Unit 1. Basic Models of Financial Markets: One-Period Finite State Model, Securities and Their payoffs, Securities as Vectors, Operations on Securities
- The Matrix as a Collection of Securities
- Matrix Multiplication and portfolios
- Systems of Equations and Hedging
- Linear Independent and Redundant Securities
- The Structure of the Marketed Subspace
- The Identity Matrix and Arrow-Debreu Securities
- Complete Market Hedging Formula
Unit 2. Arbitrage and Pricing in the One-Period Model
Unit 3. Pricing in Dynamically Complete Markets
Unit 4. Towards Continuous Time
Unit 5. Brownian motion and Ito Formulae
Unit 6. Black-Scholes Formula