# Notes on Financial Engineering

## Professor K. Sigman

### Lecture Notes

- Interest rates and present value
- Internal rate of return, bonds, yield
- Portfolio mean and variance, the Markowitz problem
- One-fund and Two-fund theorems
- Binomial Lattice Model for stocks and option pricing
- Capital Asset Pricing Model
- Factor models
- Gambler's ruin problem
- Introduction to Brownian motion
- Geometric Brownian motion,
modeling stock prices in continuous time, Black-Scholes option pricing formula
- Introduction to Ito integration, Ito's rule,
derivation of Black-Scholes PDE

Professor Karl Sigman

Department of Industrial Engineering and Operations Research

Phone: (212) 854-3556

FAX: (212) 854-8103

karl.sigman@columbia.edu

http://www.columbia.edu/~ks20