Carnegie Mellon University

Stochastic Calculus for Finance I

Course Number: 46944

Concentration: Mathematics
Semester(s): Spring, Mini 3
Required/Elective: Required
Prerequisite(s): MSCF Math and Markets Prep, MSCF Probability Prep

The main focus of this course is to understand the basics of arbitrage free pricing, and the mathematical tools used to price securities. We will begin with a rapid introduction to the multi-period Binomial model, and then mainly focus on continuous time markets. The mathematical tools we will use include conditional expectation, martingales, Brownian motion, Itô integrals and Itô's formula, exponential martingales, the Girsanov theorem and risk neutral measures. The course will cover the Black-Scholes option pricing model in detail, and may touch upon the fundamental theorems of asset pricing. Prerequisite: MSCF Math and Markets Prep, MSCF Probability Prep