorting VIX or selling prem in options

not true.
short-vol
=
Picking up pennies in front of a steamroller

make pennies in 6 mths, but, that one VIX spike would kill your acct.

from below chart

$VIX & #RV suppression came slowly, taking months (vol clustering),
but
$VIX & #RV spike would come fast and furious (sometime when you're asleep) when everybody bought into the "FOMO", euphoria headlines on majow news & FinTwit

market-top clues from below?

Juse one model does not make a trend:

so, I gathered all of my old notes & Vol modelling programs for comparison purposes:

Garman Klass
incorporates open, lo-hi-close of a security
it extends Parkinson's vol by taking into account the opening & closing price.

spreads = clues

I marked al of the "the calm before the storm" periods, when both $VIX & #RV are manipulated & suppressed just before the "storm" coming from nowhere, fast & furious, most likely overnight $VIX spiking 50-100%

Garman Klass is a better model to detect spread & ensuing VIX spikes

Rogers-Satchell- measuring the vol with an avg return not equal to 0

Unlike Parkinson, Garman-Klass, Rogers-Satchell incorporates drift term (mean return not equal to 0). As a result, it provides a better vol est when underlying is trending

Rogers-Satchell is even better👌

again, I marked all of "the calm before the storm" period
when both $VIX & #RV manipulated & suppressed just before the "storm", coming from nowhere, fast & furious, likely overnight $VIX spiking 50-100%

all models from hgih level looked similar, but, if I zoomed in, very diff

In 2000 Yang-Zhang created a powerful volmeasure that handles both opening jumps & drift. It is the sum of the ON vol (close to open vol) & a weighted avg of the Rogers-Satchell vol & the open to close vol

Yang-Zhang
equation was modified to include the log of the open price divided by preceding close price. As a result, this function uses the open, high, low & close prices to estimate vol
This modification allows the volatility estimator to account for opening jumps

a nice one👌

GARCH (2,2)

from 1998 to 2021

GARCH (2,2) conditional volatility est annualized to compare with $VIX & Historial close-close vol- 21d (HV-21d)

GARCH (N,N) has a total of (2*N+1) pars to tune; it is more powerful with fast response time during extreme price volatility spikes

GARCH (2,2)

from 2008 to 2013 zoomed version
to see the details of faster response time

During vol spikes, GARCH (2,2) over-estimating
GARCH > VIX

during vol-suppression period,
GARCH (2,2) < $VIX

again,

the calm before the storm
Spreads predict ensuing Vol Spikes

Bonus

1 day rolling prediction for $SPX return-vol

compared wih $VIX options prediction

since both are used to predict the future SPX price return vol, so we can't conclude which one is better

but, we can use our prediction to front-run VIX to make money using VIX calls👌🧐