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Front Cover
Algorithmic Trading Methods
Algorithmic Trading Methods: Applications using Advanced Statistics, Optimization, and Machine Learning Techniques
Copyright
Contents
Preface
Acknowledgments
1 - Introduction
WHAT IS ELECTRONIC TRADING?
WHAT IS ALGORITHMIC TRADING?
TRADING ALGORITHM CLASSIFICATIONS
TRADING ALGORITHM STYLES
INVESTMENT CYCLE
INVESTMENT OBJECTIVE
INFORMATION CONTENT
INVESTMENT STYLES
INVESTMENT STRATEGIES
RESEARCH DATA
BROKER TRADING DESKS
RESEARCH FUNCTION
SALES FUNCTION
IMPLEMENTATION TYPES
ALGORITHMIC DECISION-MAKING PROCESS
2 - Algorithmic Trading
ADVANTAGES
DISADVANTAGES
GROWTH IN ALGORITHMIC TRADING
MARKET PARTICIPANTS
CLASSIFICATIONS OF ALGORITHMS
TYPES OF ALGORITHMS
ALGORITHMIC TRADING TRENDS
DAY OF WEEK EFFECT
INTRADAY TRADING PROFILES
TRADING VENUE CLASSIFICATION
Displayed Market
Dark Pool
Dark Pool Controversies
TYPES OF ORDERS
REVENUE PRICING MODELS
Order Priority
EXECUTION OPTIONS
ALGORITHMIC TRADING DECISIONS
Macro Level Strategies
Micro Level Decisions
Limit Order Models
Smart Order Routers
ALGORITHMIC ANALYSIS TOOLS
Pre-Trade Analysis
Intraday Analysis
Post-Trade Analysis
HIGH FREQUENCY TRADING
Auto Market Making
Quantitative Trading/Statistical Arbitrage
Rebate/Liquidity Trading
DIRECT MARKET ACCESS
3 - Transaction Costs
WHAT ARE TRANSACTION COSTS?
WHAT IS BEST EXECUTION?
WHAT IS THE GOAL OF IMPLEMENTATION?
UNBUNDLED TRANSACTION COST COMPONENTS
Commission
Fees
Taxes
Rebates
Spreads
Delay Cost
Price Appreciation
Market Impact
Timing Risk
Opportunity Cost
TRANSACTION COST CLASSIFICATION
TRANSACTION COST CATEGORIZATION
TRANSACTION COST ANALYSIS
Measuring/Forecasting
Cost vs. Profit and Loss.
IMPLEMENTATION SHORTFALL
Complete Execution
Opportunity Cost (Andre Perold)
Expanded Implementation Shortfall (Wayne Wagner)
IMPLEMENTATION SHORTFALL FORMULATION
Trading Cost/Arrival Cost
EVALUATING PERFORMANCE
Trading Price Performance
Benchmark Price Performance
VWAP Benchmark
Participation-Weighted Price Benchmark
Relative Performance Measure
Pretrade Benchmark
Index-Adjusted Performance Metric
Z-Score Evaluation Metric
Market Cost-Adjusted Z-Score
Adaptation Tactic
COMPARING ALGORITHMS
Nonparametric Tests
Paired Samples
Sign Test
Wilcoxon Signed Rank Test
INDEPENDENT SAMPLES
Mann-Whitney U Test
MEDIAN TEST
DISTRIBUTION ANALYSIS
CHI-SQUARE GOODNESS OF FIT
KOLMOGOROV-SMIRNOV GOODNESS OF FIT
EXPERIMENTAL DESIGN
Proper Statistical Tests
Small Sample Size
Data Ties
Proper Categorization
Balanced Data Sets
FINAL NOTE ON POSTTRADE ANALYSIS
4 - Market Impact Models
INTRODUCTION
DEFINITION
Example 1: Temporary Market Impact
Example 2: Permanent Market Impact
Graphical Illustrations of Market Impact
Illustration #1: Price Trajectory
Illustration #2: Supply-Demand Equilibrium
After Shares Transact, We Face Some Uncertainty-What Happens Next?
