Transition from discrete- to continuous-time models. Review of partial differential equations emphasizing the heat equation. Formal approach to Ito's lemma. Use of Ito's lemma in financial modeling: applications to options pricing. Derivation of Black-Scholes equation. Solution by analytical and numerical methods. Modifications for early exercise. Modeling and solutions for Asian and other path dependent options. Introduction to the classical single-factor interest rate models. Basics of pricing bond options. 3 hrs. lec.
