Quantitative Finance
Learn quantitative finance from pricing and portfolio construction through backtesting, execution, and production systems
The book spans 4 volumes. Read in order, or browse the contents to find the topic you need.
3,288 pages across 79 chapters
Browse contentsRead Quantitative Finance free online
Quantitative Finance connects mathematical finance with the work of researching, testing, and running trading strategies. We move from pricing and portfolio construction through calibration, backtesting, risk, execution, and production.
Explore the book’s 4 volumes
Quantitative Finance is organised into 4 volumes. Each volume covers a subject, divided into parts and chapters. Read from the beginning, or choose the volume you need.
79 published chapters · Free to read online
Volume 1Foundations and Financial Instruments4 parts · 24 chaptersBuy this volumeBuy PDF · $29
Part I
Mathematical Foundations
9 chapters01Time Value of Money and Interest RatesUnderstanding present and future value concepts, compounding, discounted cash flows, and the relationship between interest rates and valuation.52 min02Probability Theory FundamentalsBasics of probability, random variables, distributions, expected value, variance, conditional probability, and Bayes' Theorem in finance.59 min03Common Probability Distributions in FinanceKey distributions (normal, lognormal, binomial, Poisson, fat-tailed) and their applications in financial modeling and risk management.73 min04Statistical Data Analysis and InferenceDescriptive statistics, estimation concepts, Central Limit Theorem, hypothesis testing, and confidence intervals for financial data.48 min05Linear Algebra for Quantitative FinanceVectors, matrices, linear equations, and matrix decompositions with applications to portfolio analysis and factor models.57 min06Differential Calculus and Optimization BasicsDerivatives, marginal effects, multivariable calculus, constrained optimization, and convexity in portfolio optimization.76 min07Integral Calculus and Differential EquationsIntegrals, continuous compounding, differential equations, and foundations for continuous-time finance models.55 min08Numerical Methods and Algorithms in FinanceRoot-finding algorithms, interpolation techniques, and numerical integration for solving financial problems.63 min09Data Handling and VisualizationImporting and managing financial datasets, organizing time series data, and creating effective visualizations.41 min
Part II
Equity and Fixed Income Markets
4 chapters10Equity Markets and Stock InstrumentsStock ownership, market structure, trading mechanics, equity returns, and fundamental market concepts.55 min11Bond Fundamentals and PricingBond types, cash flows, pricing by discounting, yield to maturity, and day-count conventions.42 min12Term Structure of Interest RatesYield curves, zero rates, spot rates, forward rates, and bootstrapping techniques.47 min13Bond Risk Measures and ImmunizationDuration, convexity, interest rate risk measurement, and immunization strategies for bond portfolios.51 min
Part III
Forwards, Futures, and Options
6 chapters14Forwards and Futures - Instrument BasicsForward and futures contracts, contract specifications, margin requirements, and market mechanics.46 min15Forward and Futures Pricing and HedgingCost-of-carry pricing, arbitrage relationships, and basic hedging strategies using futures contracts.51 min16Commodity Markets and FuturesCommodity market structure, contango and backwardation, convenience yield, and hedging physical commodities.40 min17Foreign Exchange Markets and Currency ForwardsFX market structure, exchange rate quotes, interest rate parity, and currency forwards for hedging.48 min18Option Basics - Calls, Puts, and PayoffsCall and put options, payoff structures, moneyness, put-call parity, and fundamental option concepts.47 min19Option Strategies and Payoff CombinationsSpreads, straddles, strangles, covered calls, protective puts, and constructing complex payoff profiles.63 min
Part IV
Swaps and Credit Derivatives
