Re: David Orrell's q-variance paper in Wilmott
Posted: September 17th, 2025, 9:07 pm
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.
@ "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.