The Feynman-Kac Formula and Applications to Finance

This paper is an exposition on the basics of Brownian Motion and Stochastic Calculus that culminates with a derivation of the Feynman-Kac formula that has substantial applications in finance. The only prerequisites are a basic understanding of probability, a strong understanding of martingales, and some background in analysis (particularly measure theory, ODEs, and PDEs). The presented material can be found in Michael Steele’s book Stochastic Calculus and Financial Applications [1].