5 chapters20Interest Rate Swaps - FundamentalsSwap structure, fixed-floating exchanges, notional principal, and applications in interest rate management.43 min21Interest Rate Swap Valuation and ApplicationsValuing swaps as bond portfolios, swap curves, and practical uses in hedging and synthetic asset creation.58 min22Credit Default Swaps (CDS) and Credit DerivativesCDS structure, credit risk protection, spread pricing, default probabilities, and recovery rates.46 min23Structured Credit Products (CDOs and Securitizations)Asset securitization, CDO structures, tranching, credit risk distribution, and valuation challenges.45 min24Convertible Bonds and Hybrid SecuritiesConvertible bonds as hybrid instruments, conversion features, valuation approaches, and other hybrid securities.51 min
Volume 2Derivative Pricing and Interest Rate Models3 parts · 16 chaptersBuy this volumeBuy PDF · $29
Part V
Stochastic Calculus and Pricing Theory
8 chapters25Stylized Facts of Financial ReturnsEmpirical features of returns: heavy tails, skewness, volatility clustering, and implications for modeling.45 min26Brownian Motion and Random Walk ModelsRandom walks, Brownian motion, Wiener processes, and Geometric Brownian Motion for stock prices.47 min27Itô's Lemma and Stochastic CalculusStochastic differential equations, Itô's Lemma, and changing variables in stochastic processes.44 min28No-Arbitrage Principle and Risk-Neutral ValuationFundamental theorem of asset pricing, risk-neutral probabilities, and arbitrage-free pricing frameworks.53 min29Derivation of the Black-Scholes-Merton PDEDeriving the Black-Scholes PDE through dynamic hedging, assumptions, and implications.45 min30Black-Scholes Formula and European Option PricingClosed-form solutions for European calls and puts, formula components, and basic Greeks introduction.58 min31The Greeks and Option Risk ManagementDelta, Gamma, Theta, Vega, Rho: measuring and managing option portfolio risk sensitivities.59 min32Implied Volatility and Volatility SmileComputing implied volatility, volatility surfaces, smile patterns, and market implications.54 min
Part VI
Numerical Methods for Derivative Pricing
5 chapters33Binomial Tree Option PricingDiscrete-time lattice models, backward induction, American options, and convergence to Black-Scholes.53 min34Monte Carlo Simulation for Derivative PricingSimulating price paths, valuing path-dependent options, Monte Carlo error, and convergence.43 min35Variance Reduction Techniques in SimulationAntithetic variates, control variates, stratified sampling for improving simulation efficiency.54 min36Finite Difference Methods for Option PricingExplicit, implicit, and Crank-Nicolson schemes for solving the Black-Scholes PDE numerically.51 min37Exotic Options and Complex DerivativesAsian options, barrier options, lookbacks, digitals, compound options, and their pricing approaches.63 min
Part VII
Interest Rate Models and Derivatives
3 chapters38Short-Rate Interest Rate ModelsVasicek, Cox-Ingersoll-Ross models: modeling rate evolution with mean reversion.54 min39Advanced Interest Rate Models (HJM and LMM)Heath-Jarrow-Morton framework, Libor Market Model, and calibration to market data.62 min40Valuation of Interest Rate DerivativesCaps, floors, swaptions, and pricing interest rate options using various models.55 min
Volume 3Econometrics, Portfolio Construction, and Risk3 parts · 18 chaptersBuy this volumeBuy PDF · $29
Part VIII
Econometrics and Statistical Modeling
5 chapters41Time-Series Models for Financial DataAR, MA, ARMA, ARIMA models for stationary and non-stationary financial time series.53 min42Modeling Volatility and GARCH FamilyARCH, GARCH models for time-varying volatility, volatility clustering, and forecasting.51 min43Regression Analysis for Financial RelationshipsOLS regression, factor exposures, hypothesis testing, and addressing time-series regression issues.49 min44Principal Component Analysis and Factor ExtractionDimension reduction, identifying principal components in yield curves and equity returns.47 min45Calibration and Parameter Estimation in ModelsFitting models to market data, optimization techniques, overfitting concerns, and model stability.72 min
Part IX
Portfolio Theory and Investment Analysis