Illustration #3: Temporary Impact Decay Function
Example #3: Temporary Decay Formulation
Illustration #4: Various Market Impact Price Trajectories
Developing a Market Impact Model
Essential Properties of a Market Impact Model
The Shape of the Market Impact Function
Example: Convex Shape
Example: Linear Shape
Example: Concave Shape
DERIVATION OF MODELS
Almgren and Chriss Market Impact Model
Random Walk With Price Drift-Discrete Time Periods
Random Walk With Market Impact (No Price Drift)
I-STAR MARKET IMPACT MODEL
MODEL FORMULATION.
I-Star: Instantaneous Impact Equation
The Market Impact Equation
Derivation of the Model
Cost Allocation Method
I∗ Formulation
Comparison of Approaches
5 - Probability and Statistics
INTRODUCTION
RANDOM VARIABLES
PROBABILITY DISTRIBUTIONS
Example: Discrete Probability Distribution Function
Example: Continuous Probability Distribution Function
Descriptive Statistics
PROBABILITY DISTRIBUTION FUNCTIONS
CONTINUOUS DISTRIBUTION FUNCTIONS
Normal Distribution
Standard Normal Distribution
Student's t-Distribution
Log-Normal Distribution
Uniform Distribution
Exponential Distribution
Chi-Square Distribution
Logistic Distribution
Triangular Distribution
DISCRETE DISTRIBUTIONS
Binomial Distribution
Poisson Distribution
END NOTES
6 - Linear Regression Models
INTRODUCTION
Linear Regression Requirements
Regression Metrics
LINEAR REGRESSION
True Linear Regression Model
Simple Linear Regression Model
Solving the Simple Linear Regression Model
Step 1: Estimate Model Parameters
Step 2: Evaluate Model Performance Statistics
Standard Error of the Regression Model
R2 Goodness of Fit
Step 3: Test for Statistical Significance of Factors
T-test: Hypothesis Test:
F-test: Hypothesis Test:
Example: Simple Linear Regression
Multiple Linear Regression Model
Solving the Multiple Linear Regression Model
Step 1: Estimate Model Parameters
Step 2: Calculate Model Performance Statistics
Standard Error of the Regression Model
R2 Goodness of Fit
Step 3: Test for Statistical Significance of Factors
T-test: Hypothesis Test:
F-test: Hypothesis Test:
Example: Multiple Linear Regression
MATRIX TECHNIQUES
Estimate Parameters
Compute Standard Errors of b
R2 Statistic
F-Statistic
LOG REGRESSION MODEL.
Example: Log-Transformation
Example: Log-Linear Transformation
POLYNOMIAL REGRESSION MODEL
FRACTIONAL REGRESSION MODEL
7 - Probability Models
INTRODUCTION
DEVELOPING A PROBABILITY MODEL
Comparison of Linear Regression Model to Probability Model
Power Function Model
Logit Model
Probit Model
Comparison of Logit and Probit Models
Outcome Data
Model Formulation
Mean
Variance
Grouping Data
Solving Binary Output Models
Step 1: Specify Probability Function
Step 2: Set Up a Likelihood Function Based on Actual Outcome Results for all Observations. For Example, If We Have n Observ ...
SOLVING PROBABILITY OUTPUT MODELS
EXAMPLES
Example 7.1 Power Function
Example 7.2 Logit Model
COMPARISON OF POWER FUNCTION TO LOGIT MODEL
Example 7.3 Logistic Regression
CONCLUSIONS
8 - Nonlinear Regression Models
INTRODUCTION
REGRESSION MODELS
Linear Regression Model
Polynomial Regression Model
Fractional Regression Model
Log-linear Regression Model
Logistic Regression Model
Nonlinear Model
NONLINEAR FORMULATION
SOLVING NONLINEAR REGRESSION MODEL
ESTIMATING PARAMETERS
Maximum Likelihood Estimation (MLE)
Step I: Define the Model
Step II: Define the Likelihood Function
Step III: Maximize the Log-Likelihood Function
NONLINEAR LEAST SQUARES (NON-OLS)
Step I: Define the Model
Step II: Define the Error Term
Step III: Define a Loss Function-Sum of Square Errors
Step IV: Minimize the Sum of Square Error
HYPOTHESIS TESTING
EVALUATE MODEL PERFORMANCE
SAMPLING TECHNIQUES
RANDOM SAMPLING
SAMPLING WITH REPLACEMENT
SAMPLING WITHOUT REPLACEMENT
MONTE CARLO SIMULATION
BOOTSTRAPPING TECHNIQUES
JACKKNIFE SAMPLING TECHNIQUES
Important Notes on Sampling in Nonlinear Regression Models
9 - Machine Learning Techniques.
