Introduction - Quantitative Finance with OCaml

Quantitative Finance with OCaml A comprehensive guide to building correct, performant, and maintainable financial systems using OCaml. About This Book Quantitative finance sits at the intersection of mathematics, statistics, and software engineering. Most practitioners reach for Python for its rapid prototyping or C++ for raw speed — but OCaml offers something rare: a language that is simultaneously expressive, correct by construction, and fast enough for production trading systems. This book teaches quantitative finance through the lens of OCaml. You will learn to price derivatives, manage risk, model credit, build trading algorithms, and design robust financial infrastructure — all while exploiting OCaml's type system to make whole classes of financial programming errors impossible at compile time. What makes this book different: Every concept is accompanied by production-quality OCaml code Mathematical derivations are presented honestly, not buried in appendices We build reusable, well-typed libraries that accumulate across chapters Performance and correctness are treated as equal concerns Coverage extends to modern OCaml 5 features (domains, effects, OxCaml extensions) How to Read This Book The book is organized into seven parts that can be read sequentially or used as a reference: PartChaptersTopics I1–4OCaml essentials, mathematics, probability II5–8Fixed income, bonds, yield curves, rates derivatives III9–14Equity markets, Black-Scholes, Monte Carlo, volatility IV15–17Credit risk, CDOs, multi-asset models V18–21Market risk, Greeks, XVA, portfolio optimization VI22–25Algorithmic trading, execution, HFT infrastructure VII26–31Advanced stochastic calculus, ML, regulatory, OxCaml Readers with OCaml experience may skim Chapters 1–2. Readers with finance experience may skim Chapters 5 and 9. Table of Contents Part I: Foundations Chapter 1 — Why OCaml for Quantitative Finance? Chapter 2 — OCaml Essentials for Finance Chapter 3 — Mathematical Foundations Chapter 4 — Probability and Statistics Part II: Fixed Income and Interest Rates Chapter 5 — Time Value of Money Chapter 6 — Bonds and Fixed Income Instruments Chapter 7 — The Yield Curve Chapter 8 — Interest Rate Derivatives Part III: Equity and Derivatives Chapter 9 — Equity Markets and Instruments Chapter 10 — The Black-Scholes Framework Chapter 11 — Numerical Methods for Option Pricing Chapter 12 — Monte Carlo Methods Chapter 13 — Volatility Chapter 14 — Exotic Options Part IV: Credit and Multi-Asset Chapter 15 — Credit Risk and Credit Derivatives Chapter 16 — Portfolio Credit Derivatives Chapter 17 — Multi-Asset Models and Correlation Part V: Risk Management Chapter 18 — Market Risk Chapter 19 — Greeks and Hedging Chapter 20 — Counterparty Credit Risk Chapter 21 — Portfolio Risk and Optimization Part VI: Algorithmic Trading and Market Microstructure Chapter 22 — Market Microstructure Chapter 23 — Execution Algorithms Chapter 24 — Quantitative Trading Strategies Chapter 25 — High-Performance Trading Infrastructure Part VII: Advanced Topics Chapter 26 — Stochastic Calculus and Advanced Pricing Chapter 27 — Machine Learning in Quantitative Finance Chapter 28 — Regulatory and Accounting Frameworks Chapter 29 — Systems Design for Quant Finance Chapter 30 — Capstone: A Complete Trading System Appendices Appendix A — OCaml Quick Reference for Finance Appendix B — Mathematical Reference Appendix C — Financial Glossary Appendix D — Further Reading and Resources Appendix E — Setting Up the Development Environment Appendix F — Correctness by Construction Companion Code Each chapter directory contains: chXX-topic/ ├── README.md ← chapter text ├── lib/ ← reusable library modules ├── examples/ ← worked examples ├── exercises/ ← practice problems └── benchmarks/ ← performance experiments Building the Examples # Install dependencies opam install core owl zarith menhir ppx_deriving # Build all examples cd quantitative-finance-with-ocaml dune build # Run tests dune test A Note on Notation Throughout this book: OCaml code is shown in syntax-highlighted blocks Mathematical formulas use standard notation: $S_t$ for asset price at time $t$, $\sigma$ for volatility, $r$ for risk-free rate Types are given in OCaml notation, e.g., float -> float -> float Module paths are written Module.function, e.g., Black_scholes.price Version 1.0 — February 2026. Corrections and contributions welcome via the project repository.