6 chapters46Modern Portfolio Theory and Mean-Variance OptimizationMarkowitz framework, efficient frontier, diversification benefits, and portfolio optimization.54 min47Capital Market Theory - CAPM and the Efficient FrontierCAPM equilibrium, market portfolio, Security Market Line, beta, alpha, and model limitations.55 min48Arbitrage Pricing Theory and Multi-Factor ModelsAPT framework, multi-factor models, Fama-French factors, and factor risk premia.51 min49Portfolio Performance MeasurementSharpe ratio, information ratio, maximum drawdown, benchmarking, and risk-adjusted returns.50 min50Performance Attribution and Investment AlphaBrinson attribution, factor-based attribution, separating alpha from beta exposures.44 min51Advanced Portfolio Construction TechniquesBlack-Litterman model, robust optimization, risk parity, and practical constraints.54 min
Part X
Risk Management and Financial Risk Controls
7 chapters52Overview of Financial Risks and Regulatory FrameworksMarket, credit, liquidity, operational, model risk; regulatory standards and risk management objectives.59 min53Market Risk Measurement - VaR and BeyondValue-at-Risk calculation methods, Expected Shortfall, stress testing, and scenario analysis.48 min54Credit Risk FundamentalsProbability of Default, Loss Given Default, Exposure at Default, and expected loss calculations.52 min55Credit Risk Modeling ApproachesStructural models (Merton), reduced-form models, credit scoring, and portfolio credit risk.67 min56Counterparty Risk and CVACounterparty default risk, Credit Valuation Adjustment, exposure profiles, and CVA hedging.55 min57Liquidity Risk and Other Non-Market RisksMarket and funding liquidity risk, operational risk, model risk, and qualitative assessments.65 min58Risk Management Practices and PoliciesRisk limits, hedging strategies, CRO role, risk committees, and firm-wide risk culture.60 min
Volume 4Quant Trading, Execution, and Deployment5 parts · 21 chaptersBuy this volumeBuy PDF · $29
Part XI
Quantitative Trading Strategies
6 chapters59Overview of Quantitative Trading StrategiesAlpha generation concepts, strategy categories, development workflow, and backtesting importance.51 min60Mean Reversion and Statistical ArbitrageMean reversion concepts, pairs trading, statistical arbitrage portfolios, and regime risks.63 min61Trend Following and Momentum StrategiesTime-series and cross-sectional momentum, CTA strategies, behavioral sources, and reversal risks.43 min62Factor Investing and Long/Short EquityValue, growth, size, quality factors; constructing factor portfolios and long/short hedge funds.46 min63Volatility Trading and Arbitrage StrategiesTrading volatility as an asset class, delta-hedged strategies, dispersion trading, and vol risks.63 min64Event-Driven and Arbitrage StrategiesMerger arbitrage, earnings trading, fixed income arbitrage, and event-specific risk management.48 min
Part XII
Market Making and High-Frequency Trading
4 chapters65Market Making and Liquidity ProvisionAutomated market making, bid-ask spread capture, inventory risk, and adverse selection.56 min66High-Frequency Trading and Latency ArbitrageHFT strategies, cross-market arbitrage, technology infrastructure, and competitive dynamics.60 min67Market Microstructure: Order Books & Execution MechanicsOrder books, limit vs market orders, order priority, execution mechanics, and dark pools.54 min68Optimal Execution Algorithms: TWAP, VWAP & Market ImpactMaster execution algorithms from TWAP and VWAP to Almgren-Chriss optimal trading. Learn to balance market impact against timing risk for superior results.52 min
Part XIII
Machine Learning and Alternative Data
4 chapters69Machine Learning Techniques for TradingSupervised and unsupervised learning, feature engineering, model validation, and overfitting prevention.51 min70Machine Learning in Trading Strategy DesignML for signal generation, sentiment analysis, alternative data, reinforcement learning applications.62 min71Alternative Data and NLP in Quant StrategiesNon-traditional data sources, natural language processing, sentiment extraction, and compliance.56 min72Cryptocurrency Markets and Quant TradingCrypto market structure, unique characteristics, quantitative strategies in crypto, and specific risks.56 min
Part XIV
Strategy Development and Backtesting
4 chapters73Backtesting & Simulation: Frameworks for Strategy ValidationProper backtesting methodology, avoiding biases, performance metrics, and out-of-sample testing.48 min74Transaction Costs & Market Impact: Models & AnalysisCommission, spreads, slippage, market impact modeling, and incorporating costs in strategy design.56 min75Position Sizing & Leverage: Kelly Criterion StrategyMaster optimal position sizing using the Kelly Criterion, risk budgeting, and volatility targeting. Learn how leverage impacts drawdowns and long-term growth.48 min76Case Study - Building a Quantitative Strategy from ScratchEnd-to-end strategy development: from idea generation through backtesting to deployment readiness.51 min
