Quantitative Finance Reading List – Theoretical Foundations

Not everybody wants to become a theoretical physicist. Some consider the academic environment too relaxed, others are not keen on the politics or the necessity to continually hunt for funding early in their career. A job in Quantitative Finance offers an attractive alternative.

Financial engineering has both strong theoretical and applied components, is immensely intellectually stimulating and fast-paced. A significant degree of background knowledge and an exceptional academic record are required even to achieve an interview. If you have recently decided that academia is not where your career path lies and you possess strong technical skills then the reading list outlined below will get you started towards becoming a quant.

This is the first part in a multi-part series on textbooks suitable for becoming a quantitative analyst. The remaining parts will focus on implementation, further mathematical excursions, interview skills and numerical methods. This article will concentrate on the theory of financial engineering for those who have not had an exposure to finance before.

Mathematical Finance

A great place to start learning about the world of derivatives is with the classic text Options, Futures and Other Derivatives by John Hull. It is light on the mathematics, but covers a lot of ground. Specifically, it is a good introduction to derivative markets for those who haven’t had prior exposure to finance.

Once you’re comfortable with the concepts used in the financial markets the next step is to begin learning about arbitrage and the Black-Scholes model in a more mathematical manner. Dan Stefanica’s A Primer for the Mathematics of Financial Engineering will provide all of the calculus (differentiation, integration, taylor expansion etc) needed to tackle the Black-Scholes equation. It will also cover “the Greeks” and basic risk neutral pricing. This is a great book for somebody who doesn’t have the required undergraduate mathematical background needed for later texts.

At this stage you will be ready to tackle the intermediate works such as Mark Joshi’s Concepts and Practice of Mathematical Finance (an excellent book, highly recommended), Paul Wilmott on Quantitative Finance (extremely comprehensive and humourous explanations!), Baxter and Rennie’s Financial Calculus and Salih Neftci’s Introduction to the Mathematics of Financial Derivatives. A good working knowledge of the contents of these books is sufficient theory for any front office desk quant interviews.

If you wish to delve deeper into the mathematical theory underpinning derivatives pricing then Bernt Oksendal’s Stochastic Differential Equations is a great start, as it has plenty of SDE exercises to work through.

A rather heavy going text for desk work, but an essential book for researching financial engineering, is the two volume masterpiece by Steven Shreve – Stochastic Calculus for Finance (Vol I and Vol II). Vol I concentrates on the discrete pricing models while Vol II focuses on continuous models. Be warned that for the Vol II, a strong background in undergraduate mathematics is required – particularly in Real Analysis, Probability Theory and Measure Theory.

Summary and Suggested Reading Chronology

  1. Options, Futures and Other Derivatives – John Hull
  2. A Primer for the Mathematics of Financial Engineering – Dan Stefanica
  3. The Concepts and Practice of Mathematical Finance – Mark Joshi
  4. Financial Calculus: An Introduction to Derivative Pricing – Martin Baxter, Andrew Rennie
  5. Stochastic Calculus for Finance II: Continuous-Time Models – Steven Shreve

In the next article, texts on implementation will be presented which will give you the knowledge you need to begin creating your own quant models.