Rimaneggiamento osseo pt.3

Algorithmic Trading Overview

• Algorithmic trading uses computer programs to execute trades based on predefined rules.
• It is also known as automated trading, black-box trading, or algo-trading.
• Trades are executed automatically, eliminating manual intervention.
• Algorithms follow rules based on price, timing, quantity, or mathematical models.
• Algorithms execute trades at high speeds, capitalizing on small price discrepancies.
• Algorithms reduce emotional bias, leading to more consistent trading.

Algorithmic Trading Strategies

• Trend Following: Capitalizes on market trends by buying during uptrends and selling during downtrends.
• Mean Reversion: Identifies assets with prices deviating from their average and bets on a return to the mean, e.g., pairs trading.
• Arbitrage: Exploits price differences for the same asset on different exchanges by simultaneously buying and selling.
• Market Making: Places buy and sell orders to profit from the bid-ask spread, providing liquidity.
• High-Frequency Trading (HFT): Executes very high-speed transactions to capture fleeting market inefficiencies.

Advantages of Algorithmic Trading

• Faster trade execution.
• Reduced transaction costs due to efficiency.
• Algorithms can be backtested on historical data.
• Algorithms can trade 24/7.

Disadvantages of Algorithmic Trading

• Susceptible to system failures and connectivity issues.
• Risk of over-optimization, which leads to poor performance in live trading.
• Requires expertise in programming, quantitative analysis, and market dynamics.
• Subject to regulatory scrutiny due to potential market manipulation.

Mean Reversion Strategy in Detail

• Operates on the assumption that asset prices revert to their historical average.
• Assumes that significant deviations from the mean will eventually correct.

Implementation Steps for Mean Reversion

• Data Collection: Gather and clean historical price data for the asset.
• Calculate the Mean: Compute the moving average (MA) of the asset's price over a certain period.
  • Moving Average (MA) = (∑ Price_i) / n , where n is the number of periods.
• Calculate Standard Deviation: Measure price volatility around the moving average.
  • Standard Deviation (σ) = √((∑ (Price_i - MA)^2) / n).
• Define Entry and Exit Rules:
  • Entry Rule: Buy if Price < MA - 2σ (example).
  • Exit Rule: Sell if Price ≥ MA (example).
• Risk Management: Use stop-loss orders and determine trade size based on risk tolerance.
• Backtesting: Evaluate the strategy's performance using historical data and adjust parameters.
• Execution: Implement the strategy using an automated trading platform and monitor trades.

Code Example Considerations

• Market Conditions: Mean reversion works best in stable markets.
• Parameter Tuning: Moving average window and standard deviation thresholds must be tuned carefully.
• Transaction Costs: Must account for transaction costs.

Lab 2: Modeling the Motion of Falling Objects

Objective

• Model motion of falling objects with and without air resistance.

Activity 1: Free Fall

• Initial conditions: object at the origin, not moving.
• Simulation parameters: m = 1 kg, g = 9.8 m/s², Δt = 0.01 s.
• The object falls with a constant acceleration.
• Final speed of the object is equal to the acceleration due to gravity times the time interval.

Activity 2: Free Fall with Air Resistance

• Same initial conditions and simulation parameters as in Activity 1, plus air resistance.
• Air resistance is proportional to the square of the object's velocity.
• Drag coefficient: b = 0.1 kg/m.
• The object initially accelerates, but then the acceleration decreases as air resistance increases.
• Terminal speed is reached when air resistance equals the force of gravity.
• Terminal speed is equal to the square root of the object's weight divided by the drag coefficient: vt = √(mg/b).

Activity 3: Analyze the Skydiver's Motion

• Use video analysis to track the skydiver's motion.
• Terminal speed of the skydiver was approximately 55 m/s.
• Estimated drag coefficient of the skydiver was approximately 0.2 kg/m.
• The skydiver's motion is similar to that of an object with air resistance.
• The skydiver's terminal speed is much higher due to a larger surface area.

Conclusion

• The motion with air resistance is more complex.
• The terminal speed depends on the object's weight and drag coefficient.