INTRODUCTION
TYPES OF MACHINE LEARNING
EXAMPLES
Cluster Analysis
CLASSIFICATION
REGRESSION
NEURAL NETWORKS
10 - Estimating I-Star Market Impact Model Parameters
INTRODUCTION
I-STAR MARKET IMPACT MODEL
SCIENTIFIC METHOD
Step 1: Ask a Question
Step 2: Research the Problem
Step 3: Construct a Hypothesis
Step 4: Test the Hypothesis
Step 6: Conclusions Communicate
Solution Technique
The Question
Research the Problem
Construct a Hypothesis
Test the Hypothesis
Underlying Data Set
Data Definitions
Imbalance/Order Size
Average daily volume
Actual market volume
Stock volatility
POV Rate
Arrival Cost
Imbalance Size Issues
Model Verification
Model Verification #1: Graphical Illustration
Model Verification #2: Regression Analysis
Model Verification #3: z-Score Analysis
Model Verification #4: Error Analysis
Stock Universe
Analysis Period
Time Period
Number of Data Points
Imbalance
Side
Volume
Turnover
VWAP
First Price
Average Daily Volume
Annualized Volatility
Size
POV Rate
Cost
Estimating Model Parameters
Sensitivity Analysis
Cost Curves
Statistical Analysis
Error Analysis
Stock-Specific Error Analysis
11 - Risk, Volatility, and Factor Models
INTRODUCTION
VOLATILITY MEASURES
Log-Returns
Average Return
Variance
Volatility
Covariance
Correlation
Dispersion
Value-at-Risk
IMPLIED VOLATILITY
Beta
Range
FORECASTING STOCK VOLATILITY
Volatility Models
Returns
Historical Moving Average (HMA)
Exponential Weighted Moving Average (EWMA)
ARCH Volatility Model
GARCH Volatility Model
HMA-VIX Adjustment Model
Determining Parameters via Maximum Likelihood Estimation
Likelihood Function
Measuring Model Performance.
Root Mean Square Error (RMSE).
Algorithmic Trading Methods
Algorithmic Trading Methods: Applications using Advanced Statistics, Optimization, and Machine Learning Techniques
Copyright
Contents
Preface
Acknowledgments
1 - Introduction
WHAT IS ELECTRONIC TRADING?
WHAT IS ALGORITHMIC TRADING?
TRADING ALGORITHM CLASSIFICATIONS
TRADING ALGORITHM STYLES
INVESTMENT CYCLE
INVESTMENT OBJECTIVE
INFORMATION CONTENT
INVESTMENT STYLES
INVESTMENT STRATEGIES
RESEARCH DATA
BROKER TRADING DESKS
RESEARCH FUNCTION
SALES FUNCTION
IMPLEMENTATION TYPES
ALGORITHMIC DECISION-MAKING PROCESS
2 - Algorithmic Trading
ADVANTAGES
DISADVANTAGES
GROWTH IN ALGORITHMIC TRADING
MARKET PARTICIPANTS
CLASSIFICATIONS OF ALGORITHMS
TYPES OF ALGORITHMS
ALGORITHMIC TRADING TRENDS
DAY OF WEEK EFFECT
INTRADAY TRADING PROFILES
TRADING VENUE CLASSIFICATION
Displayed Market
Dark Pool
Dark Pool Controversies
TYPES OF ORDERS
REVENUE PRICING MODELS
Order Priority
EXECUTION OPTIONS
ALGORITHMIC TRADING DECISIONS
Macro Level Strategies
Micro Level Decisions
Limit Order Models
Smart Order Routers
ALGORITHMIC ANALYSIS TOOLS
Pre-Trade Analysis
Intraday Analysis
Post-Trade Analysis
HIGH FREQUENCY TRADING
Auto Market Making
Quantitative Trading/Statistical Arbitrage
Rebate/Liquidity Trading
DIRECT MARKET ACCESS
3 - Transaction Costs
WHAT ARE TRANSACTION COSTS?
WHAT IS BEST EXECUTION?
WHAT IS THE GOAL OF IMPLEMENTATION?
