
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 learnWhat 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.
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“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.”
Exact contents
16 chapters across 3 parts
Every linked chapter is free to read online.
Part V: Stochastic Calculus and Pricing Theory
- 01Stylized Facts of Financial Returns
Empirical features of returns: heavy tails, skewness, volatility clustering, and implications for modeling.
- 02Brownian Motion and Random Walk Models
Random walks, Brownian motion, Wiener processes, and Geometric Brownian Motion for stock prices.
- 03Itô's Lemma and Stochastic Calculus
Stochastic differential equations, Itô's Lemma, and changing variables in stochastic processes.
- 04No-Arbitrage Principle and Risk-Neutral Valuation
Fundamental theorem of asset pricing, risk-neutral probabilities, and arbitrage-free pricing frameworks.
- 05Derivation of the Black-Scholes-Merton PDE
Deriving the Black-Scholes PDE through dynamic hedging, assumptions, and implications.
- 06Black-Scholes Formula and European Option Pricing
Closed-form solutions for European calls and puts, formula components, and basic Greeks introduction.
- 07The Greeks and Option Risk Management
Delta, Gamma, Theta, Vega, Rho: measuring and managing option portfolio risk sensitivities.
- 08Implied Volatility and Volatility Smile
Computing implied volatility, volatility surfaces, smile patterns, and market implications.
Part VI: Numerical Methods for Derivative Pricing
- 01Binomial Tree Option Pricing
Discrete-time lattice models, backward induction, American options, and convergence to Black-Scholes.
- 02Monte Carlo Simulation for Derivative Pricing
Simulating price paths, valuing path-dependent options, Monte Carlo error, and convergence.
- 03Variance Reduction Techniques in Simulation
Antithetic variates, control variates, stratified sampling for improving simulation efficiency.
- 04Finite Difference Methods for Option Pricing
Explicit, implicit, and Crank-Nicolson schemes for solving the Black-Scholes PDE numerically.
- 05Exotic Options and Complex Derivatives
Asian options, barrier options, lookbacks, digitals, compound options, and their pricing approaches.
Part VII: Interest Rate Models and Derivatives
- 01Short-Rate Interest Rate Models
Vasicek, Cox-Ingersoll-Ross models: modeling rate evolution with mean reversion.
- 02Advanced Interest Rate Models (HJM and LMM)
Heath-Jarrow-Morton framework, Libor Market Model, and calibration to market data.
- 03Valuation 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
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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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
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.