This page contains links to lecture notes prepared for Math 621 and Math 622. These notes are based closely on the books by Steve Shreve, Stochastic Calculus for Finance I and II, published by Springer Verlag, which is used as a text in Math 621 and 622. The approach to the subject, much notation, and many results are taken from these texts. My lecture notes were prepared to to help guide students through the material I considered most essential, as I taught the courses. Please send any corrections to ocone@math.rutgers.edu.
1. 621 Lecture 1: Foundations and No-Arbitrage Pricing for Discrete Models
2. 621 Lecture Notes 2: Pricing for the Multiperiod Binomial Model
3. 621 Lecture 3 slides: Probability Spaces, Random Variables, and Derivative Pricing
4. 621 Lecture Notes 4: Sigma algebras and Conditional Expection
5. 621 Lecture Notes 5, part I: Conditional Expection and Derivative Pricing
6. 621 Lecture Notes 5, part II: Martingales and risk neutral pricing in discrete time
7. 621 Lecture Notes 6: Introduction to stochastic integration with respect to Brownian motion