Derivatives

Mathematical Foundations for Finance Students

By: Declan French

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eText | 4 June 2026 | Edition Number 1

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Derivatives: Mathematical Foundations for Finance Students is written for students of finance and actuarial science who want to understand derivatives not just as formulas but as ideas that make sense. The goal is to build the mathematical foundations up step by step - starting from the familiar territory of first-year undergraduate probability and statistics and moving all the way to stochastic calculus and the principles of risk-neutral pricing, which form the heart of modern financial mathematics.

This text will enable the reader to:

• understand models of asset price behavior and apply stochastic calculus
• use stochastic simulations in R to investigate processes and price options
• price options with the binomial model
• derive solutions to the Black-Scholes equation using risk-neutral pricing
• price interest-rate derivatives using Black's model, short-rate models and the Heath-Jarrow-Morton (HJM) framework
• tackle quantitative finance exam questions.

It incorporates a range of learning features to aid student understanding, including boxed examples, end-of-chapter summaries, selected questions from Society of Actuaries (US) Quantitative Finance examinations and further reading suggestions. The book is also supported by a suite of digital learning resources, including PowerPoint slides, multiple choice questions, instructor manual/advice document for lecturers and a test bank.

This book will appeal to both undergraduate and postgraduate students who wish to understand the principles of stochastic calculus and option pricing.