UNBUNDLED TRANSACTION COST COMPONENTS
Commission
Fees
Taxes
Rebates
Spreads
Delay Cost
Price Appreciation
Market Impact
Timing Risk
Opportunity Cost
TRANSACTION COST CLASSIFICATION
TRANSACTION COST CATEGORIZATION
TRANSACTION COST ANALYSIS
Measuring/Forecasting
Cost vs. Profit and Loss.
IMPLEMENTATION SHORTFALL
Complete Execution
Opportunity Cost (Andre Perold)
Expanded Implementation Shortfall (Wayne Wagner)
IMPLEMENTATION SHORTFALL FORMULATION
Trading Cost/Arrival Cost
EVALUATING PERFORMANCE
Trading Price Performance
Benchmark Price Performance
VWAP Benchmark
Participation-Weighted Price Benchmark
Relative Performance Measure
Pretrade Benchmark
Index-Adjusted Performance Metric
Z-Score Evaluation Metric
Market Cost-Adjusted Z-Score
Adaptation Tactic
COMPARING ALGORITHMS
Nonparametric Tests
Paired Samples
Sign Test
Wilcoxon Signed Rank Test
INDEPENDENT SAMPLES
Mann-Whitney U Test
MEDIAN TEST
DISTRIBUTION ANALYSIS
CHI-SQUARE GOODNESS OF FIT
KOLMOGOROV-SMIRNOV GOODNESS OF FIT
EXPERIMENTAL DESIGN
Proper Statistical Tests
Small Sample Size
Data Ties
Proper Categorization
Balanced Data Sets
FINAL NOTE ON POSTTRADE ANALYSIS
4 - Market Impact Models
INTRODUCTION
DEFINITION
Example 1: Temporary Market Impact
Example 2: Permanent Market Impact
Graphical Illustrations of Market Impact
Illustration #1: Price Trajectory
Illustration #2: Supply-Demand Equilibrium
After Shares Transact, We Face Some Uncertainty-What Happens Next?
Illustration #3: Temporary Impact Decay Function
Example #3: Temporary Decay Formulation
Illustration #4: Various Market Impact Price Trajectories
Developing a Market Impact Model
Essential Properties of a Market Impact Model
The Shape of the Market Impact Function
Example: Convex Shape
Example: Linear Shape
Example: Concave Shape
DERIVATION OF MODELS
Almgren and Chriss Market Impact Model
Random Walk With Price Drift-Discrete Time Periods
Random Walk With Market Impact (No Price Drift)
I-STAR MARKET IMPACT MODEL
MODEL FORMULATION.
I-Star: Instantaneous Impact Equation
The Market Impact Equation
Derivation of the Model
Cost Allocation Method
I∗ Formulation
Comparison of Approaches
5 - Probability and Statistics
INTRODUCTION
RANDOM VARIABLES
PROBABILITY DISTRIBUTIONS
Example: Discrete Probability Distribution Function
Example: Continuous Probability Distribution Function
Descriptive Statistics
PROBABILITY DISTRIBUTION FUNCTIONS
CONTINUOUS DISTRIBUTION FUNCTIONS
Normal Distribution
Standard Normal Distribution
Student's t-Distribution
Log-Normal Distribution
Uniform Distribution
Exponential Distribution
Chi-Square Distribution
Logistic Distribution
Triangular Distribution
DISCRETE DISTRIBUTIONS
Binomial Distribution
Poisson Distribution
END NOTES
6 - Linear Regression Models
INTRODUCTION
Linear Regression Requirements
Regression Metrics
LINEAR REGRESSION
True Linear Regression Model
Simple Linear Regression Model
Solving the Simple Linear Regression Model
Step 1: Estimate Model Parameters
Step 2: Evaluate Model Performance Statistics
Standard Error of the Regression Model
R2 Goodness of Fit
Step 3: Test for Statistical Significance of Factors
T-test: Hypothesis Test:
F-test: Hypothesis Test:
Example: Simple Linear Regression
Multiple Linear Regression Model
Solving the Multiple Linear Regression Model
Step 1: Estimate Model Parameters
Step 2: Calculate Model Performance Statistics
Standard Error of the Regression Model
R2 Goodness of Fit
Step 3: Test for Statistical Significance of Factors
T-test: Hypothesis Test:
F-test: Hypothesis Test:
Example: Multiple Linear Regression
MATRIX TECHNIQUES
Estimate Parameters
Compute Standard Errors of b
R2 Statistic
F-Statistic
LOG REGRESSION MODEL.