Part XV
Trading Systems and Production Deployment
3 chapters77Quant Trading Systems: Architecture & InfrastructureExplore the architecture of quantitative trading systems. Learn to build robust data pipelines, strategy engines, risk controls, and execution infrastructure.65 min78Research Pipeline & Deployment: Strategy Lifecycle GuideBuild a robust quantitative research pipeline. From hypothesis formulation and backtesting to paper trading and live production deployment strategies.62 min79Ethical Quant Trading: Regulations & Market ManipulationMaster ethical quantitative trading by learning to detect spoofing, navigate Reg NMS and MiFID II, implement kill switches, and ensure data privacy compliance.61 min
More about the book
Master the complete quantitative toolkit: stochastic calculus and Itô's lemma, Black-Scholes and beyond, interest rate models, credit derivatives, and exotic options. But theory alone doesn't make money. Learn how to calibrate models to market data, understand when elegant mathematics meets messy reality, and develop the judgment to know which simplifications matter and which don't.
Portfolio construction is where alpha meets risk management. From Markowitz mean-variance optimization to Black-Litterman, from factor models to risk parity, understand the frameworks that institutional investors actually use. Then go further: transaction cost modeling, execution algorithms, market microstructure, and the infrastructure that turns a promising backtest into a profitable live strategy.
Whether you're preparing for quant interviews, transitioning from academia to industry, or building systematic trading strategies, this handbook provides the end-to-end coverage you need. Pricing, portfolios, execution, risk management, and deployment: the complete journey from mathematical theory to production trading system.
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Reader verdict
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12 five-star reader reviews
Genuine feedback, with names abbreviated for privacy.
Meet the community“I am enjoying reading your writings. I appreciate the effort you put into it. I want to drop a note of thanks. Thank you!”
“I would like to thank you for your work. Specifically, the chapter: 'LIME Explainability: Complete Guide to Local Interpretable Model-Agnostic Explanations' was extremely helpful for me in understanding LIME and communicating to colleagues. Your work is inspiring and valuable. Thank you for doing it.”
“I just came across your website where your books are available for free to read. Thank you so much for making this available to the public. This will help a lot of people.”
“I found your book Language AI Handbook's explanations of Transformer architectures and production deployment strategies to be exceptionally clear and insightful”
“Your writing feels like a treasure trove of great material. So, thank you for compiling everything on your website!”
“Really appreciate the way you have explained the concepts. Simple to understand, yet builds up knowledge exponentially, all while reinforcing it with examples repeatedly. I've read the last two chapters `74.Self-attention & 75.Q,K,V` and I've to admit, my concepts have never been clearer. You really are doing an amazing job breaking down maths and complex concepts like a story!”
“Thank you Michael. It's top!”
“I read a few of your blogs on NLP and oh WOW, they really are something, now I exactly know how all of the terms Entropy, Cross-entropy and how it is connected to Perplexity, will definitely read more of your blogs.”
“I came across your collection of online handbooks covering quantitative finance, AI, and machine learning. I wanted to reach out and thank you for making such high-quality material openly available. They are incredibly helpful for my CFA Level II review and for brushing up ahead of ML interviews.”
“Thanks so much for establishing such an amazing community. I appreciate the opportunity to be a learner and a contributor to the community.”
“Thanks for putting cool stuff out into the world.”
