Chaos_Theory_and_Modern_Trading

Report
By
Paul Cottrell, BSc, MBA, ABD
 Author
 Complexity Science, Behavioral
Finance, Dynamic Hedging,
Financial Statistics, Chaos
Theory
 Proprietary Trader
 Energy and Currency
 Dissertation
 Dynamically Hedging Oil and
Currency Futures Using
Receding Horizontal Control
and Stochastic Programming
 The behavior of dynamic systems
 Many systems are non-linear
 Unpredictable results can occur
 Deterministic chaos
 Simple chaos where no stochastic functions are in the system
 Non-deterministic chaos
 Complex Chaos where stochastic function are in the system
Double fulcrum Pendulum
Lorenz System
• Human misbehavior
• Random news events
• Feedback loops
Unknowable
Knowable
 Theory of Emergence
 Started in cosmology
 Big Bang leads to further particle evolution and the
emergence of materials.
 Which leads to further complex arrangement
 Life
 Social Organization
 Economic or financial emergence
 Economic development
 Systemic risk
 Contagion
 Key takeaway
 A complex system can evolve into unpredicted pathways
 Complexity Science
 The study of complex systems
 Using simple rules for agents
 Self organizing behavior
 Interactions that have a magnifying effect
• The “Market”
• Complex organism
• Self organizing
•Adam’s invisible hand
• Price action
•Asymmetric
• Information
•Asymmetric
• Traders use models
• Models have certain
assumptions on price action
• Models can be used
incorrectly and cause a
system failure
• Lehman Crash
• Flash Crash (Maybe?)
• Account drawdown
• Mass unemployment
• Big Macs too expensive
 The Efficient Market Hypothesis
 Assumptions
 Rational investors
 Information cannot be used to make above normal profits
 The stochastic variations in returns mean to zero
 The market should always be in steady state
 Problems
 Traders are greedy and not rational
 Due to the Dopamine response mechanism
 New information is not completely in the price
 Profits can be statistically above average for some groups
 Stochastic variations in returns can lead to bubbles and bursts.
 Fundamental Equilibrium
 When price is close to “economic value”
 Could be assumed at a 200 moving average on a long
duration chart
 Fundamental analysis rule the game
 Speculative Equilibrium
 When price is above or below “economic value”
 Chartists or Quants rule the game
 Most assets are in Speculative Equilibrium
 Evidence in the 50 period moving average
 Has mean reverting characteristics
• Returns graphed
• Daily Returns, Weekly, Monthly
• S&P 500
• Lower Right Graph
• Dow 30
• Monthly
• State Space
• X-axis return (t-1)
• Y-axis return (t)
• Empirical evidence
• That returns are stationary
•In daily returns
• Non-stationary
•At larger time scales.
• Shows emergence of tend
• Ratio to determine level of chaos
• “C” is the return at time (t)
• Ratio = 1
• Pure trending
•Ratio = 0
• Pure Chaos
H < 0.5
mean reversion
H = 0.5
Brownian Motion
H > 0.5
Trending
A possible method to describe the market in terms of smoothness.
Lower “H” value the smoother the surface of the market.
 There is trading time and clock time
 Clock time is standard time and is constant in velocity
 Trading time is changing
 Velocity (first derivative) depends on the speed of price

For example:
 During high volatile market days price action is higher


Leading to faster time in trade time
Lower volatile days have slow trade time
 Many traders use terms like
 Rapid price movement or it was a slow trading day
 Time is relative to the level of the price change
 Can be used to help model discontinuous markets.
 Bridge gap with a Brownian motion bridge.

Mandelbrot Time can help frame volatility in terms of delta time.
 Similar to space-time bending with gravity.
 Trade-time bends with level of price action.

The market is a complex system

Usually in speculative equilibrium


Volatility and correlations are not
constant

Market participants can profit on
average above zero mean

Systems that can monitor the telemetry
of the “market” might be able to
monitor the endogenous risk in the
market (Dragon Kings)

Exogenous risks do exist (Black Swans)

Hedging strategies can, to some degree,
mitigate risk factors.

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