Thanks, makes it simpler!

Just to clarify, those references are from a related 2024 paper on implied volatility ("A quantum model of implied volatility"). Q-variance is about asset price volatility , and does not involve option prices or implied volatility. There is a direct connection between q-variance and the im...

Maybe they were thinking of:

Hmm, a word “suggests” something so you are “guessing” that I do something with “windows” to obtain Gaussians which are mixed with Poisson weights in a “purely classical construction”. Tell you what, just wait for the book to come out (some time next year – it is with a tiny little academic press an...

For those interested in looking at actual data, here is an updated version of the QVar app with some more bells and whistles on the Data tab: 

http://david-systemsforecasting.shinyapps.io/qvar

"The distribution corresponding to each level is Gaussian, because we are summing over an uncorrelated ensemble. The net result is a Poisson-weighted sum of Gaussians." That's definitely not true. In the harmonic‑oscillator, after an energy measurement the system is in level n and the pos...

Will add some diagnostics to the app to check this kind of thing ...

Further to Paul’s comment, as someone who has dabbled in science communication, I find it fascinating how this model is perfectly poised to be very simple but understandable by almost no one. (This is based not on this chat – I thank everyone for bearing with it – but on several years experience.) P...

This might be a bit of a side-topic then, but one question – which would also shed light on the q-distribution – is how to obtain a simulated time series of daily data which respects q-variance. The quantum model gives log price changes and variance over a period T such as a week or month, but does ...

Nice music! Let’s do q-variance first. The probability function of a coherent state is a normal distribution moving from side to side with amplitude x and period T. As you point out, the variance at any time is sigma^2. But what we use in the model is the variance over a complete period, which is si...

No thanks. One problem is that you seem to be confusing the 1/2 coefficient in q-variance, with lambda. The first comes from a simple energy balance – perturbing the oscillator by an amount z increases the energy and therefore the variance by this amount. The Qvar app is testing this relation. Lambd...

Nearly! The model uses a QHO coherent state to model price change over a period T. It’s not an analogy (nothing to do with subatomic particles), it’s the result of quantizing a linear entropic force, so the model can be viewed as a first-order approximation to the underlying probabilistic dynamics. ...

I put up a new version of the app which now allows you to combine data from up to 4 stocks. The time range for periods is shortened to 1 to 26 weeks. This allows for multiple stocks without using too much memory, but also at 26 weeks there are about 50 points which is about as low as you can go to g...

My aim isn't to convince anyone, that is far too hard!

Yes, the model applies for all T, but the agreement with data will only ever be as good as the uncertainty. If you average over many period lengths T then that reduces the noise so you get a better idea of the fit. Another way as you suggest is to look at multiple stocks. The lower plot does this fo...