Asset Pricing and Derivatives

Reading order

1. Fundamentals of Futures and Options Markets

   John C. Hull Beginner

   An introductory textbook on derivatives that explains how futures, forwards, swaps and options work, how they are priced and how they are used for hedging and speculation. It treats much of the ground of Hull's longer text in simpler language and without calculus, using numerical examples and market practice throughout.

   Prerequisites: An introductory finance course and comfort with algebra, logarithms and basic probability are helpful; calculus is not required.

2. Options, Futures, and Other Derivatives

   John C. Hull Intermediate

   A standard textbook on derivative securities that explains how forwards, futures, swaps and options work, how they are priced and how they are used for hedging and risk management. It combines institutional detail about markets with the main valuation models, keeping the mathematics accessible while showing how practitioners apply the results.

   Prerequisites: An introductory finance course, basic probability and statistics, and some calculus are assumed.

3. Arbitrage Theory in Continuous Time

   Tomas Björk Advanced

   A rigorous graduate-level guide to arbitrage theory, spanning discrete and continuous time models, complete and incomplete markets, and practical applications in derivative pricing, portfolio optimization, and risk management.

   Prerequisites: For the opening chapters, advanced calculus and elementary probability are the stated background. Work toward stochastic calculus and financial modeling as the text develops; later equilibrium and control topics need stronger mathematical preparation.

4. Introduction to Stochastic Calculus Applied to Finance

   Damien Lamberton; Bernard Lapeyre Advanced

   Graduate-level introduction to stochastic calculus in finance, combining rigorous theory with applications in option pricing, risk management, and financial modeling.

   Prerequisites: Probability, calculus and basic derivatives pricing are recommended. Comfort with conditional expectations and Brownian motion helps; study stochastic integration and numerical examples together rather than treating formulas as recipes.

5. Martingale Methods in Financial Modelling

   Marek Musiela; Marek Rutkowski Advanced

   Graduate-level exploration of martingale methods in financial modelling, combining rigorous theory with applications in derivatives pricing, interest rate modelling, and risk management.

   Prerequisites: Measure-theoretic probability, martingales, stochastic integration and derivatives pricing are recommended. Be ready for Itô calculus, changes of measure and model assumptions; advanced chapters build on that foundation.

6. Modern pricing of interest-rate derivatives: The LIBOR market model and beyond

   Riccardo Rebonato Advanced

   A comprehensive treatment of the LIBOR market model and its applications in pricing interest-rate derivatives. It bridges the gap between theory and practice, providing both rigorous mathematical foundations and practical calibration techniques.

   Prerequisites: Interest-rate products, stochastic calculus, probability and numerical modeling are recommended. Review covariance, yield curves and hedging; distinguish the book's historical LIBOR framework from later benchmark conventions.

7. Monte Carlo Methods in Financial Engineering

   Paul Glasserman Advanced

   Graduate-level exploration of Monte Carlo methods in financial engineering, combining rigorous theory with applications in derivatives pricing, interest rate modelling, and risk management.

   Prerequisites: The publisher identifies continuous-time financial modeling and key ideas of stochastic calculus as important preparation. Basic option pricing helps but is not essential; programming and probability support the simulation exercises.

8. Notes on Stochastic Finance

   Nicolas Privault Advanced Open access

   Read the official free edition ↗

   A free complete author text developing no-arbitrage pricing and hedging through discrete markets, stochastic calculus, exotic options, rates and jump models.

   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.

9. Numerical Solution of Stochastic Differential Equations with Jumps in Finance

   Eckhard Platen; Nicola Bruti-Liberati Advanced

   A research monograph on discrete-time numerical approximation of stochastic differential equations driven by Wiener processes and jump measures. It covers strong and weak schemes, exact simulation, estimation and filtering, stability, hedge ratios and variance reduction, with finance as the motivating application and exercises with solutions.

   Prerequisites: Graduate probability, stochastic calculus and numerical analysis. Review Itô integration, Wiener and Poisson processes, Monte Carlo error and strong versus weak convergence of discretization schemes.