Derivatives Pricing

A masters-level introduction offering a unique compromise between intuition and the mathematics underlying derivatives pricing.

Frédéric D. Vrins (Author)

9781009554657, Cambridge University Press

Paperback / softback, published 20 March 2025

494 pages
24.5 x 16.8 x 2.6 cm, 0.85 kg

'This textbook is a master's-level exposition of mathematical concepts in financial derivatives pricing, useful for both industry and academia … [It] offers an interesting introduction to the field of financial derivatives and their valuation, enabling readers without prior exposure to mathematical finance or probability theory to develop a solid understanding of this area.' MathSciNet

This 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.

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.

Subject Areas: Applied mathematics [PBW]