These free financial mathematics books in PDF cover the math behind money, from compound interest to option pricing. You can read every mathematical finance book online or download it in one click.
Most of them are lecture notes from real university courses. They go from interest theory to the pricing models used in quantitative finance.
New to the subject? Start with interest theory, then move on to stochastic calculus and option pricing.
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Interest Theory
Financial Mathematics Books
These financial mathematics books start with the basics: simple and compound interest, annuities, loans and bonds. Marcel Finan's course and the Exam FM study notes make this the right place to prepare for actuarial exams.
A complete open textbook on simple and compound interest, annuities, loans, bonds and investment decisions. Every topic is solved twice, with the formula and with a financial calculator, plus hundreds of worked examples.
A full course in the theory of interest built for the actuarial Exam FM, from compound interest and annuities to loans, bonds and yield rates. The last part covers derivatives markets, with hundreds of solved problems.
Study notes for the actuarial Exam FM that walk through interest rates, annuities, loan amortization, bonds and yield curves. Each chapter pairs clear definitions with exercises and full solutions.
University lecture notes on the time value of money, interest rates, discount factors, annuities and loans. They cover much of the actuarial CT1 syllabus with worked examples and a first look at simple financial instruments.
A study guide to the quantitative analysis of financial deals: accumulation and discounting, yield of investment projects, risk-free securities and optimal portfolios of risky assets. Includes formulas, examples and practice tasks.
Course notes on effective and nominal interest rates, annuities, loan repayment and bonds, written for an actuarial science class. Each definition comes with a short solved example.
A compact unit on simple and compound interest, depreciation, present and future value and the main types of annuities. Short lessons with learning goals and solved examples make it a good first read.
A quick overview of interest theory for students preparing the actuarial Exam FM. It summarizes interest, annuities, loans and bonds in a few pages, ideal for a last review before the test.
Shows how geometric sequences and series explain loans, mortgages, savings and investments, with the amortisation formula derived step by step. Packed with exam-style questions and full solutions.
A school-level chapter on simple and compound interest, growth, decay and depreciation. Clear formulas and many practice exercises make it a gentle start before university material.
These mathematical finance notes show how to put a price on derivatives, from the binomial model to Black-Scholes. Each one walks through the math behind forwards, futures and options.
An open textbook that builds option pricing from the binomial model to Black-Scholes, then shows how to compute prices with numerical methods. Includes exercises and computational examples throughout.
Lecture notes on financial derivatives: forwards, futures and options, payoff functions, the binomial tree and the Black-Scholes model. A rigorous and complete course for math students.
Graduate lecture notes on interest rate calculations, bond portfolios, interest rate models, futures and options. They cover the binomial model, Black-Scholes, currency and interest rate options and volatility trading, with plenty of figures.
Lecture notes that introduce mathematical finance through the binomial model: portfolios, arbitrage, martingales and the pricing of contingent claims. They finish with the Black-Scholes formula as the limit of the discrete model.
A short, readable introduction to how quants price derivatives. It explains arbitrage, the binomial model and the ideas behind Black-Scholes without heavy machinery.
Master's level notes on no-arbitrage pricing in discrete time, including markets with transaction costs and other frictions. A concise path into the fundamental theorem of asset pricing.
A short paper on how integration theory supports the pricing of options and other derivatives since the work of Black, Scholes and Merton. Useful for readers curious about the math under the pricing formulas.
Stochastic processes drive modern financial models, and these books teach them from the ground up. You'll work through Brownian motion, martingales and Itô's formula.
A clear introduction to stochastic calculus by a leading probabilist, from discrete martingales and Brownian motion to Itô's formula and stochastic differential equations. Examples from finance appear throughout, with exercises in every chapter.
A course book that goes from option pricing basics to martingales, Brownian motion, Wiener and Itô integrals and Itô's formula. It ends by deriving and solving the Black-Scholes partial differential equation.
Graduate lecture notes on continuous-time finance: options and arbitrage, the Black-Scholes model, stochastic integration and pricing in complete markets. A solid bridge between probability theory and financial models.
Lecture notes on Brownian motion, local martingales, Itô integration, Itô's formula and stochastic differential equations. Rigorous and compact, with pointers to the standard references.
Covers the core of stochastic analysis, including Itô's formula, martingale representation and Girsanov's theorem, then moves to stochastic differential equations and the Feynman-Kac formula. The final part applies these tools to quantitative finance.
Quantitative finance turns formulas into working models, with code in Python, MATLAB, R and C++. These books cover portfolio theory, Monte Carlo methods and numerical pricing.
A comprehensive guide to portfolio design, from Markowitz mean-variance to risk parity, robust and drawdown portfolios, index tracking and pairs trading. It connects every formulation with practical numerical algorithms.
Learn Python for economic and financial modeling with NumPy, SciPy, pandas and Matplotlib. Written by Thomas Sargent and John Stachurski, with runnable code in every lecture.
A hands-on introduction to computational finance: Black-Scholes, Monte Carlo methods, the binomial model, discrete hedging and jump diffusion, explained with numerical experiments. Written for readers who want working methods, not only theory.
A collection of C++ algorithms for finance: present value, bonds and term structure, mean-variance portfolios, binomial trees, Black-Scholes and Monte Carlo pricing. Each method comes with the formula and working code.
Explains the mathematics behind portfolio analysis, from matrices and orthogonal projection to Markowitz efficient portfolios and the CAPM. Proofs and worked examples make each model easy to follow.
Lecture notes on Monte Carlo simulation, from random number generation to estimating probabilities and expected values, with R code. The last chapters price European, Asian and binary options by simulation.
A set of MATLAB programs for a first course in financial mathematics, covering probability, geometric Brownian motion, interest rates, the binomial model and Black-Scholes. Each section includes problems to run and modify.
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