Future History of Poseidon by Paul Cottrell

Poseidon is from Greek mythology.  In Wikipedia the following is written.

Poseidon one of the twelve Olympian deities of the pantheon in Greek mythology. His main domain is the ocean, and he is called the "God of the Sea". Additionally, he is referred to as "Earth-Shaker" due to his role in causing earthquakes, and has been called the "tamer of horses". He is usually depicted as an older male with curly hair and beard.

The name of the sea-god Nethuns in Etruscan was adopted in Latin for Neptune in Roman mythology; both were sea gods analogous to Poseidon. Linear B tablets show that Poseidon was venerated at Pylos and Thebes in pre-Olympian Bronze Age Greece as a chief deity, but he was integrated into the Olympian gods as the brother of Zeus and Hades.  According to some folklore, he was saved by his mother Rhea, who concealed him among a flock of lambs and pretended to have given birth to a colt, which was devoured by Cronos.

There is a Homeric hymn to Poseidon, who was the protector of many Hellenic cities, although he lost the contest for Athens to Athena. According to the references from Plato in his dialogue Timaeus and Critias, the island of Atlantis was the chosen domain of Poseidon.

Poseidon is also software developed by Reykjavik, which is my research trading company.  In terms of the history of Reykjavik and the software development of Poseidon, let’s start with the genesis of Reykjavik.  Reykjavik is my research and trading company, whereby all my proprietary trading and financial research is developed through it.  Reykjavik is established in the financial district of Lower Manhattan.  There are two main reasons for the name of the company.  First is that during the winter Lower Manhattan is extremely cold, and hence the name Reykjavik—a major city in Iceland.  The second reason is due to my experience moving from Detroit, Michigan to Manhattan.  When I finished my MBA, I moved to New York in late 2008—which of course was during the financial crash of 2008.  Reykjavik, the city, was one of the first mortgage default hotspots in the world.  I figured to name my company after the city that started the contagion of over leveraged mortgage markets and one of the causes of the major volatility dynamics of our financial markets.

As for the Poseidon software, it is developed under Reykjavik—which is a financial research studio owned solely by me.  The design ethos is to provide the financial industry with surfacing tools to produce analysis of econometrics and financial data.  The intent is to also provide a predictive set of tools for quantitative trading and to allow traders to manage risk by understanding volatility graphically.

Future development of the Poseidon software will be using crash prediction utilizing log periodic fitting and the use of crash hazard rates.  Dynamic hedging will also be incorporated into the software using standard hedging methods, as well as artificial intelligent methods.  As for advanced research being done by Reykjavik, visualization in a virtual reality engine is being developed.  Experiments are also being conducted to utilize pattern recognition from market telemetry.  All of this future development will be in future production releases of Poseidon. 

What problems can be visualized in topographic finance? By Paul Cottrell

Three possible problem types can be visualized through topographic financial techniques, albeit this is not an exhaustive listing.  We will look at econometric problems first.  Econometric information can be very data intensive.  We need a means to be able to data mine and visualize these sorts of econometric problems.  One such three–dimensional dataset is unemployment, time, and gross domestic product.  By having all three factors in one graph will allow for easier analysis to be accomplished.  Another econometric problem is related to tax rates.  By using a Laffer curve we can see how tax rates can affect actual tax revenue.  But what if we wanted to understand tax rates and tax revenue over time?  We can accomplish this by using topographic finance.  A Laffer surface can be created, whereby the three dimensions are tax rate, time, and tax revenues.  By using this sort of economic analysis, with respect to tax rates, we can determine an optimized tax policy.

The second type of problem that topographical finance can solve is visualization of financial information.  In terms of fundamental analysis, financial ratios, balance sheets, and income statements can be visualized.  For example, price-to-earnings ratio, revenue growth rates, and time can be inputted into a three–dimensional graph to help compare different companies to determine if an investor should invest into that company.  Another example within the fundamental analysis domain is long–term debt, time, and earnings.  As can be imagined, there are countless configurations to graph financial problems. 

