How to Learn Algorithmic Trading: Part 2

Excellent readership and thoughtful comments on the original How to Learn Algorithmic Trading have motivated two follow-up posts on learning quantitative / algorithmic trading (while retrospectively revising the original to improve consistency). This Part focuses on the cross-discipline foundations of financial mathematics, whose knowledge is generally assumed by practitioners and financial modeling literature. The subsequent, Part 3, focuses on modern financial modeling and analysis.

Depending on reader interest, this topic may warrant a future series of posts to delve into seminal literature in selected trading disciplines, such as suggested by etrading on the Penn-Lehman Automated Trading Project.

Thanks to awwthor, quant.this, Josh Ulrich, Gappy, and Bjørn for their comments and recommendations. As with the original post, the following is intended to inform retail quantitative trading with a bias to equity, exchange-traded derivatives, and FX.

To begin, start with solid theoretical econometrics, with emphasis on time series, and meet regression (assuming solid background in linear and matrix algebra):

• Time Series Analysis, by Hamilton: classic text on time series econometrics
• Econometric Analysis, by Greene: classic text on theoretical econometrics

Next, dive into filtering and wavelets and meet Fourier:

• Wavelet Methods for Time Series Analysis, by Percival and Walden: standard theoretical text on wavelets
• A Wavelet Tour of Signal Processing: The Sparse Way (3rd Ed), by Mallat and Peyré: applied filtering and wavelets for finance and economics

Explore modern statistical / machine learning and meet reinforcement and (un)supervision, descendant of original Turing / von Neumann “AI” tradition:

• Artificial Intelligence: A Modern Approach, by Russell and Norvig: standard introduction to classic AI
• The Elements of Statistical Learning, by Hastie, Tibshirani, and Friedman: standard intermediate statistical learning
• Pattern Recognition and Machine Learning, by Bishop: intermediate classification and learning
• Pattern Classification, by Duda: standard introductory classification

Review operations research and meet duality, with focus on mathematical optimization (not to be confused with computer science “programming”); thanks to Gappy, since my references pre-date many of these:

• Linear and Nonlinear Programming, by Luenberger: standard introduction to optimization
• Nonlinear Programming, by Bazaraa et al.: standard non-linear optimization
• Convex Optimization, by Boyd and Vandenberghe: standard convex optimization (generalization of linear methods, including LP, OLS, etc.), including approximation, fitting, and estimation

Finally, for those interested in options and vol, review modern stochastic calculus and meet Itō (presuming working knowledge of measure theory and stochastic processes):

• Financial Calculus, by Baxter and Rennie: pleasant intuitive introduction
• Stochastic Calculus for Finance I, by Shreve: gentle introduction via binomial
• Stochastic Calculus for Finance II, by Shreve: gentle continuous-time introduction

Continue on to Part 3 to dive into modern financial modeling and analysis.