Derivatives Pricing
$79.99
USDThis is a masters-level overview of the mathematical concepts needed to fully grasp the art of derivatives pricing, and a must-have for anyone considering a career in quantitative finance in industry or academia. Starting from the foundations of probability, this textbook allows students with limited technical background to build a solid knowledge of the most important principles. It offers a unique compromise between intuition and mathematics, even when discussing abstract ideas such as change of measure. Mathematical concepts are introduced initially using toy examples, before moving on to examples of finance cases, both in discrete and continuous time. Throughout, numerical applications and simulations illuminate the analytical results. The end-of-chapter exercises test students' understanding, with solved exercises at the end of each part to aid self-study. Additional resources are available online, including slides, code and an interactive app.
- Introduces the foundations of derivatives pricing in a rigorous, intuitive, and complete manner with very few prerequisites
- Uses toy examples featuring coins and dice to introduce mathematical concepts, helping the reader first to get familiar with the concepts before applying them to pricing cases
- Covers numerical examples featuring trees and Monte Carlo simulations helping students to visualize how replication works not only 'on average', but on every trajectory
- An interactive app illustrating replication strategies associated with various models is available from: http://derivativespricing.uclouvain.be/home
Reviews & endorsements
‘Derivatives Pricing is the ideal introduction to the modeling of arbitrage-free derivatives prices. Vrins explains the subject from the bottom up, from foundations to applications, with a natural and accessible style that all readers will appreciate. This is a go-to reference!’ Darrell Duffie, Stanford University
‘This book strikes a valuable balance between mathematical rigor and financial intuition. It provides self-contained coverage of mathematical concepts, and it combines these theoretical tools with numerical illustrations and exercises that enhance the book's pedagogical value, particularly for readers new to quantitative finance.’ Paul Glasserman, Columbia Business School
‘The book covers key concepts in derivatives pricing and financial modeling, including essential mathematical background. The author's expertise as a quant, influential researcher and exceptional teacher makes this an ideal reference for master’s students in business, engineering or actuarial sciences aiming for a career in quantitative finance.’ Geneviève Gauthier, HEC Montréal
‘This book addresses the primary challenge of option pricing – mathematical complexity. Professor Vrins simplifies the equations while prioritizing economic intuition about asset pricing, all without sacrificing intellectual rigor.’ Roberto Renò, ESSEC Business School
‘Derivatives Pricing by Frédéric Vrins fills a gap between elementary textbooks on finance and advanced courses on the field. It will be a main reference for students, who will appreciate the numerous examples as well as the exercises with solutions. Many comments underline the difficulties and conduct the reader to clarify the results. The various pricing rules are well presented and the link between them described in detail. For all these reasons, this is a must-have.’ Monique Jeanblanc, L'Université d'Évry Val d'Essonne
Product details
June 2025Paperback
9781009554657
460 pages
253 × 203 mm
Not yet published - available from June 2025
Table of Contents
- Foreword
- General Introduction
- Part I. Probability Theory:
- 1. Probability space
- 2. Random variables and distributions
- 3. Moments and measure changes
- 4. Dealing with partial information
- 5. Sampling and Monte Carlo simulation
- 6. Solved exercises
- Part II. Pricing by Risk-Neutral Expectation:
- 7. Stochastic process and related concepts
- 8. The random walk
- 9. Derivative pricing using CRR
- 10. The Brownian motion
- 11. Derivative pricing using GBM
- 12. Solved exercises
- Part III. Pricing by Dynamic Replication:
- 13. Stochastic integrals
- 14. Stochastic differential equations
- 15. Itô calculus
- 16. The Black-Scholes-Merton equation
- 17. Solved exercises
- Part IV. Hedging and Beyond:
- 18. Replication and hedging
- 19. Fundamental theorems of asset pricing
- 20. Pricing via change of numéraire
- 21. Beyond Black-Scholes-Merton
- 22. Solved exercises
- Part V. Appendices: Appendix A. Short-selling in a nutshell
- Appendix B. Important functions of distributions
- Appendix C. Covergence of random variables
- Appendix D. Quadratic variation of smooth functions
- Appendix E. Connections between CRR and GBM
- Appendix F. Pricing Asian options via Monte Carlo
- Appendix G. Itô vs Stratanovich integrals
- Appendix H. Itô's lemma: sketch of proof
- Appendix I. Acronyms
- Bibliography
- Index.
