Description

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.

Table of Contents

Part I: Background 

1. Calculus background 

2. Statistical background 

3. Introduction to derivative securities 

Part II: Stochastic Calculus 

4. Standard Brownian motion 

5. Itô formula 

6. Stochastic integrals 

Part III: Pricing Derivatives 

7. Geometric Brownian Motion 

8. The binomial model 

9. Black-Scholes equation 

10. Option pricing in continuous time 

11. Option Greeks 

Part IV: Interest Rate Derivatives 

12. Fixed-income instruments 

13. Black’s model 

14. Short-rate models 

15. Heath–Jarrow–Morton model.

Critics' Reviews

“Declan French has produced an exceptional text, combining rigour and practical relevance. Using examples and simulations, the book moves with remarkable accessibility from core calculus and probability to stochastic calculus, Itô’s formula, and risk-neutral pricing. French’s ability to connect theory with real-world applications makes this an invaluable resource for finance and actuarial students.”

John O.S. Wilson, Professor, University of St Andrews, UK

“This excellent textbook makes quantitative finance simple and intuitive. Its mathematical content is succinct, engaging, and focused on key concepts, making it ideal for new undergraduates studying option pricing or derivatives modules who want a solid grounding in mathematics, statistics, and probability to support their understanding.”

Danny McGowan, Professor of Business, Durham University, UK