Algorithmic Trading Systems and Strategies

• Algorithmic trading (AT) has changed finance through technology improvements, increased data, and demand for fast execution
• Algorithmic trading uses computer programs with defined instructions to place trades

Algorithmic Trading System

• Algorithm development involves creating strategies based on math models and data
• Backtesting uses data to simulate the algorithm's performance
• Risk parameters are set to control losses and ensure compliance
• Order generation makes buy/sell orders based on conditions
• Execution routes orders to venues for trade
• Monitoring tracks market conditions and makes needed adjustments

Algorithmic Trading Strategies

• Trend Following capitalizes on market trends
• Mean Reversion bets on prices reverting to their average
• Arbitrage exploits price differences in markets
• Market Making uses buy/sell orders, profiting from the bid-ask spread
• Execution Algorithms optimize order execution to minimize transaction costs
• Statistical Arbitrage identifies pricing anomalies, profiting from short-term mispricings

High-Frequency Trading (HFT)

• HFT is a type of AT using extremely high speeds, turnover rates, and short-term positions
• HFT firms use co-location for minimizing latency
• HFT strategies might include market making, quote stuffing, and latency arbitrage

Order Book Dynamics

• An order book contains outstanding buy and sell orders organized by price
• It provides data about liquidity, price levels, and market depth
• The order book is a key input for AT strategies

Order Book Example

• Here is a basic Level II Order Book example:

Order Types

• Market Order is used to buy/sell fast at the best price
• Limit Order buys/sells at a specified price
• Stop Order becomes a market order when the stop hits the price
• Stop-Limit Order becomes a limit order when the stop hits the price
• Hidden (Iceberg) Order only shows a partial quantity in the order book

Market Impact

• AT can have market dynamics effects
• Large orders by algorithms can move prices quickly
• Execution algorithms aim to minimize effects by having smaller pieces over time

Regulation and Ethics

• AT has regulatory oversight to prevent manipulation
• Ethical considerations include transparency, fairness, and avoiding market destabilization

Conclusion

• Understanding algorithmic trading and its effects on order books is essential

Algorithmic Complexity

What is it?

• It is a measure of the resources (time, storage) needed for an algorithm
• It is shown as a function of the size of a problem
• It compares algorithms independently of implementation and hardware

Why is it Important?

• It helps to pick the correct algorithm
• Knowing an algorithms scales lets you predict performance on inputs
• It avoids nasty surprises!

How is it Measured?

• Time complexity is the number of operations an algorithm performs
• Space Complexity is the amount of memory an algorithm uses
• Time complexity is focussed on, but space can also be crucial
• Worst case scenario is usually the thing to focus on

Big O Notation

• Describes the upper bound of an algorithms complexity
• Focuses on ignoring constant factors and lower order terms
• Describes how resources grow as inputs increase
• Examples:
  • $O(1)$ - Constant
  • $O(\log n)$ - Logarithmic
  • $O(n)$ - Linear
  • $O(n \log n)$ - "Linearithmic"
  • $O(n^2)$ - Quadratic
  • $O(2^n)$ - Exponential
  • $O(n!)$ - Factorial

Common Complexities

Practical Implications

• $O(n)$ scales better than $O(n^2)$
• Algorithm choice is more important as n grows
• An $O(n^2)$ algorithm might be faster for small n but slower for large n

Tips

• Know the complexities of common algorithms
• Be aware of hidden complexity
• Test with large datasets to confirm expected performance