Spot vol correlation

Spot vol covariance is the correlation between the underlying price of an equity and its
overall implied volatility.

Overvixed: There is a clear correlation between the VIX and percent change in SPX.
Overvixed – overstatement of VIX – is when VIX runs higher than the SPX change implies.

undervixed definition ; There is a clear correlation between the VIX and percent change
in SPX. Undervixed – understatement of VIX – is when VIX runs lower than the SPX
change implies.

Skew: The rate of change of implied volatility on an option chain. Vertical skew refers to
the implied volatility change within an expiration from one strike to another. Horizontal
skew refers to implied volatility change at a fixed strike over different expirations

In quant circles spot vol correlation is used as a way of calculating skew in an option
chain.

Market Makers know that more people tend to buy options as the price of something
falls versus rising as seen here.
So, the typical relationship is that implied volatility goes up as the price of equity
declines.

This is because most market participants are net long in their equities, and options are
being used as insurance that can be shown here.

So that begs the question: what kind of implied volatility are we talking about?

There are 3 possible answers to that question, namely fixed strike volatility, fixed delta
volatility, and VIX.

Fixed strike volatility is the implied volatility of a particular strike option on a chain.

Because of skew, in general the IV of an option away from the money is higher than at
the money.

If the market moves, the fixed strike volatility is the implied volatility change of that one
strike relative to the spot-vol covariance.

So let’s say, for example SPY is currently at 390, and the 390 fixed strike volatility is
about 20%. The fixed strike vol of the 360 strike is about 30%, so let’s say SPY falls to
360, and the IV of that strike goes unchanged at 30%. That means that the fixed-strike
vol is unchanged, and as far as that strike is concerned, the implied volatility did not
move at all.

However, there is a good possibility that as the skew adjusts, particularly on the side of
the price movement, so this would stay like this but then the skew would adjust on
these strikes here.

And that can drive some vanna strength.

Fixed delta vol, or floating strike volatility, measures the implied volatility of whatever a
certain delta on the option chain is. Using this same example of 390 at 20%, we are
assuming that this is the 50 delta at this point, at the beginning of the day.

And then, at the end of the day, price falls to 360 and this is the 50 delta.

Even though fixed strike vol did not change because this stays the same at 30%, the
fixed delta vol increases by 10 points, because the 50 delta implied volatility increased
from 20 to 30.

Finally, VIX is an index calculated using quote data up and down the SPX chain.

It approximates implied volatility including skew into one concise number.

The most popular version that makes the VIX index uses an approximate 30-day
calculation.

But you can use the same formula and adjust the days you want to calculate.

For instance, the 30-day formula is used for the VIXing, spot vol covariance, and is the
same across all equities offered by volland.

However, the Vanna calculation based on individual strikes as we have it in Volland

But with millions of strikes in expirations, we were forced to approximate this

It can also be expressed at how much delta changes with a one-point move in fixed
strike implied volatility. Therefore, skew is very important to vanna’s impact in the
markets. So if skew is steep, and implied volatility does not react as strongly as skew
implied, then the vanna effect will actually act as a headwind to a move. In short, this is
the true impact of over- and under-vixing.

For long options, vanna itself is negative below the money, no matter what type of
option it is.

And it would be positive above the money.

It can be thought of as this; For an in-the-money put and an out-of-the-money call, an

With the opposite being true below-the-money options.

On both sides, the intensity of vanna peaks at around the 20 delta where the premium
of options starts to wane (disappear), and therefore, the impact of implied volatility
changes also wane.

At 50 delta, vanna is zero because there is still an equal chance to go above or below
the money, regardless of how volatile the underlying is.

Considering that vanna flips the sign whether the option is above or below the money,
the effect of a strong vanna strike crates a magnet effect. For example, let’s say a dealer
is long a 50 delta option. If the price goes up, the vanna becomes negative, and the
implied volatility of that fixed strike vol typically goes down.

As the implied volatility goes down, the deltas go up, which means the dealer must sell
to stay risk-neutral, and the price of the underlying comes back down.

Conversely, consider the dealer is short the 50 delta option and the price goes up. The
vanna becomes positive, and the implied volatility of that fixed strike vol typically goes
up.
As the implied volatility goes down, the deltas go down which means the dealer must
buy more to stay risk-neutral, and the price of the underlying accelerates instead of
comes back.

In short, dealer long vanna positions are magnets, and short option vanna repels the
price.

So we can take a look at gamma to determine whether they are long or short options,
especially at the money where vanna equals zero.

It would be attractive here.

However, for short options, it would create a repelling force.

So if something happens in which the price passes a negative option, you can see it
would create a “blow-off-top” kind of effect.
That means that this typical GEX action attributed to gamma is a product of vanna. If
customers sold all calls and bought all puts, dealer long options would be magnets
through vanna, and their short puts support any downside.

If gamma was the cause of the magnet, the dealer long call would NOT be a magnet; it
would be a very strong resistance and never reach that strike.

Vanna increases in impact the closer you are to expiration, but because there are less
strikes in that 10-30 delta area, both above and below the money, in the scope of the
entire dealer book, vanna has less impact on near-term options unless you are pinned
to a strike that has a strong positive vanna presence.

In that way you can make short gamma positions in opex week, if you notice that this is
what’s happening. Even though vanna is 0 at the money, if you go to the gamma chart
and see a strong gamma level at the money, you will likely be a strong pin to that strike.