46-944 Stochastic Calculus for Finance I

6 units, Carnegie Mellon University

The 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. Non-MSCF students may not take this course without the instructor's written permission. To be eligible, you must be a BSCF student or a graduate student enrolled in an MSCF participating college/department (Stats & Data Science, Tepper, Computer Science Dept., or Math Sciences). PhD students with relevant research may be eligible with the instructor's permission.

Prerequisites: none listed

Offered: Fall 2026, Fall 2025

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