Our third example is technical or quantitative financial problems.  We can utilize topographic finance by graphing price, time, and volatility; therefore allowing for an understanding of how volatility evolves through time and affects the price of an asset.  Another good example is the volatility surface for an option contract. When making a volatility surface for options strike price, time-to-maturity, and volatility are used. 

Again, topographic finance can graph many different types of problems and will most likely evolve into utilizing hypercubes, whereby multiple three–dimensional spaces are compared with each other to understand high dimensional dynamics.  Many traders use lots of price charts with many indicators, which is utilizing hypercube faces to understand the dynamics of the market.

Chaos Theory in Trading by Paul Cottrell

It is possible to graph returns to determine the level of chaotic behavior in a financial system.  This is accomplished with graphing returns along the x-axis pertaining to t-1 and the y-axis with only t, whereby t is time.  By graphing returns in this fashion we are determining the previous return affects for the next period’s return.

The empirical evidence suggests that daily returns are not autocorrected from the previous day.  But on larger time scales trends do emerge—leading to autocorrelation of previous period returns with current returns.  Another way to determine the level of chaotic behavior in a time series is to calculate the fractal efficiency ratio.  A ratio equal to 1 is a pure trending system, whereas a ratio equal to zero is considered a pure chaotic system. 

Yet another method to determine the smoothness of the market is describing the market dynamics in terms of Mandelbrot markets.  A Mandelbrot market is a method to determine the level of trending in a time series.  This smoothness is defined by the value that H holds.

A mean reverting system has H < 0.5.  A pure Brownian motion system has H = 0.5.  For H > 0.5 a trending time series is present.  Higher H values are lumpier market surfaces.

Mandelbrot–time is another way to look at the strange behavior of financial markets Mandelbrot (2004).  There are two types of time: trading–time and clock–time.  In trading–time, the time is varying where the velocity depends on the speed of the price.  This can be expressed as the first derivative, whereby delta price is divided by delta time.  For an example of trading–time, during high volatility days the price action is high—leading to faster time within trade–time.  Lower volatility days have slower trade–time.  Many traders express their perceptions of time with the following terms: rapid price movement, or a slow trading day.  Clock–time is the standard time and is constant in velocity. 

Time is relative to level of price change, which can be used to help model discontinuous markets. To fill the gap in discontinuous markets one should build a Brownian motion bridge.  Mandelbrot–time can help frame volatility in terms of delta time.  This is similar in concept to the space–time bending with gravity, whereby trade–time bends with level of price action.    

How Does Complexity Science Relate To Trading? by Paul Cottrell

 

The market is a complex organism that exhibits self–organizing behavior.  This self–organizing behavior was well articulated by Adam Smith’s invisible hand. In an economy, the individual agents of the society interact in various ways producing microeconomic activity.  This microeconomic activity allows for price discovery and equilibrium between supply and demand.  For example, a clothing retailer sells items at an acceptable price to the clothing purchaser.  This microeconomic equilibrium might not reach a macroeconomic equilibrium, but at times macroeconomic equilibrium is reached.  I suggest that macroeconomic equilibrium is a lagging equilibrium due to other factors, such as monetary policy that might not diffuse into the individual economic agent’s interactions instantaneous. In economics we call this disequilibrium as a saddle–path, whereby equilibrium is usually not reached and vacillates around equilibrium.  

Price action in the financial markets has shown asymmetric dynamics, whereby the price dynamics going up are different than price dynamics going down.  Why is price action asymmetric? Price action is asymmetric because of the behavioral effects of the trading agents.  There is a fear that takes place in depreciating asset prices leading to a stampede of sellers.

Another aspect of asymmetry is information.  In Stiglitz (2002), information is not instantaneous; therefore there are market participants that can capitalize on this information before other market participants.  In the efficient market hypothesis (EMH), information is considered symmetric and that the average trader cannot profit on new information because the current price already has that information accounted for.  EMH cannot be true because of the increasing number of market participants that can profit from news before other market participants. 

