What is a Financial Exchange.

SP500 Daily Laplace trading solution 2016 – 2021



Markets are parabolically distributed

  •  The price chart contours are the Laplace distribution constrained by an exponential step controller.
  •  The first indicator panel shows the interference they are the difference between the market and the contour they are related to.
  •  The second panel is the Poisson distribution of the first derivative of the stepped contour set. 
  •  The third is the direction signal and the fourth is the per contract return.

From an electronic engineering point of view the only difference between a telephone exchange and a financial exchange is the spelling I have always believed that Black and Scholes is based on a bad assumption and that this was their big mistake given the computing tools of the time it is easy to understand how this came about, I think  LTCM more than proves my point. Markets are not normally distributed they are parabolically distributed. The problem with current methods of doing statistical regressions, is that when you take the sum of the squares of a series you are throwing away the directional component that you need calculate future probabilities in real time

If you keep this number and handle it as a complex number you can solve this problem by using the differential equation  f(t) – e^jsdt + c = 0

Where f(t) is the market and j is the complex directional component and s is the exponential step constant for the market you are interested in and c is the initial price of the data sample. This allows you to calculate the markets exponential volatility with the directional component in tact.

Current Market Conditions.

Anyone who has seen market conditions like this is just watching and waiting for the inevitable day of reckoning when it all reverts to the mean. All the major lows of the market over the last hundred years are the same. It took thirteen years for the eighties boom to develop and it all began in the last quarter of 1974 after the oil shock and just built up from there. It is now thirteen years since the GFC and here we are again leveraged out to the twilight zone in a market that has lost all concept of rational price discovery.

I have not seen the market this dangerous since the late 1980’s the biggest surprise of the crash of 87 was when the whole global economy did not implode into a screaming heap of bad debt in the year that followed. From a pure math’s point of view markets are composed of resonating coupled oscillators, when they get out of balance and hit resonance they swing around like the Tacoma Narrows Bridge and obey the same laws of mathematics.

The objective of sound portfolio management is to remove unwanted market fluctuations / oscillations from your book to stabilize returns. The conventional wisdom would have you believe there is no relationship between the mathematics of physics and that of finance. This is simply not the case they are related by the Laplace transform just with different names for the moving parts. The rest is just testing candidate solutions like Edison until you find the one that returns the carrier wave. 

Intuition would lead you to believe that the Fourier transform would be the solution however Fourier transform converts from the time/price domain to the frequency domain which gets you nowhere the market may be cyclic but it is not periodic. What is needed is a transform that converts from the time/price domain to the time/log returns domain. 

It is just a simple matter of renaming your variables, just change price to voltage and current to volume and you discover that what you are looking at is telecommunications signal that can be spectrographically analyzed.

  • What we are looking at is telecommunications signal.
  • Prices are just numbers in databases connected to each other by telecommunications networks.
  • Money is nothing more than information transmitted by electromagnetic energy. 
  • Light and money are therefore the same thing, and obey the same laws of physics.
  • Electromagnetic energy travels in the form of waves and creates interference patterns in the medium it is travelling in.
  • This wave is a triangular ramp type with a long rise and short decay times also known as the boom and bust cycle.
  • To discover the properties of this wave we must first remove the high frequency component to discover the current long term trend.
  • To do this a band pass filter is used to remove the high end frequencies while passing the low ones the true state of the underlying trend.

The model of a normally distributed financial system is over hundred years old now and that is a long time to go without an upgrade speaking for myself if I had to manage vast sums of money I would want a risk management method so bullet proof that I would be able to sleep like Winston Churchill on the night America entered the war, safely knowing that my day job would never become the plotline of a major motion picture.