What good is a perfectly fitting stochastic volatility model for VIX such as the Rough Heston ??

[stochastix]

Let's say you have implemented a model such as the Lifted Heston or Rough Quadratic Heston
that fits the observed prices and volatility smiles very well and quite parsimoniously .

I have been told that such a thing is useless, because it will only tell you what the prices already are, and that everything that needs to be known is already in the implied volatilities and probabilities implied by the prices. They say that it can only be useful to interpolate prices for options that don't currently have a bid or offer on them.

I find this hard to believe.

Doesn't the calibrated model allow one to use the Fokker-Planck equation to evolve the probabilities forward in time, or to change parameters if one disagrees with where the market thinks things are headed?

They claim I need some sort of signal, to trigger when things are mis-priced, my idea was to just look for combos with high probability-of-profit, 90% or so. and then allocate accordingly . Selling short strangles on the near-month and buying OTM calls on the next-month to hedge against surprise on the upside and reduce margin requirements.

Everything I read says this works 99% of the time, until it doesn't, and that you can give back a years worth of profits in a day.

My question, doesnt everything involve risk? isnt this life, your living til your dead?

There is partial predictability in the VX.. im just wondering why others were trying so vigilantly to discourage me from implementing a pricing model

 

[stochastix]

Everyone says look at Feb 2018. Are there any indicators that something was amiss before Feb 2018? https://stocknews.com/have-option-gamma-trades-taken-control-of-the-market-2019-07/

What about a short-term model that forecasts VIX on a higher frequency than the 15 second intervals they use?

I think they didn't want the competition or something and were trying to lead me astray

 

[Overnight]

Everyone says look at Feb 2018. Are there any indicators that something was amiss before Feb 2018? https://stocknews.com/have-option-gamma-trades-taken-control-of-the-market-2019-07/

What about a short-term model that forecasts VIX on a higher frequency than the 15 second intervals they use?

I think they didn't want the competition or something and were trying to lead me astray

Nope. That was the new Fed Chair Jerome Powell opening his mouth and instilling uncertainty into the markets. Everyone knew Janet Yellen's track. Powell was the new guy, and "OH SHIT, WHAT DO WE HAVE NOW"?

No indicator can predict a potential fundamental shift in economic policy.

 

[stochastix]

Nope. That was the new Fed Chair Jerome Powell opening his mouth and instilling uncertainty into the markets. Everyone knew Janet Yellen's track. Powell was the new guy, and "OH SHIT, WHAT DO WE HAVE NOW"?

No indicator can predict a potential fundamental shift in economic policy.

Of course, Im used to that, whoever invented the term martingale really was all about living in the moment.
However, with things like that, if we know that they serve 4 year terms, I hope that in my time-machine I would have not left myself so exposed with a big regime-shift potentially on the calendar (deterministic). https://almostsuremath.com/2009/11/08/filtrations-and-adapted-processes/
I remember an old man once said "its like riding one of those mechanical bulls, where some guy can just flick a switch and throw ya off" and I thought it was similar to behavior of stock indices

 

[Overnight]

Of course, Im used to that, whoever invented the term martingale really was all about living in the moment.
However, with things like that, if we know that they serve 4 year terms, I hope that in my time-machine I would have not left myself so exposed with a big regime-shift potentially on the calendar (deterministic). https://almostsuremath.com/2009/11/08/filtrations-and-adapted-processes/

God GOD man!


Lemma 3 The predictable sigma-algebra is generated by the sets of the form

(1)

Proof: If

is any of the sets in the collection (1) then the process

defined by

is adapted and left-continuous, and therefore predictable. So,

.

Conversely, let X be left-continuous and adapted. Then it is the limit of the piecewise constant functions

1). So, [img src="https://s0.wp.com/latex.php?latex={X=\lim_{n\rightarrow\infty}X^n}&bg=ffffff&fg=000000&s=0&c=20201002" alt="{X=\lim_{n\rightarrow\infty}X^n}" title="{X=\lim_{n\rightarrow\infty}X^n}" class="latex" > is also measurable.

In these notes, I refer to the collection of finite unions of sets in the collection (1) as the elementary or elementary predictable sets. Writing these as

then

.

Finally, the different forms of measurability can be listed in order of generality, starting with the predictable processes, up to the much larger class of jointly measurable adapted processes..."

You don't need all of that stuff to know that when Trump tweeted "I demand all businesses to stop doing business with China.", the DOW dropped 700 points in 10 minutes.

The mathematical proof?

When Trump tweeted that in Aug 2019, the market dropped 700 points in like 10 minutes.

Maybe you are prepping for more sublime times when Biden doesn't tweet crazy shit, and so are looking for a reason for the markets to move bigly? I dunno'. But I would be surprised if the VIX ever got down to the all-time-low levels of 8-10 again.

 

[Kevin Schmit]

[I[ have implemented a [stoch vol] model that fits prices and volatility smiles very well and quite parsimoniously .

Does your model calibrate jointly to both spx vol/skew/smile and vix options vol (spx vol of vol should ~ vix options vol, usually vix options iv is too low)?

If so, infer a cleaner VIX which will act as an attractor for vix ex-conditional risk premium. Trade that.

