Markets as Wave Functions.
If you apply the function Y = 3 * Ln( close ) – 21 to the SP500 you get the following chart.
There is an overwhelming meme in modern financial theory that you cannot curve fit markets and therefore you cannot use differential calculus to discover anything useful about the underlying equations that are no doubt at work at the heart of the question.
I have always though that if you truly understand something your should be able to state it in a single breath.
If there is thing I learnt is that all the great mathematical truths are so simple that they can be expressed in a few variables and explained with a few simple statements.
I don’t see why the way money behaves should be any different.
When was Jorn Utson began to build the opera house he thought he would have to use some sort of complex polynomial to make the thing stand up and was several years into the project with major construction well underway and three million in 1960’s dollars in run time gone and did not have a clue how he was going to make it stand up.
He was in a real bind when he entered the design completion for the Opera house he thought they were after a concept building and had not figured out hoe to actually build it.
He was ready to go in and confess up to the fact hat he had nothing and resign, when he was sitting at his breakfast table pealing an orange and watching the sections drop on the table when he realised that it was sections of a sphere and not some complex polynomial and not particularly complicated at all.
He had just skipped over the simple and the obvious which is the cardinal sin of research thinking something must be complicated and rejecting all evidence to the contrary. With that in mind it is always worth thinking simply and checking what every body else thinks won’t work.
The Practical Application of this is to create a function that detects when the direction of the underlying field is changing direction and trades accordingly.
As it turns out the markets are no where near as random as it may seem it is just a matter of perspective.
The lower window is the integration of the function in SP500 points as an trade stream per contract.
Simple fact is that financial markets are nothing more than complex harmonic motion that form interference patterns with with respect to time and have knowable differential equations.