This course introduces martingales, Brownian motion, Ito integrals and Ito’s formula, in both the uni-variate and multi-variate case. This is done within the context of the Black-Scholes option pricing model and includes a detailed examination of this model. Prerequisite: Multi-Period Asset Pricing 46-941 and knowledge of calculus-based probability theory. Text: S. Shreve, Stochastic Calculus for Finance II: Continuous-Time Models, Springer-Verlag, New York, 2004. Prerequisite: Probability 46-921, Multi-Period Asset Pricing 46-941.
Lecture: 100min/wk and Recitation: 50min/wk