01 / Reading Guide
Reading Guide
Who this book is for
For graduate students in financial economics, applied mathematics or financial engineering seeking a rigorous route into derivatives. Privault builds models progressively while relating analytical and probabilistic methods. The free text has substantial worked problems and solutions, but learning requires checking assumptions and deriving results rather than simply running pricing code.
Prerequisites
Calculus, linear algebra and calculus-based probability are essential; differential equations and basic programming are helpful. Review conditional expectation and stochastic processes. The probability appendix is a reference, not a substitute for all prerequisite preparation.
What it covers
Twenty-two chapters progress from assets, portfolios and arbitrage through discrete-time pricing, Brownian motion, Black–Scholes and martingale methods. Later chapters treat volatility, barrier, lookback, Asian and American options, numéraire changes, interest-rate derivatives, jumps and basic numerical methods. A probability appendix, complete exercise solutions, references and index are provided with the chapters. No-arbitrage valuation is distinguished from forecasting market prices or promising profitable trades.
How to use it
Begin with a two-state example and derive the self-financing hedge and no-arbitrage price before moving to continuous time. State the information structure and distinguish physical from pricing probabilities. Re-derive one price by both PDE and martingale methods, checking where their assumptions agree. For an exotic option, draw the payoff and identify the required path information. Attempt exercises before opening the solutions, then diagnose the precise failed step. Use code to investigate a limiting case or numerical error after understanding the mathematical argument.
Edition and sources
The selected author-hosted text is explicitly dated May 2, 2026. Its 22 chapters and supporting sections are all freely supplied on the NTU teaching page. It is the expanded online notes, not a claim to be the 662-page 2022 printed second edition, and no print ISBN is assigned. Author-provided free reading does not establish a blanket Creative Commons redistribution or adaptation licence. Official complete reading route.
