Further readings

Below are some optional further readings intended for my students who want to dive more deeply into the area of option pricing, stochastic calculus and probability. Note that this is a tiny and biased selection of a vast range of books available in this field.

The Pricing of Options and Corporate Liabilities, by Fischer Black and Myron Scholes

The original 1973 paper published in JPE

The Theory of Rational Option Pricing, by Robert Merton

The original 1973 paper published in Bell Journal of Economics and Management Science

Options, Futures, and other Derivatives, by John Hull

A long-standing undergraduate level standard text in the study of financial derivatives.

Introduction to Derivative Securities, Financial Markets, and Risk Management, by Robert Jarrow and Arkadev Chatterjea

Professor Jarrow is an expert in option pricing, interest rate modelling and credit risk analysis. He is also one of my PhD supervisors. Can't go wrong with this text.

Stochastic Calculus for Finance I: The Binomial Asset Pricing Model, by Steven Shreve

Stochastic Calculus for Finance II: Continuous-Time Models, by Steven Shreve

A popular series of texts adopted in many MBA programs and MSc in Financial Engineering. It offers a rigorous training in financial maths for quants. The first book is on discrete-time binomial-tree model. The second book develops various asset pricing models in the more exciting continuous-time framework. The two books are related but can be read independently. Lots of useful exercises.

Probability with Martingales, by David Williams

A short and interesting book for those students who are fascinated by the mathematics of martingale which underlies the important applications in finance, economics, gambling, etc.. It serves as an entry point to advanced concepts like conditional expectation, stochastic integration, stopping time, and the martingale theory. Despite the advanced nature of the subject matter, the author is particularly good at peppering in lots of intuition, interesting examples and surprising counterexamples. I like this book a lot ever since I first came across it in my last year of undergraduate study.

Probability and Measures, by Patrick Billingsley

A graduate level text in probability and measure theory widely adopted in many graduate programs. This was also the adopted text when I studied advanced probability courses taught by my then Professor Eugene Dynkin (a giant in Markov and stochastic process theory) during my second-year PhD study.

The Mathematics of Arbitrage, by Freddy Delbaen and Walter Schachermayer

A summary on arbitrage written by the original authors who published the proof of the First Fundamental Theorem of Asset Pricing in its general form. To understand the maths requires advanced mathematics such as functional theory, but the first chapter on the intuition of no-arbitrage pricing offers an engaging read.