Stochastic Calculus for Finance Brief Lecture Notes



The purpose of these notes is to provide a rapid introduction to the Black-Scholes formula and the mathematics techniques used in this context. Most mathematical concepts used are explained and motivated, but the complete rigorous proofs are beyond the scope of these notes. These notes were written in 2017 when I was teaching a seven week course in the Masters in Computational Finance program at Carnegie Mellon University. The notes are somewhat minimal and mainly include material that was covered during the lectures itself. Only two sets of problems are included. These are problems that were used as a review for the midterm and final respectively. Supplementary problems and exams can be found on the course website: http://www.math.cmu. edu/~gautam/sj/teaching/2016-17/944-scalc-finance1 .

For more comprehensive references and exercises, I recommend:

(1) Stochastic Calculus for Finance II by Steven Shreve.

(2) The basics of Financial Mathematics by Rich Bass.

(3) Introduction to Stochastic Calculus with Applications by Fima C Klebaner.

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