Everything I read says this works 99% of the time, until it doesn't, and that you can give back a years worth of profits in a day.

If you are worried about the tail risk, trade it only in regimes where conditional risk premia have flipped signs.

 

[stochastix]

Does your model calibrate jointly to both spx vol/skew/smile and vix options vol (spx vol of vol should ~ vix options vol, usually vix options iv is too low)?

The first paper, the rough quadratic is formulated as a joint calibration problem. The issue with the rough quadratic Heston is that its quite challenging and computationally demanding to simulate; the lifted Heston works extremely well and has the same quality due to it being a finite linear combination of classical Heston processes, so simulation and estimation is much easier, and there is a characteristic function closed-form which can be Fourier-inverted to get the probability density ; BUT the Lifted Heston is not posed as a joint problem. For that, I will need to add the necessary features to the inference procedure in the lifted Heston model so that I can jointly calibrated the 'lifted' model to SPX and VIX options at the same time. Should be doable.

If so, infer a cleaner VIX which will act as an attractor for vix ex-conditional risk premium. Trade that.

That is a brilliant and fantastic idea, thank you. The idea of rough volatility is interesting, continuous but quite irregular paths. I should be able to develop a non-linear filter there measurements update some state variable that is continuously evolving. I could subscribe to all the underlying SPX option prices, or, might there be some additional information in the option prices for all the 500 SPX component stocks as well?

If you are worried about the tail risk, trade it only in regimes where conditional risk premia have flipped signs.

Flipped signs of which two measures? the risk premia inferred from near-term SPX component options vs next-term , or something else?

 

[stochastix]

God GOD man!


Lemma 3 The predictable sigma-algebra is generated by the sets of the form

(1)

Proof: If

is any of the sets in the collection (1) then the process

defined by

is adapted and left-continuous, and therefore predictable. So,

.

Conversely, let X be left-continuous and adapted. Then it is the limit of the piecewise constant functions

1). So, [img src="https://s0.wp.com/latex.php?latex={X=\lim_{n\rightarrow\infty}X^n}&bg=ffffff&fg=000000&s=0&c=20201002" alt="{X=\lim_{n\rightarrow\infty}X^n}" title="{X=\lim_{n\rightarrow\infty}X^n}" class="latex" > is also measurable.

In these notes, I refer to the collection of finite unions of sets in the collection (1) as the elementary or elementary predictable sets. Writing these as

then

.

Finally, the different forms of measurability can be listed in order of generality, starting with the predictable processes, up to the much larger class of jointly measurable adapted processes..."

You don't need all of that stuff to know that when Trump tweeted "I demand all businesses to stop doing business with China.", the DOW dropped 700 points in 10 minutes.

The mathematical proof?

When Trump tweeted that in Aug 2019, the market dropped 700 points in like 10 minutes.

Maybe you are prepping for more sublime times when Biden doesn't tweet crazy shit, and so are looking for a reason for the markets to move bigly? I dunno'. But I would be surprised if the VIX ever got down to the all-time-low levels of 8-10 again.

Yeah, yeah, i know, somebody tweets something all hell breaks loose. I dont read or follow twiter, whatever that noise is, is already factored into the market filtration of prices

 

[Overnight]

Yeah, yeah, i know, somebody tweets something all hell breaks loose. I dont read or follow twiter, whatever that noise is, is already factored into the market filtration of prices

Oy! If it was factored into the market, all hell would not have broken loose!

I admit that I have not been following how it had been affecting the VIX (or VX through ICE) for the last 2 1/2 years, as I am focused on Equity and a bit of oil and gold futures.

I can only relate to you what I have witnessed on my charts and the price action when those bombshell tweets came out. Nutso, and I do not see how an algebraic equation can prep you for that.

 

[stochastix]

actually it can, because when one (this one, i guess) reads the algebraic equations related to almost unstable hawkes processes , one understands that the vast majority of activity is reflexive and reactionary.
See
Limit theorems for nearly unstable Hawkes processes
"
... Thus, modeling financial order flows as nearly unstable Hawkes processes may be a good way to reproduce both their high and low frequency stylized facts. We then extend this result to the Hawkes-based price model introduced by Bacry et al. We show that under a similar criticality condition, this process converges to a Heston model. Again, we recover well-known stylized facts of prices, both at the microstructure level and at the macroscopic scale. "

and

From quadratic Hawkes processes to super-Heston rough volatility models with Zumbach effect
as well:
Using microscopic price models based on Hawkes processes, it has been shown that under some no-arbitrage condition, the high degree of endogeneity of markets together with the phenomenon of metaorders splitting generate rough Heston-type volatility at the macroscopic scale. One additional important feature of financial dynamics, at the heart of several influential works in econophysics, is the so-called feedback or Zumbach effect. This essentially means that past trends in returns convey significant information on future volatility. A natural way to reproduce this property in microstructure modeling is to use quadratic versions of Hawkes processes. We show that after suitable rescaling, the long term limits of these processes are refined versions of rough Heston models where the volatility coefficient is enhanced compared to the square root characterizing Heston-type dynamics. Furthermore the Zumbach effect remains explicit in these limiting rough volatility models.