This is the third in a series of three short courses on financial mathematics that take participants from pre-calculus to stochastic calculus. Like all three courses of the series, Math 3 combines self-study with three days of lectures.

Self study focuses on reviewing and mastering concepts learned in Math 2—linear algebra and probability theory. Lectures build on these foundations, exploring statistics, time series analysis, and stochastic calculus in depth.

The treatment of stochastic calculus includes basic definitions, stochastic differentials, Ito's lemma, stochastic integration, and stochastic differential equations. The goal is to get beyond the notation and provide a firm grasp of what the mathematics means. Students come away understanding intuitively what a stochastic differential equation tells them. They gain sufficient knowledge to apply stochastic calculus in subsequent financial engineering courses.

Financial applications covered in Math 3 include

optimal hedge ratios,

dynamic hedging,

efficient markets,

the capital asset pricing model,

Black-Scholes theory.

Option pricing theory arises frequently throughout the lectures. It is a unifying application that naturally motivates and builds towards an understanding of stochastic calculus.

Prerequisites are either completion of Math 1 and Math 2 or in-depth knowledge of the math covered in those courses. While Math 1 and 2 cover the basic math any financial professional should know, Math 3 is more advanced and more applied. Here, we cover specific techniques of applied math used by analysts, financial engineers, and risk managers every day on the job. In this respect, Math 3 is a culmination of the more basic work of Math 1 and Math 2.