Basic Notions

Basic notions of financial mathematics that the students should learn in a first course:

  • Arbitrage theorem (also called the fundamental theorem of financial mathematics)
  • Interest (different ways to calculate interest rates; general term structure of interest rates)
  • Non-arbitrage principle, martingale (risk-neutral) measures
  • Financial engineering products: forwards, futures, options, swaps, … why are they created, what are their uses, and their basic properties
  • Stochastic calculus (stochastic differential equation, Ito integral, Ito lemma)
  • Black-Scholes and some other derivatives pricing models
  • Risk (why risk management is important; measures of risk; hedging)
  • Elements of portfolio management / asset allocation

Recommended texts for a first course on financial mathematics:

  • Buchanan – An undergraduate introduction to financial mathematics – 2006. (As the title indicates, this book is well suited for undergraduate students)
  • Capinski and Zastawniak – Mathematics for finance: an introduction to financial engineering – 2004
  • Chourdakis – Financial engineering: a brief introduction using the Matlab system – 2008 (Matlab is one of the best computer software for doing finance)
  • Elliott and Kopp – Mathematics of financial markets, 2nd ed. – 2005
  • Focardi and Fabozzi – The mathematics of financial modeling and investment management – 2004
  • Harrison and Waldron – Mathematical economics and finance – 1998 (A rather elementary book, which also explains basic mathematical concepts such as linear algebra and elementray probability theory).
  • Hull – Options, futures, and other derivatives, 5th ed. (A rather comprehensive introduction to derivatives, which is still accessible to undergraduate students)
  • Lin – Lecture notes in mathematical finance – 1996 (This text is very mathematically-oriented)
  • Neftci – Principles of financial engineering, 2nd ed. – 2008 (a very good book with many real-world examples)
  • Pliska – Introduction to mathematical finance: discrete time models – 2001
  • Ross – An introduction to mathematical finance – 1999
  • Wilmott et al. – The mathematics of financial derivatives: a student introduction – 1996.

For Vietnamese students: I’m currently writing a textbook in Vietnamese, which will be available soon.

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