“I came across one of your books, Language AI Handbook, and man, I'm loving it. I've read many books but have never found such a comprehensive book on large models that covers everything from start to finish with such depth.”
Read all 12 reader reviews
“I would like to thank you for your work. Specifically, the chapter: 'LIME Explainability: Complete Guide to Local Interpretable Model-Agnostic Explanations' was extremely helpful for me in understanding LIME and communicating to colleagues. Your work is inspiring and valuable. Thank you for doing it.”
“Really appreciate the way you have explained the concepts. Simple to understand, yet builds up knowledge exponentially, all while reinforcing it with examples repeatedly. I've read the last two chapters `74.Self-attention & 75.Q,K,V` and I've to admit, my concepts have never been clearer. You really are doing an amazing job breaking down maths and complex concepts like a story!”
“Thanks so much for establishing such an amazing community. I appreciate the opportunity to be a learner and a contributor to the community.”
“I just came across your website where your books are available for free to read. Thank you so much for making this available to the public. This will help a lot of people.”
“I am enjoying reading your writings. I appreciate the effort you put into it. I want to drop a note of thanks. Thank you!”
“Thank you Michael. It's top!”
“Thanks for putting cool stuff out into the world.”
“I found your book Language AI Handbook's explanations of Transformer architectures and production deployment strategies to be exceptionally clear and insightful”
“Your writing feels like a treasure trove of great material. So, thank you for compiling everything on your website!”
“I came across your collection of online handbooks covering quantitative finance, AI, and machine learning. I wanted to reach out and thank you for making such high-quality material openly available. They are incredibly helpful for my CFA Level II review and for brushing up ahead of ML interviews.”
“I read a few of your blogs on NLP and oh WOW, they really are something, now I exactly know how all of the terms Entropy, Cross-entropy and how it is connected to Perplexity, will definitely read more of your blogs.”
“I came across one of your books, Language AI Handbook, and man, I'm loving it. I've read many books but have never found such a comprehensive book on large models that covers everything from start to finish with such depth.”
Author and edition details
About the author and this edition
Michael Brenndoerfer
Michael has spent more than a decade working across software engineering, data, AI, and business. He writes to understand difficult ideas more deeply and to share what he learns in a clear, practical way.
Important: This book is for education and research. It does not provide investment, trading, legal, tax, or other professional advice, and examples are not recommendations.
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Kept current, not frozen in time
Library access includes every future volume and update. When a volume changes, its updated PDF appears in My books at no extra cost.
Current release
Edition 2026.08.1
Editorial improvements.
Earlier releases2
2026.08.0
Editorial improvements throughout the book, with clearer explanations, refined presentation, improved plots and visualizations, and refreshed companion code.
2026.07.0
Initial complete-book and four-volume PDF release with companion notebooks.
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BIBTEXAcademic
@book{brenndoerfer2026quantitativefinancebook,
author = {Michael Brenndoerfer},
title = {Quantitative Finance},
year = {2026-01-25},
url = {https://mbrenndoerfer.com/books/quantitative-finance},
publisher = {mbrenndoerfer.com},
note = {Accessed: 2026-10-27}
}
APAAcademic
Michael Brenndoerfer (2026-01-25). Quantitative Finance. Retrieved from https://mbrenndoerfer.com/books/quantitative-finance
MLAAcademic
Michael Brenndoerfer. "Quantitative Finance." 2026. Web. October 27, 2026. <https://mbrenndoerfer.com/books/quantitative-finance>.
CHICAGOAcademic
Michael Brenndoerfer. "Quantitative Finance." Accessed October 27, 2026. https://mbrenndoerfer.com/books/quantitative-finance.
HARVARDAcademic
Michael Brenndoerfer (2026-01-25) 'Quantitative Finance'. Available at: https://mbrenndoerfer.com/books/quantitative-finance (Accessed: October 27, 2026).
SimpleBasic
Michael Brenndoerfer (2026-01-25). Quantitative Finance. https://mbrenndoerfer.com/books/quantitative-finance
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