Qvar, an online app to explore q-variance
The Qvar Shiny app is now live at:
https://david-systemsforecasting.shinyapps.io/qvar/
The app provides an interactive way to explore q-variance - a property that links price changes and volatility in a way not anticipated by traditional models. It draws on ideas from quantum probability to test whether a universal variance relationship holds across major stocks.
What Is Q-Variance?
In the q-variance framework, the annualized variance over a period T follows to good approximation the formula
V(z)=0^2+z^2/2
where z=xT, x is log return over the period corrected for drift, and 0 is a minimum volatility parameter that is estimated from the data.
This formula implies that variance grows quadratically with the scaled price displacement z, in contrast to classical models where it is constant (e.g. Black-Scholes) or varies randomly. The app illustrates this for a range of assets including 355 S&P 500 stocks that have been in the index for at least 75% of trading days between 1992-01-02 and 2025-04-17.
What You Can Do in the App
Pick any of 355 S&P 500 stocks
Choose time periodsfrom 1 to 26 weeks
Compare actual market behaviourto the q-variance prediction
Download the raw datato analyse yourselfWhy It's Worth a Look
- Reveals patterns hidden in noisy financial data
- Helps test whether the quantum-inspired model matches reality
- Useful for researchers, students, and anyone curious about volatility
How to Use the App
Plots tab - Choose a stock ticker and range of periods T (1-26 weeks).
The upper plot shows variance vs z for selected periods. Blue line is average variance as a function of z, red line is the q-variance curve.
The lower plot shows the average density (blue) compared with the quantum model (red).
Data tab - View/download the time series for the selected asset(s), including prices and computed variables.
Try it now:
https://david-systemsforecasting.shinyapps.io/qvar/
See also: QEF15 - A quantum oscillator model of stock markets 2: q-variance and theq-distribution