Algorithmic Trading: Mathematical & Strategic Theories

Master mathematical models, backtesting frameworks, risk controls to design and deploy algorithmic trading strategies.

What you'll learn

Apply probability, time series analysis, and stochastic calculus to model asset price dynamics and forecast market behavior.

Design and implement mean reversion, trend following, pairs trading, and arbitrage strategies using statistical and machine learning methods.

Build event-driven backtesting frameworks, simulate execution costs, and evaluate strategy performance with Sharpe, Sortino, and drawdown metrics.

Implement risk management controls including position sizing, stop-loss, and value-at-risk to protect capital and optimize portfolio stability.

Requirements

Basic programming skills in Python, foundational knowledge of calculus, linear algebra, probability, and statistics, familiarity with trading concepts, and access to Python with numpy, pandas, and scikit-learn.

Description

Welcome to our comprehensive Algorithmic Trading course, where you will embark on a detailed journey through the mathematical and strategic underpinnings of automated trading systems. Over a series of modular chapters, you will explore essential quantitative techniques, understand the theoretical foundations of price dynamics, and master the design of robust trading strategies. From probability distributions and time series decomposition to stochastic calculus and machine learning, this course offers a rigorous exploration of the models that drive algorithmic approaches. You will also gain hands-on experience building event-driven backtesting frameworks, simulating realistic market conditions, and evaluating performance metrics such as Sharpe ratio, drawdown, and information ratio. By blending theory with practical examples, you will develop the competence to transform quantitative insights into live trading signals and maintain systems that adapt to evolving market regimes.In the Mathematical Foundations section, you will start with a comprehensive review of probability and statistics, covering expectations, variance, covariance, correlation, risk measures, inferential methods, and hypothesis testing. The time series analysis module will guide you through concepts of stationarity, autocorrelation functions, and decomposition techniques to uncover seasonal patterns and trends in financial data. You will then study stochastic processes such as random walks, Brownian motion, Poisson processes, and martingales to establish a probabilistic framework for asset price modeling. Finally, you will learn the basics of stochastic calculus, including Ito's lemma and stochastic differential equations, and apply optimization algorithms to calibrate model parameters and balance risk-return trade-offs in your trading portfolio.Strategy Design and Development delves into a variety of systematic trading approaches. You will explore mean reversion strategies based on Ornstein-Uhlenbeck processes, set up z-score entry and exit rules, and optimize parameters to capture volatility-driven opportunities. Trend following techniques will employ moving averages, momentum indicators, and breakout systems to ride persistent market moves. Advanced topics include pairs trading with cointegration tests, statistical arbitrage and risk arbitrage models, market making algorithms that manage inventory and execution risk, and factor-based alpha generation using multifactor regression models. You will also integrate machine learning tools such as decision trees, random forests, and neural networks to refine signals and implement walk-forward analysis that safeguards against overfitting.In the Implementation and Risk Management section, you will learn how to acquire and preprocess data from APIs and real-time feeds, clean and normalize historical price series, and handle corporate actions or missing values. You will design a robust event-driven backtesting framework that accounts for slippage, transaction costs, and realistic order execution. Execution algorithm modules will cover VWAP, TWAP, implementation shortfall, and iceberg orders, enabling you to mitigate market impact. Advanced risk controls will teach you position sizing techniques using the Kelly criterion, volatility parity, and value-at-risk measures, as well as stop-loss, take-profit, and drawdown limit rules. You will also build live monitoring dashboards, set up alerts for performance degradation, and explore infrastructure considerations for low-latency deployment and disaster recovery.By the end of this course, you will have the knowledge and practical skills to design, test, and deploy algorithmic trading strategies with a deep understanding of their mathematical basis and operational requirements. Whether you are a quantitative analyst, a software engineer, or a finance professional, you will be equipped to translate quantitative research into automated systems that operate in markets around the globe. You will also receive guidance on best practices for continuous learning, community engagement, and career pathways in the field of systematic trading. Take the next step in your quantitative journey and start building sophisticated, scalable trading strategies today. Enroll now and transform your analytical skills into actionable trading insights.

Overview

Section 1: Intro

Lecture 1 Hello and Welcome

Section 2: Mathematical Foundations

Lecture 2 Probability and Statistics Review

Lecture 3 Time Series Analysis Essentials

Lecture 4 Stochastic Processes and Models

Lecture 5 Stochastic Calculus Basics

Lecture 6 Optimization Techniques

Lecture 7 Machine Learning Foundations

Lecture 8 Performance Metrics and Evaluation

Lecture 9 Lesson 2.8 Statistical Testing and Overfitting

Section 3: Strategy Design and Development

Lecture 10 Mean Reversion Strategies

Lecture 11 Trend Following Strategies

Lecture 12 Pairs Trading and Cointegration

Lecture 13 Statistical and Risk Arbitrage

Lecture 14 Market-Making and Microstructure

Lecture 15 Factor Models and Alpha Generation

Lecture 16 Machine Learning in Strategy Development

Lecture 17 Strategy Optimization and Walk-Forward Analysis

Section 4: Implementation and Risk Management

Lecture 18 Data Acquisition and Preprocessing

Lecture 19 Backtesting Framework Architecture

Lecture 20 Execution Algorithms and Order Types

Lecture 21 Transaction Costs and Slippage Modeling

Lecture 22 Risk Management and Position Sizing

Lecture 23 Performance Monitoring and Real-Time Analytics

Lecture 24 Deployment and Infrastructure Considerations

This course is intended for quantitative analysts, traders, data scientists, and software developers who want to master the mathematical and strategic foundations of automated trading. Ideal for professionals and students with a programming and math background eager to design, backtest, and deploy systematic trading algorithms.