Quite the opposite. I wrote before that the mathematical formalism you're trying to use is a general framework for linear restoring forces; it isn't tied to any subatomic ontology. You also don't need physics metaphysics here. And it's perfectly fine to use "quantum" math wherever it works - after all, finance already uses PDEs (via Feynman-Kac/HJB), spectral decompositions, Fourier transforms, Green functions, Schroedinger bridge ideas, ...  - these are general applied math tools, not something tied from quantum mechanics. My objection is about claims vs mechanics in your write-up - what's a genuine quantum consequence and derivation vs classical modelling choice.

@ "In fact the model here boils down to saying that the normal distribution of the classical model oscillates from side to side, increasing the variance. Not actually that hard."

If you mean a bell curve of fixed width whose mean slides side-to-side (or a bouncing "nice boob", as these guys would explain it...), it sounds to me like the law of total variance: after averaging over time/phase, total variance = intrinsic variance + variance of the moving mean.
For a sinusoid that adds amplitude^2/2. Turning that amplitude into a single realised window move z is a modelling identification (work of a sizable group of underpant gnomes - I'm not thinking a full filharmonic orchestra, which you still need to justify mixing up the energy and position observables when using Poisson weights, but something like a chamber orchestra; and obviously smaller in size because they are gnomes), not a quantum derivation. Also it obviously doesn't explain heavier *shoulders* (the tail is still Gaussian) you later get by mixing Gaussians. This and the earlier mentioned mathematical identifications aren't justified by QHO maths. A simple derivation like eg the Bayesian one I sketched above is a mathematically honest way to get the formula, and it separates the conditional variance rule from the unconditional genuine heavy tails.

kat, this sounds like something that could be simulated. Could you do a simulation and upload it here?

Maybe they were thinking of:

David, 
I really enjoyed your talk last during the CFQ conference, certainly cleared a few things up in the concepts for me. 
Thanks! 

End-of-year Competition

As you probably know, we have been promoting David Orrell's q-variance volatility model for a while. The model relates actual volatility to asset returns in a way that seems to be consistent across all finance data and all time scales. And only has the one parameter. Perhaps uniquely in finance, the theory, inspired by the mathematical tools of quantum mechanics, came first before any observations. (Usually in finance an observation comes first, followed by the energetic torturing of models to fit the data in a way that often flies in the face of common sense! But, hey ho...)

Rather annoyingly, the q-variance property has so far remained stubbornly resistant to simulation tools. That is what the competition is about: Find a way to simulate an asset price path such that it exhibits the q-variance relationship between actual volatility over a period and the return over the same period. This is nothing about options, or implied volatility, anything like that. No, we want you to simulate paths for the asset itself, its share price. 

(Alternatively, you could demonstrate that the model is nonsense, perhaps the q-variance property is just a statistical thing, a bias possibly.)


Closing date: None

Prize: One-year subscription to WILMOTT magazine and publication of the technique

Further model information: Q-Variance: or, a Duet Concerning the Two Chief World Systems. Wilmott 2025 (138)

Further competition information: https://github.com/q-variance/challenge

Email admin@wilmott.com if you have any questions

"Find a way to simulate the q-variance model. "

The model is dead and alive until the simulation is observed?

For those who may enter the competition and would like to do some background reading, here are links to the References to the three papers cited on the GitHub entry:

1a. Wilmott P, Orrell D (2025) Q-Variance: or, a Duet Concerning the Two Chief World Systems. Wilmott 2025(138).

2a. Orrell D (2025) A Quantum Jump Model of Option Pricing. The Journal of Derivatives 33(2): 9-27.
https://www.researchgate.net/publicatio ... on_Pricing (must request)

3a. Orrell D (2025) Quantum impact and the supply-demand curve. Philosophical Transactions of the Royal Society A 383(20240562).
https://papers.ssrn.com/sol3/papers.cfm ... id=4100792 

(Edited for relevance to this particular project.)

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 implied volatility smile, but that is not the subject of this competition.

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 implied volatility smile, but that is not the subject of this competition.

Yes, I see now.  Sorry about that. I have edited the list so people will not waste time on the wrong References for this particular project.

Community service becomes community disservice in that case. Good luck to those who will give it a try.

Thanks, makes it simpler!