Example: Log-Transformation
Example: Log-Linear Transformation
POLYNOMIAL REGRESSION MODEL
FRACTIONAL REGRESSION MODEL
7 - Probability Models
INTRODUCTION
DEVELOPING A PROBABILITY MODEL
Comparison of Linear Regression Model to Probability Model
Power Function Model
Logit Model
Probit Model
Comparison of Logit and Probit Models
Outcome Data
Model Formulation
Mean
Variance
Grouping Data
Solving Binary Output Models
Step 1: Specify Probability Function
Step 2: Set Up a Likelihood Function Based on Actual Outcome Results for all Observations. For Example, If We Have n Observ ...
SOLVING PROBABILITY OUTPUT MODELS
EXAMPLES
Example 7.1 Power Function
Example 7.2 Logit Model
COMPARISON OF POWER FUNCTION TO LOGIT MODEL
Example 7.3 Logistic Regression
CONCLUSIONS
8 - Nonlinear Regression Models
INTRODUCTION
REGRESSION MODELS
Linear Regression Model
Polynomial Regression Model
Fractional Regression Model
Log-linear Regression Model
Logistic Regression Model
Nonlinear Model
NONLINEAR FORMULATION
SOLVING NONLINEAR REGRESSION MODEL
ESTIMATING PARAMETERS
Maximum Likelihood Estimation (MLE)
Step I: Define the Model
Step II: Define the Likelihood Function
Step III: Maximize the Log-Likelihood Function
NONLINEAR LEAST SQUARES (NON-OLS)
Step I: Define the Model
Step II: Define the Error Term
Step III: Define a Loss Function-Sum of Square Errors
Step IV: Minimize the Sum of Square Error
HYPOTHESIS TESTING
EVALUATE MODEL PERFORMANCE
SAMPLING TECHNIQUES
RANDOM SAMPLING
SAMPLING WITH REPLACEMENT
SAMPLING WITHOUT REPLACEMENT
MONTE CARLO SIMULATION
BOOTSTRAPPING TECHNIQUES
JACKKNIFE SAMPLING TECHNIQUES
Important Notes on Sampling in Nonlinear Regression Models
9 - Machine Learning Techniques.
INTRODUCTION
TYPES OF MACHINE LEARNING
EXAMPLES
Cluster Analysis
CLASSIFICATION
REGRESSION
NEURAL NETWORKS
10 - Estimating I-Star Market Impact Model Parameters
INTRODUCTION
I-STAR MARKET IMPACT MODEL
SCIENTIFIC METHOD
Step 1: Ask a Question
Step 2: Research the Problem
Step 3: Construct a Hypothesis
Step 4: Test the Hypothesis
Step 6: Conclusions Communicate
Solution Technique
The Question
Research the Problem
Construct a Hypothesis
Test the Hypothesis
Underlying Data Set
Data Definitions
Imbalance/Order Size
Average daily volume
Actual market volume
Stock volatility
POV Rate
Arrival Cost
Imbalance Size Issues
Model Verification
Model Verification #1: Graphical Illustration
Model Verification #2: Regression Analysis
Model Verification #3: z-Score Analysis
Model Verification #4: Error Analysis
Stock Universe
Analysis Period
Time Period
Number of Data Points
Imbalance
Side
Volume
Turnover
VWAP
First Price
Average Daily Volume
Annualized Volatility
Size
POV Rate
Cost
Estimating Model Parameters
Sensitivity Analysis
Cost Curves
Statistical Analysis
Error Analysis
Stock-Specific Error Analysis
11 - Risk, Volatility, and Factor Models
INTRODUCTION
VOLATILITY MEASURES
Log-Returns
Average Return
Variance
Volatility
Covariance
Correlation
Dispersion
Value-at-Risk
IMPLIED VOLATILITY
Beta
Range
FORECASTING STOCK VOLATILITY
Volatility Models
Returns
Historical Moving Average (HMA)
Exponential Weighted Moving Average (EWMA)
ARCH Volatility Model
GARCH Volatility Model
HMA-VIX Adjustment Model
Determining Parameters via Maximum Likelihood Estimation
Likelihood Function
Measuring Model Performance.
Root Mean Square Error (RMSE).