The standard reference for derivative pricing and the role of Ito calculus are still the books by Shreve called [Stochastic Calculus I][1] (discrete) and [Stochastic Calculus II][2] (continuous). The whole theory is developed from a mathematical viewpoint with definitions and theorems and proofs; so if you appreciate the standard math textbook approach to life then you will find the presentation pleasantly familiar.

The material is developed slowly (I think most people who have taken a course in probability even at the undergraduate level can safely skip Shreve I) but by the end one starts to see and use non-trivial results. 

These books are used in the Intro math finance classes at [Chicago][3] and [Rutgers][4], both of which have well-reputed math-finance programs.


  [1]: http://www.amazon.com/Stochastic-Calculus-Finance-Binomial-Textbooks/dp/0387249680
  [2]: http://www.amazon.com/Stochastic-Calculus-Finance-II-Continuous-Time/dp/0387401016
  [3]: http://galton.uchicago.edu/~mykland/345A08/index.html
  [4]: http://www.finmath.rutgers.edu/index.php?d=courses&p=621