The scientist does not study nature because it is useful; he studies it because he delights in it, and he delights in it because it is beautiful. If nature were not beautiful, it would not be worth knowing, and if nature were not worth knowing, life would not be worth living.
by Henri Poincaré (1854-1912)

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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