Minicourse: The Black-Scholes Model and Beyond

This mini-course introduces the famous Black-Scholes model for pricing options and explores generalizations of the model. The course begins with the Black-Scholes differential equation, its connection to the heat equation, and method of solution. Applications are given to pricing European options. The course then treats extensions of the Black-Scholes model to variable interest rates and volatility. No background in finance is assumed (e.g., all relevant terminologies from options theory are introduced).

Prerequisites: introductory probability, linear algebra, and multivariable calculus.