In terms of models, traders need ways to evaluate the current state of the financial market or economy.  These traders, or market participants, use models to perform an analysis if the market is fairly priced or not.  But models have assumptions and therefore can only represent a shadow of reality pertaining to financial dynamics.  Some models are more accurate than others; but due to the feedback loops of agent’s behaviors, the dynamics change in a reflexive way—leading to possible model failure.

Models have certain assumptions on price action and these assumptions can lead to malignant states within the financial markets, whereby the herd effect of traders using a certain model paradigm can cause system failure, i.e. financial crash. When these models are used incorrectly—either by mistake or on purpose—contagion can arise.  The following are examples of when models misbehave.

  • Lehman Crash
  • Flash Crash
  • Accounting drawdowns in a portfolio
  • Mass Unemployment
  • Inflation volatility—measured  in CPI

What is Chaos Theory? by Paul Cottrell, MBA

What is Chaos Theory?

Chaos Theory is the means to study the behavior of dynamic systems.  Dynamic systems are different from static systems due to the sheer fact that static systems are non–changing, whereas dynamic systems are changing.  A pure cybernetic system can be classified as a static system, e.g. a clock or oscillating fan.  These pure cybernetic systems are designed with all their component interactions predicted and calibrated during its architectural and manufacturing phase.  Dynamic systems are systems that change, either form endogenous factors or exogenous factors.  Some dynamic systems can be very complex, e.g. the human body—while other dynamic systems are quite simple, such as the unfolding dynamics of a salt crystal with water.

Dynamic systems are nonlinear systems.  These nonlinear systems can be unpredictable and can possess amplifying feedback loops.  In terms of chaos theory, there are deterministic chaos and non–deterministic chaos.  Deterministic chaos is simple chaos, whereby no stochastic functions are in the system.  Examples of deterministic chaotic systems are Lorenz Systems and double fulcrum pendulums. 

In deterministic chaotic systems, though there are no stochastic perturbations in the system, there are unpredictable behaviors exhibited in these systems.  In a typical Lorenz system there are two chaotic attractors.  One can predict an overall trend within the Lorenz system but cannot provide exact position.  In the double fulcrum pendulum example, all the mechanics of this system can be expressed in a mathematical formula—but the design of this system will still exhibit nonlinear behavior.  When the double fulcrum pendulum moves back-and-forth with high velocity the two fulcrums start to exhibit their degrees of the free, whereby the lower level can move erratically in a circular pattern.

In non–deterministic chaotic systems there are complex chaos.  Complex chaos is where there are stochastic functions present in the system.  Examples of non–determinist chaotic systems are social systems and financial markets.  Another interesting complex chaotic system is the evolution of a particular war.  In battle, due to the high degrees of freedom on the field, the conflict can evolve in unexpected ways.   The evolution of war is quite similar to the evolution of weather, whereby there are feedback loops that change the present dynamics of the system leading to unpredictable behavior.

In terms of financial markets, human misbehavior, random news events, and feedback loops contribute to the changing dynamics. Behavioral finance articulates these forces on the market to help explain bubbles and crashes.  In Soros (2003), reflexivity is a process in which self–reinforcing processes produce disequilibrium in financial markets. 

When modeling financial markets there is a degree of error, which is quite different when modeling the motion of objects with Newton’s Laws.  Why is it that a financial model is less accurate than models in physics?  The basic answer is that the laws of physics do not change—they are stationary in a sense.  But financial dynamics are very complex and have changing attributes, similar to history.  History does not repeat, but it rhymes.  Within this rhythm of history are the stochastic perturbations that are forceful enough to make the system different.  We call this a path dependency, whereby the acts of the past and current states affect future states.  In quantitative finance we call this path dependency a Markov chain when only the present state is affecting future states.