Quantitative Finance, Volume Two: Derivative Pricing and Interest Rate Models cover

Volume 2 of 4 · PDF edition

Derivative Pricing and Interest Rate Models

Move from stochastic processes and no-arbitrage pricing to Black-Scholes, simulation, finite differences, exotic options, and interest rate models calibrated to market data.

Part of Quantitative Finance. The online chapters are free to read; the PDF edition is yours to keep, with future updates included.

Build the judgment to work confidently in quantitative finance.

Understand the assumptions behind a pricing model, the evidence behind a strategy, and the limits of a result. The book connects mathematical foundations to practical quantitative work so you can explain your choices and investigate what needs to change.

See what you’ll learn

What you will learn

  • Derive risk-neutral pricing results from Brownian motion, Itô's lemma, dynamic hedging, and the no-arbitrage principle.
  • Choose between trees, Monte Carlo simulation, and finite differences for different derivative-pricing problems.
  • Model rates and price caps, floors, swaptions, and other interest rate derivatives with practical calibration constraints in view.

Who this volume is for

  • Quantitative analysts, financial engineers, and advanced students who need to understand how derivative models are built, solved, calibrated, and used.

Prerequisites: Comfort with probability and calculus is helpful. Volume 1 develops that foundation, but experienced readers can start here.

Volume 2 PDF + code

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Keep the PDF and companion notebooks for offline reading, with future updates included. The corresponding chapters stay free online.

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Reader verdict

5.0

out of 5

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!”
Krishnan S.Researcher
“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.”
Will G.Data Scientist
“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.”
Vikas C.AI/ML Engineer
“I found your book Language AI Handbook's explanations of Transformer architectures and production deployment strategies to be exceptionally clear and insightful”
San Z.Researcher
“Your writing feels like a treasure trove of great material. So, thank you for compiling everything on your website!”
Griffin P.Quantitative Researcher
“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!”
Muhammad H.AI/ML Engineer
“Thank you Michael. It's top!”
David X.Data Scientist
“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.”
Kanishk K.Reader
“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.”
Karim Z.Reader
“Thanks so much for establishing such an amazing community. I appreciate the opportunity to be a learner and a contributor to the community.”
Cyrille L.AI/ML Engineer
“Thanks for putting cool stuff out into the world.”
Charlie B.Applied AI
“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.”
Uon L.Reader
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.”
Will G.Data Scientist
“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!”
Muhammad H.AI/ML Engineer
“Thanks so much for establishing such an amazing community. I appreciate the opportunity to be a learner and a contributor to the community.”
Cyrille L.AI/ML Engineer
“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.”
Vikas C.AI/ML Engineer
“I am enjoying reading your writings. I appreciate the effort you put into it. I want to drop a note of thanks. Thank you!”
Krishnan S.Researcher
“Thank you Michael. It's top!”
David X.Data Scientist
“Thanks for putting cool stuff out into the world.”
Charlie B.Applied AI
“I found your book Language AI Handbook's explanations of Transformer architectures and production deployment strategies to be exceptionally clear and insightful”
San Z.Researcher
“Your writing feels like a treasure trove of great material. So, thank you for compiling everything on your website!”
Griffin P.Quantitative Researcher
“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.”
Karim Z.Reader
“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.”
Kanishk K.Reader
“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.”
Uon L.Reader

Exact contents

16 chapters across 3 parts

Every linked chapter is free to read online.

Part V: Stochastic Calculus and Pricing Theory

  1. 01
    Stylized Facts of Financial Returns

    Empirical features of returns: heavy tails, skewness, volatility clustering, and implications for modeling.

  2. 02
    Brownian Motion and Random Walk Models

    Random walks, Brownian motion, Wiener processes, and Geometric Brownian Motion for stock prices.

  3. 03
    Itô's Lemma and Stochastic Calculus

    Stochastic differential equations, Itô's Lemma, and changing variables in stochastic processes.

  4. 04
    No-Arbitrage Principle and Risk-Neutral Valuation

    Fundamental theorem of asset pricing, risk-neutral probabilities, and arbitrage-free pricing frameworks.

  5. 05
    Derivation of the Black-Scholes-Merton PDE

    Deriving the Black-Scholes PDE through dynamic hedging, assumptions, and implications.

  6. 06
    Black-Scholes Formula and European Option Pricing

    Closed-form solutions for European calls and puts, formula components, and basic Greeks introduction.

  7. 07
    The Greeks and Option Risk Management

    Delta, Gamma, Theta, Vega, Rho: measuring and managing option portfolio risk sensitivities.

  8. 08
    Implied Volatility and Volatility Smile

    Computing implied volatility, volatility surfaces, smile patterns, and market implications.

Part VI: Numerical Methods for Derivative Pricing

  1. 01
    Binomial Tree Option Pricing

    Discrete-time lattice models, backward induction, American options, and convergence to Black-Scholes.

  2. 02
    Monte Carlo Simulation for Derivative Pricing

    Simulating price paths, valuing path-dependent options, Monte Carlo error, and convergence.

  3. 03
    Variance Reduction Techniques in Simulation

    Antithetic variates, control variates, stratified sampling for improving simulation efficiency.

  4. 04
    Finite Difference Methods for Option Pricing

    Explicit, implicit, and Crank-Nicolson schemes for solving the Black-Scholes PDE numerically.

  5. 05
    Exotic Options and Complex Derivatives

    Asian options, barrier options, lookbacks, digitals, compound options, and their pricing approaches.

Part VII: Interest Rate Models and Derivatives

  1. 01
    Short-Rate Interest Rate Models

    Vasicek, Cox-Ingersoll-Ross models: modeling rate evolution with mean reversion.

  2. 02
    Advanced Interest Rate Models (HJM and LMM)

    Heath-Jarrow-Morton framework, Libor Market Model, and calibration to market data.

  3. 03
    Valuation of Interest Rate Derivatives

    Caps, floors, swaptions, and pricing interest rate options using various models.

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Author and edition details

About the author and this edition

Michael Brenndoerfer, author of Quantitative Finance

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.

Edition
First edition
Published
Last reviewed

Version history

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
  1. 2026.08.0

    Editorial improvements throughout the book, with clearer explanations, refined presentation, improved plots and visualizations, and refreshed companion code.

  2. 2026.07.0

    Initial complete-book and four-volume PDF release with companion notebooks.