Quantum finance equation explanation please

[yosmod04]

TL;DR

I am interested in knowing how to connect the eigenvalues of a non harmonic Schrodinger equation with the price levels of exchange rates.

Dear all,
Dr. Raymond S. T. Lee in his book on Quantum Finance (page 112), normalizes quantum price return QPR(n) using the following scaling:

Normalized QPR(n)=1+0.21*sigma*QPR(n).

I don't know of any way of explaining this equation.
sigma is the standard deviation of the wave function solution of a Schrödinger equation.
QPR(n)=E(n)/E(0), where E are the eigenvalues of an an-harmonic quantum oscillator (Schrödinger equation with a quadratic and a quartic term)
Thanks!

 

[jedishrfu]

Have you checked out the wiki article on QF?

https://en.wikipedia.org/wiki/Quantum_finance

It seems to cover what the constants and variables mean.

and here's some related QF information although its rather general in scope:

 

[yosmod04]

Many thanks. The wiki article is interesting but it deals with other aspects of the theory, like the quantum binomial model. I am looking for the explanation of a very specific question regarding the scaling/normalization of the price function.

 

[anorlunda]

I am looking for the explanation of a very specific question regarding the scaling/normalization of the price function.

In that case, I would ask economists, not physicists.

 

[yosmod04]

Economists know nothing about Quantum Mechanics. This is a question about re-scaling of a function, that is not the wave function but a distribution function. The model is for economists but the theory is pure physics. I thought is related to some kind of statistics because of the presence of sigma.

 

[DrClaude]

Economists know nothing about Quantum Mechanics. This is a question about re-scaling of a function, that is not the wave function but a distribution function. The model is for economists but the theory is pure physics. I thought is related to some kind of statistics because of the presence of sigma.

This is nothing to do with physics. Might as well call this Quiddich Finance instead of Quantum Finance. I don't have access to the book, but by what can be read in Google Books, the author understands virtually nothing about quantum mechanics (the introduction reads like a bad popular science explanation of QM).

 

[yosmod04]

Agree with you on that, the book is terribly written. I am giving him the benefit of the doubt and trying to make sense of his model. You will find hard to believe, but the book was published by Springer. Springer used to be a very serious editorial house. I wrote to the author but haven't received any answer from him regarding this issue.

 

[DrClaude]

Editors are always dependent on referees/external advisors.

I had never hear of quantum finance before reading your post. It appears to be an actual academic field, but I am not yet convinced it is a legitimate field of academia.

 

[anorlunda]

Just because an equation has the same form as an equation used in physics, that does not mean that it relates to physics.

There are only a finite number of simple useful equations to share among all fields.

Newton's second law F=ma. Can you think of equations in economics that have the same form? That does not relate them to Newton.

 

[yosmod04]

I think that it is not as bad as you suggest. There are some very serious people that have published good work: Haven, Emmanuel (2002). "A discussion on embedding the Black–Scholes option pricing model in a quantum physics setting". Physica A: Statistical Mechanics and Its Applications. 304 (3–4): 507–524., and Baaquie, Belal E.; Coriano, Claudio; Srikant, Marakani (2002). "Quantum Mechanics, Path Integrals and Option Pricing: Reducing the Complexity of Finance". Nonlinear Physics. Nonlinear Physics - Theory and Experiment Ii. p. 8191 .